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Showing papers in "Journal of Vibration and Acoustics in 2020"


Journal ArticleDOI
TL;DR: In this paper, the authors analyzed dissipative multiresonant pillared and trampoline effect-enhanced elastic metamaterials for the amplification of local resonance bandgaps.
Abstract: The present study deals with the analysis of dissipative multiresonant pillared and trampoline effect–enhanced elastic metamaterials for the amplification of local resonance bandgaps. The study is conducted through a finite element–based numerical technique and substantiated with a discrete mass-in-mass analytical model. The band structures and wave dispersion characteristics of the multiresonant pillars erected on a thin elastic plate foundation are analyzed. Compared to a single-resonant metamaterial, this multiresonant structure innovatively creates wider bandgaps due to the coupling of resonance frequencies of the pillar modes with the base plate. For trampoline metamaterials, a periodic array of holes is made inside the plate. The holes forge the plate to work as a compliance base that enhances the system resonance frequency through intensive vibration of pillar-plate structure resulting in further amplified local resonance bandgaps. The enlargement of bandgaps also depends upon the height of the pillar and diameter of holes. Extremely wide low-frequency bandgaps can be achieved for a larger pillar height and a bigger hole diameter. Through a frequency response study, reported bandgaps are compared and an infinite unit cell model (band structure) is validated. The introduction of material loss factor (material damping) resulted in a broadband vibration attenuation zone spread throughout the frequency spectrum. Compared to a standard multiresonant pillared-plate model, the bandgap amplification caused by the trampoline effect induces a relatively larger bandwidth, and this superior characteristic together with the dissipative nature of the medium may facilitate potential design outcomes for manipulating subwavelength metamaterial properties over a broad range of frequencies.

29 citations


Journal ArticleDOI
TL;DR: The computer simulation results for a mechanism with four flexible links and closed-loop configuration have been presented and the Gibbs-Appell (G-A) formulation has been applied to get rid of these Lagrange multipliers and to ease the extraction of governing motion equations.
Abstract: This paper has focused on the dynamic analysis of mechanisms with closed-loop configuration while considering the flexibility of links. In order to present a general formulation for such a closed-loop mechanism, it is allowed to have any arbitrary number of flexible links in its chain-like structure. The truncated assumed modal expansion technique has been used here to model link flexibility. Moreover, due to the closed nature of the mentioned mechanism, which imposes finite holonomic constraints on the system, the appearance of Lagrange multipliers in the dynamic motion equations obtained by Lagrangian formulation is unavoidable. So, the Gibbs-Appell (G-A) formulation has been applied to get rid of these Lagrange multipliers and to ease the extraction of governing motion equations. In addition to the finite constraints, the impulsive constraints, which originate from the collision of system joints with the ground, have also been formulated here using the Newton's kinematic impact law. Finally, to stress the generality of the proposed formulation in deriving and solving the motion equations of complex closed-loop mechanisms in both the impact and non-impact conditions, the computer simulation results for a mechanism with four flexible links and closed-loop configuration have been presented.

21 citations


Journal ArticleDOI
Yekai Sun1, Jie Yuan1, Luca Pesaresi1, Enora Denimal1, Loic Salles1 
TL;DR: In this article, a numerical methodology is described to study the influence of the contact location and contact condition of friction damper in aircraft engines, and the results have proved that the uncertainties that involved contact surfaces do not have significant effects on the performance of frictional damper.
Abstract: A numerical methodology is described to study the influence of the contact location and contact condition of friction damper in aircraft engines. A simplified beam model is used to represent the blade for the preliminary design stage. The frictional damper is numerically analyzed based on two parameters, contact angle and vertical position of the platform. The nonlinear modal analysis is used to investigate the nonlinear dynamic behavior and damping performances of the system. The harmonic balanced method with the continuation technique is used to compute the nonlinear modes for a large range of energy levels. By using such a modeling strategy, the modal damping ratio, resonant amplitude, and resonant frequency are directly and efficiently computed for a range of design parameters. Monte Carlo simulations together with Latin hypercube sampling is then used to assess the robustness of the frictional damper, whose contact parameters involve much uncertainties due to manufacturing tolerance and also wear effects. The influences of those two parameters are obtained, and the best performances of the frictional damper can be achieved when the contact angle is around 25 deg-30 deg. The vertical position of the platform is highly mode dependent, and other design considerations need to be accounted. The results have proved that the uncertainties that involved contact surfaces do not have significant effects on the performance of frictional damper.

21 citations


Journal ArticleDOI
TL;DR: In this paper, a novel isolator inspired by rigid-flexible coupling characteristics of folded structure is proposed for the Momentum wheel assemblies (MWAs), which can effectively isolate vibration in lowfrequency and a wide-frequency range under three excitation directions.
Abstract: Momentum wheel assemblies (MWAs) play an important role in the attitude adjustment of the satellite by momentum exchange. The micro-vibration induced by the MWAs affects attitude adjustment and leads to unclear imaging and imprecise position. Considering the isolation of multi-directional vibration and transmission of the torque, a novel isolator inspired by rigid-flexible coupling characteristics of folded structure is proposed for the MWAs in this paper. Through the orthogonal arrangement of two Z-folded beams, the isolator has low stiffness in the translational directions and high stiffness in the direction of rotation. An equivalent dynamic model is developed to characterize the isolator. The experimental results verify that the developed model accurately predicts the response of the isolator under different excitations. The results also demonstrate that the prototype can effectively isolate vibration in low-frequency and a wide-frequency range under three excitation directions. Moreover, the isolator has been tested to verify that it has enough stiffness for torque transmission. The design is compact and can be applied to the MWAs of the satellite for multi-direction vibration isolation without influence on the attitude adjustment of the MWAs to the satellite.

19 citations


Journal ArticleDOI
TL;DR: In this paper, the amplitude-independent and passive non-reciprocal wave motion can be achieved in a one-dimensional (1D) discrete chain of masses and springs with bilinear elastic stiffness.
Abstract: Significant amplitude-independent and passive non-reciprocal wave motion can be achieved in a one-dimensional (1D) discrete chain of masses and springs with bilinear elastic stiffness. Some fundamental asymmetric spatial modulations of the bilinear spring stiffness are first examined for their non-reciprocal properties. These are combined as building blocks into more complex configurations with the objective of maximizing non-reciprocal wave behavior. The non-reciprocal property is demonstrated by the significant difference between the transmitted pulse displacement amplitudes and energies for incidence from opposite directions. Extreme non-reciprocity is realized when almost-zero transmission is achieved for the propagation from one direction with a noticeable transmitted pulse for incidence from the other. These models provide the basis for a class of simple 1D non-reciprocal designs and can serve as the building blocks for more complex and higher dimensional non-reciprocal wave systems.

18 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed a nonlinear identification procedure that consists of two steps: first, the raw data is filtered by the Double Reverse Multimodal Decomposition method that involves system reconstruction, expansion, and filtering twice.
Abstract: Jointed interfaces, damage, wear, or non-idealized boundary conditions often introduce nonlinear characteristics to assembled structures. Consequently, extensive research has been carried out regarding nonlinear system identification. The development of nonlinear system identification is also enabling the intentional application of nonlinearities towards practical fields such as vibration control and energy harvesting. This research proposes a nonlinear identification procedure that consists of two steps: first, the raw data is filtered by the Double Reverse Multimodal Decomposition method that involves system reconstruction, expansion, and filtering twice. Second, the Peak Finding and Fitting method is applied to the filtered signal to extract the instantaneous amplitude and frequency. The identification procedure is applied to the measured responses from a jointed structure to assess its efficacy. The results are compared with those obtained from other well-known methods—the Hilbert transform and zero-crossing methods. The comparison results indicate that the Peaking Finding and Fitting method extracts the amplitude of the response signal more accurately. Consequently, this yields a higher signal-to-noise ratio in the extracted damping values. As a recommended last step, uncertainty assessment is conducted to calculate the 95% confidence intervals of the nonlinear properties of the system.

17 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of uncertainties in material and geometric parameters on the acoustic performance of a viscoelastic coating is investigated by examining the mean, envelopes and probability distribution of the monopole resonance frequency and sound transmission through the coating.
Abstract: The effect of uncertainties in material and geometric parameters on the acoustic performance of a viscoelastic coating is investigated. The model of the coating comprises a structure conventionally used in underwater applications, namely a soft elastic matrix embedded with periodic arrangements of voids. To investigate the effect of uncertainties on the acoustic performance of the coating, stochastic models based on the non-intrusive polynomial chaos expansion (PCE) method and Monte Carlo (MC) simulations are developed. The same analytical formulation of the acoustic coating is employed in both stochastic models. In the PCE method, the analytical model is transformed into a computationally efficient surrogate model using stochastic collocation. The effect of uncertainty in an individual geometric or material parameter on the acoustic performance of the coating is investigated by examining the mean, envelopes and probability distribution of the monopole resonance frequency and sound transmission through the coating. The effect of variation in combinations of geometric and material parameters is then examined. Uncertainty in the geometric parameters is observed to have a greater impact on the resonance frequency of the voids and sound transmission through the coating compared to uncertainty in the material properties.

16 citations


Journal ArticleDOI
TL;DR: This paper improves the recently established first-order eigen perturbation (FOP) technique by creating a stabilization process for adapting to ill-conditioned matrices with close eigenvalues, and establishes the robustness of the proposed methods for a range of engineering applications.
Abstract: Eigen-decomposition remains one of the most invaluable tools for signal processing algorithms. Although traditional algorithms based on QR decomposition, Jacobi rotations and block Lanczos tridiagonalization have been proposed to decompose a matrix into its eigenspace, associated computational expense typically hinders their implementation in a real-time framework. In this paper, we study recursive eigen perturbation (EP) of the symmetric eigenvalue problem of higher order (greater than one). Through a higher order perturbation approach, we improve the recently established first-order eigen perturbation (FOP) technique by creating a stabilization process for adapting to ill-conditioned matrices with close eigenvalues. Six algorithms were investigated in this regard: first-order, second-order, third-order, and their stabilized versions. The developed methods were validated and assessed on multiple structural health monitoring (SHM) problems. These were first tested on a five degrees-of-freedom (DOF) linear building model for accurate estimation of mode shapes in an automated framework. The separation of closely spaced modes was then demonstrated on a 3DOF + tuned mass damper (TMD) problem. Practical utility of the methods was probed on the Phase-I ASCE-SHM benchmark problem. The results obtained for real-time mode identification establishes the robustness of the proposed methods for a range of engineering applications.

15 citations


Journal ArticleDOI
TL;DR: This work attempts to identify the joint dynamics using the system equivalent model mixing (SEMM) decoupling method with a virtual point description of the interface with a typical dove-tail assembly.
Abstract: A joint between two components can be seen as a means to transmit dynamic information from one side to the other. To identify the joint, a reverse process called decoupling can be applied. This is not as straightforward as the coupling, especially when the substructures have three-dimensional characteristics, or sensor mounting effects are significant, or the interface degrees-of-freedom (DoF) are inaccessible for response measurement and excitation. Acquiring frequency response functions (FRFs) at the interface DoF, therefore, becomes challenging. Consequently, one has to consider hybrid or expansion methods that can expand the observed dynamics on accessible DoF to inaccessible DoF. In this work, we attempt to identify the joint dynamics using the system equivalent model mixing (SEMM) decoupling method with a virtual point description of the interface. Measurements are made only at the internal DoF of the uncoupled substructures and also of the coupled structure assuming that the joint dynamics are observable in the assembled state. Expanding them to the interface DoF and performing coupling and decoupling operations iteratively, the joint is identified. The substructures under consideration are a disk and blade—an academic test geometry that has a total of 18 blades but only one blade-to-disk joint is considered in this investigation. The joint is a typical dove-tail assembly. The method is shown to identify the joint without any direct interface DoF measurement.

15 citations


Journal ArticleDOI
TL;DR: A vehicle–track coupled dynamics model was established for analysis and calculations and showed that the dynamic features of the wheel with a flat fault were more pronounced under traction and braking conditions, whereas the variations in the features under coasting conditions were insignificant.
Abstract: Wheel faults are the main causes of safety issues in railway vehicles. The modeling and analysis of wheel faults is crucial for determining and studying the dynamic characteristics of railway vehicles under variable speed conditions. Hence, a vehicle–track coupled dynamics model was established for analysis and calculations. The results showed that the dynamic features of the wheel with a flat fault were more pronounced under traction and braking conditions, whereas the variations in the features under coasting conditions were insignificant. In this paper, a short-time fast Fourier transform and reassignment method was used to process the signals, because the results were unclear when the time–frequency graph was processed only by short time Fourier transform, especially under braking conditions. The variation in the fault frequency under variable speed conditions was determined. Finally, statistical indicators were used to describe the vibration behaviors caused by the wheel flat fault.

14 citations


Journal ArticleDOI
TL;DR: This work refines a recently formalized methodology proposed by D.J. Ewins consisting of ten steps for model validation of nonlinear structures, revealing that many standard test setup assumptions that are made when performing dynamic testing are invalid and need to be evaluated for each structure.
Abstract: This work refines a recently formalized methodology proposed by D.J. Ewins consisting of ten steps for model validation of nonlinear structures. This work details, through a series of experimental studies, that many standard test setup assumptions that are made when performing dynamic testing are invalid and need to be evaluated for each structure. The invalidation of the standard assumptions is due to the presence of nonlinearities, both known and unrecognized in the system. Complicating measurements, many nonlinearities are currently characterized as constant properties instead of variables that exhibit dependency on system hysteresis and actuation amplitude. This study reviews current methods for characterizing nonlinearities and outlines gaps in the approaches. A brief update to the CONCERTO method, based on the accelerance of a system, is derived for characterizing a system’s nonlinearities. Finally, this study ends with an updated methodology for model validation and the ramifications for modeling assemblies with nonlinearities are discussed.

Journal ArticleDOI
TL;DR: In this article, a pendulum-type tuned mass damper (TMD)-tuned sloshing damper system is proposed as a cost-effective device to reduce wind-induced structural motion.
Abstract: A pendulum-type tuned mass damper (TMD)-tuned sloshing damper (TSD) system is proposed as a cost-effective device to reduce wind-induced structural motion. Lagrange's principle is employed to develop an equivalent mechanical model for the system. The sloshing liquid provides additional gravitational restoring force to the pendulum TMD but does not provide a corresponding increase to its inertia. As a result, the natural frequency of the pendulum TMD is increased due to the TSD degree-of-freedom. Shake table testing is conducted on several pendulum TMD-TSD systems that are subjected to harmonic base excitation at discrete frequencies near the natural frequency of the pendulum TMD. The modeled and experimental results are in reasonable agreement when the liquid is not shallow or the response amplitude is not large. The pendulum TMD-TSD is coupled to a linear structure, and it is demonstrated through an analytical study that the device provides performance that is comparable to a traditional TMD. The proposed system is advantageous because it does not require a viscous damping system that is often one of the most costly components of traditional TMDs.

Journal ArticleDOI
TL;DR: The EGA-IHB method has high efficiency and good robustness for both polynomial and non-polynomial nonlinearities, and it has considerable advantages over the other methods.
Abstract: An efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method is developed based on the fast Fourier transform (FFT) and tensor contraction to increase efficiency and robustness of the IHB method when calculating periodic responses of complex nonlinear systems with non-polynomial nonlinearities. As a semi-analytical method, derivation of formulae and programming are significantly simplified in the EGA-IHB method. The residual vector and Jacobian matrix corresponding to nonlinear terms in the EGA-IHB method are expressed using truncated Fourier series. After calculating Fourier coefficient vectors using the FFT, tensor contraction is used to calculate the Jacobian matrix, which can significantly improve numerical efficiency. Since inaccurate results may be obtained from discrete Fourier transform-based methods when aliasing occurs, the minimal non-aliasing sampling rate is determined for the EGA-IHB method. Performances of the EGA-IHB method are analyzed using several benchmark examples; its accuracy, efficiency, convergence, and robustness are analyzed and compared with several widely used semi-analytical methods. The EGA-IHB method has high efficiency and good robustness for both polynomial and non-polynomial nonlinearities, and it has considerable advantages over the other methods.


Journal ArticleDOI
TL;DR: In this paper, a high-static-low-dynamic stiffness (HSLDS) isolator with an adjustable cam profile is presented, where the interaction force between the cam and roller provides the negative stiffness force and the linear spring provides the positive stiffness force in the HSLDS isolator.
Abstract: This paper presents a new design of a high-static-low-dynamic stiffness (HSLDS) isolator with an adjustable cam profile. The interaction force between the cam and roller provides the negative stiffness force and the linear spring provides the positive stiffness force in the HSLDS isolator. Unlike previous studies, the cam profile in this paper can be individually designed to meet different working conditions. Firstly, the harmonic balance method is used to acquire the dynamic response of the HSLDS isolator. Then, the effects of the damping ratio, stiffness ratio, and external force amplitude on the frequency response amplitude and force transmissibility are discussed. Finally, the frequency responses of four designed nonlinear HSLDS isolators and a linear isolator are acquired by the numerical method. The results show that the nonlinear isolator begins to achieve vibration isolation at 0.11 Hz and the linear one is 8.9 Hz. The proposed HSLDS isolator realizes lower vibration isolation frequency than the linear isolator.

Journal ArticleDOI
TL;DR: In this paper, the authors used Digital Image Correlation (DIC) with a high-speed camera to observe the local motion at the edge of the interface of a bolted lap joint.
Abstract: The dynamics of structures with joints commonly show nonlinearity in their responses. This nonlinear behaviour can arise from the local dynamics of the contact interfaces. The nonlinear mechanisms at an interface are complicated to study due to the lack of observability within the contact interface itself. In this work, Digital Image Correlation (DIC) is used in combination with a high-speed camera to observe the local motion at the edge of the interface of a bolted lap joint. Results demonstrate that it is possible to use this technique to monitor the localised motion of an interface successfully. It is observed that the two beam parts of the studied lap joint separate when undergoing bending vibrations, and that there is a clear asymmetry in the response of the left and the right end of the interface. Profilometry indicates that the asymmetry in the response is due to the mesoscale topography of the contact interface, highlighting the importance of accounting for surface features in order to model the nonlinearities of a contact interface accurately. ∗Address all correspondence to this author.

Journal ArticleDOI
TL;DR: In this article, an efficient rotordynamic stability approach for non-axisymmetric rotor-bearing systems with complex shapes using three-dimensional solid finite elements is presented, where the 10-node quadratic tetrahedron element is used for the rotor formulation.
Abstract: Although rotors are simplified to be axisymmetric in rotordynamic models, many rotors in the industry are actually non-axisymmetric. Several authors have proposed methods using 3D finite element, rotordynamic models, but more efficient approaches for handling a large number of degrees-of-freedom (DOF) are needed. This task becomes particularly acute when considering parametric excitation that results from asymmetry in the rotating frame. This paper presents an efficient rotordynamic stability approach for non-axisymmetric rotor-bearing systems with complex shapes using three-dimensional solid finite elements. The 10-node quadratic tetrahedron element is used for the finite element formulation of the rotor. A rotor-bearing system, matrix differential equation is derived in the rotor-fixed coordinate system. The system matrices are reduced by using Guyan reduction. The current study utilizes the Floquet theory to determine the stability of solutions for parametrically excited rotor-bearing systems. Computational efficiency is improved by discretization and parallelization, taking advantage of the discretized monodromy matrix of Hsu's method. The method is verified by an analytical model with the Routh–Hurwitz stability criteria, and by direct time-transient, numerical integration for large order models. The proposed and Hill's methods are compared with respect to accuracy and computational efficiency, and the results indicate the limitations of Hill's method when applied to 3D solid rotor-bearing systems. A parametric investigation is performed for an asymmetric Root's blower type shaft, varying bearing asymmetry and bearing damping.

Journal ArticleDOI
Gang Li1, Zhaokun Nie1, Yan Zeng1, Jiacheng Pan1, Zhenqun Guan1 
TL;DR: A novel simplified dynamic modeling method via structural static analysis is proposed to simulate dynamical response of nonlinear bolted flange joints of launch vehicle, in which only static analysis of the detailed finite element model or static experiment is used for parameter identification of the model.
Abstract: The bolted flange joint is an important source of nonlinearity in dynamical analysis of launch vehicles, which will lead to both longitudinal and transversal responses simultaneously subject to transversal dynamic loads, and may result in the failure of the connection structure. In this paper, a novel simplified dynamic modeling method via structural static analysis is proposed to simulate dynamical response of nonlinear bolted flange joints of launch vehicle, in which only static analysis of the detailed finite element model or static experiment is used for parameter identification of the model. Two types of nonlinear springs are designed for different tensile and compressive stiffness of the bolted flange joint, which affect longitudinal dynamic behaviour of the connection, and a shear spring is used to modify the transversal stiffness. The sections of launch vehicle are modeled as linear beams for efficiency. Effectiveness of the proposed modeling method is confirmed by a typical connection structure, bolted flange connected cylindrical shells, whose finite element models are verified with dynamic experiments. Superiority of the simplified dynamic model from the proposed method is demonstrated by comparing with the previous simplified model. The connection structures with different numbers of bolts are studied, and most of the dynamic responses calculated from the proposed model agree well with those from the finite element model. The coupling vibration of the connection structure is predicted successfully, in which longitudinal response of the structure is excited by the transversal load.

Journal ArticleDOI
TL;DR: In this paper, the authors presented a vibration control unit formed by an electromagnetic proof-mass transducer connected to a sweeping resistive-inductive (RL)-shunt, which can be used to control broadband flexural vibrations of thin structures.
Abstract: This paper presents a vibration control unit formed by an electromagnetic proof-mass transducer connected to a sweeping resistive–inductive (RL)-shunt, which can be used to control broadband flexural vibrations of thin structures. The shunt is composed of a resistor and an inductor in series, whose values vary harmonically in time. The design and practical implementation of an electromagnetic transducer and harmonically varying shunt is first discussed. The unit is then tested on a thin-walled cylinder exposed to a broadband disturbance, considering two operation modes: fixed and sweeping RL-shunts. The former mode sets the unit to control the resonant response of a target flexural mode of the cylinder. The latter mode sets the unit to control the resonant responses of multiple modes of the cylinder with natural frequencies confined in a target frequency band. The study demonstrates the practical feasibility of a unit, which sweeps the natural frequency and the damping ratio of the transducer between 36 Hz and 187 Hz and between 4% and 60%. Also, it shows the unit generates broadband control of the flexural vibration of a cylinder, with reductions of the peak responses of the natural modes resonating in frequency band of the sweep comprised between 2 and 13 dB.

Journal ArticleDOI
TL;DR: In this paper, the effect of temperature on planetary systems nonlinear vibration under the thermal equilibrium state was investigated. But the results indicated that the methods used to determine the TTVMS and backlash of gear pairs were effective and the trends of the change in the nonlinear dynamic characteristics with temperature were obtained.
Abstract: The thermal deformation of gears will affect the vibration of the planetary system; this research mainly studied the effect of thermal conditions on planetary systems nonlinear vibration under the thermal equilibrium state. To study the influence of gear temperature on the planetary gear system, a nonlinear dynamic model considering thermal deformation was established. The mathematical expression of the thermal time-varying mesh stiffness (TTVMS) varied with temperature, and the backlash caused by the temperature change was also computed. The influence of temperature on the TTVMS was investigated. The calculation results indicated that the methods used to determine the TTVMS and backlash of gear pairs were effective, and the trends of the change in the nonlinear dynamic characteristics with temperature were obtained. According to the fast Fourier transform (FFT) spectrums and root-mean-square (RMS) analysis, the influence of temperature change on the nonlinear dynamic characteristics of the system was analyzed. When the temperature was lower than 80 °C, the vibration displacement and the supporting shaft load remained unchanged or decreased. Once the temperature was higher than 80 °C, the vibration displacement and load of the system were strengthened.

Journal ArticleDOI
TL;DR: In this article, a dual control strategy is proposed and implemented on the piezoelectrically generated bistable laminate, which consists of only macro fiber composites (MFCs) in a [0MFC/90MFC]T layup.
Abstract: Although there have been numerous efforts into harnessing the snap through dynamics of bistable structures with piezoelectric transducers to achieve large energy conversion, these same dynamics are undesirable under morphing applications where stationary control of the structure’s configuration is paramount. To suppress cross-well vibrations that primarily result from periodic excitation at low frequencies, a novel control strategy is proposed and implemented on the piezoelectrically generated bistable laminate, which consists of only macro fiber composites (MFCs) in a [0MFC/90MFC]T layup. While under cross-well regimes such as subharmonic, chaotic, or limit cycle oscillations, a single MFC is actuated to the laminate’s limit voltage to eliminate one of its potential wells and force it into the remaining stable state. Simultaneously, a positive position feedback (PPF) controller suppresses the resulting single-well oscillations through the other MFC. This dual control strategy is numerically and experimentally demonstrated through the suppression of various cross-well regimes and results in significant reduction of amplitude. The active control capability of the laminate prevents snap through instability when under large enough external vibrations.

Journal ArticleDOI
TL;DR: In this paper, a simple bilaterally coupled FSI model for a wing subject to single-degree-of-freedom (SDOF) flapping is presented, which can be solved several orders of magnitude faster than direct computational methods.
Abstract: Flapping wings deform under both aerodynamic and inertial forces. However, many flapping wing fluid–structure interaction (FSI) models require significant computational resources which limit their effectiveness for high-dimensional parametric studies. Here, we present a simple bilaterally coupled FSI model for a wing subject to single-degree-of-freedom (SDOF) flapping. The model is reduced-order and can be solved several orders of magnitude faster than direct computational methods. To verify the model experimentally, we construct a SDOF rotation stage and measure basal strain of a flapping wing in-air and in-vacuum. Overall, the derived model estimates wing strain with good accuracy. In-vacuum, the wing has a large 3ω response when flapping at approximately one-third of its natural frequency due to a superharmonic resonance, where the superharmonic occurs due to the interaction of inertial forces and time-varying centrifugal softening. In-air, this 3ω response is attenuated significantly as a result of aerodynamic damping, whereas the primary ω response is increased due to aerodynamic loading. These results highlight the importance of (1) bilateral coupling between the fluid and structure, since unilaterally coupled approaches do not adequately describe deformation-induced aerodynamic damping and (2) time-varying stiffness, which generates superharmonics of the flapping frequency in the wing’s dynamic response. The simple SDOF model and experimental study presented in this work demonstrate the potential for a reduced-order FSI model that considers both bilateral fluid–structure coupling and realistic multi-degrees-of-freedom flapping kinematics moving forward.

Journal ArticleDOI
TL;DR: In this article, the Riemann-Liouville fractional derivative of order 0 < α ≤ 1 was used to model the dynamic response of fractionally damped viscoelastic plates subjected to a moving point load.
Abstract: The dynamic response of fractionally damped viscoelastic plates subjected to a moving point load is investigated. In order to capture the viscoelastic dynamic behavior more accurately, the material is modeled using the fractionally damped Kelvin–Voigt model (rather than the integer-type viscoelastic model). The Riemann–Liouville fractional derivative of order 0 < α ≤ 1 is applied. Galerkin's method and Newton–Raphson technique are used to evaluate the natural frequencies and corresponding damping coefficients. The structure is subject to a moving point load, traveling at different speeds. The modal summation technique is applied to generate the dynamic response of the plate. The influence of the order of the fractional derivative on the free and transient vibrations is studied for different velocities of the moving load. The results are compared with those using the classical integer-type Kelvin–Voigt viscoelastic model. The results show that an increase in the order of the fractional derivative causes a significant decrease in the maximum dynamic amplification factor, especially in the “dynamic zone” of the normalized sweep time. The dynamic behavior of the plate is verified with ansys.

Journal ArticleDOI
TL;DR: In this paper, a proper orthogonal decomposition (POD)-based polynomial chaos expansion (PCE) is utilized for the uncertainty quantification (UQ) of an impact dynamic oscillator.
Abstract: A proper orthogonal decomposition (POD)-based polynomial chaos expansion (PCE) is utilized in this article for the uncertainty quantification (UQ) of an impact dynamic oscillator. The time-dependent nonsmooth behavior and the uncertainties are decoupled using the POD approach. The uncertain response domain is reduced using the POD approach, and the dominant POD modes are utilized for the UQ of the response quantity. Furthermore, the PCE model is utilized for the propagation of the input uncertainties. Two different cases of impact oscillator are considered, namely, single impact and multiple impact. The contact between two bodies is modeled by Hertz's law. For both the cases, UQ is performed on the projectile displacement, projectile velocity, and contact force. A highly nonsmooth behavior is noticed for the contact force. For that reason, most number of POD modes are required to assess the UQ of contact force. All the results are compared with the Monte Carlo simulation (MCS) and time domain PCE results. Very good accuracies are observed for the PCE and the POD-PCE predicted results using much less number of model evaluations compared to MCS. As the PCE coefficients are dependent on time, the PCE model is computed at each time step. On the contrary, for the POD-PCE model, the PCE coefficients are computed for the number of POD modes only: it is much less than the PCE model.

Journal ArticleDOI
TL;DR: In this article, the capacity of an augmented proportional-integral-derivative controller to maintain the stability of a rotating machine supported on AMBs during severe foundation excitation was investigated.
Abstract: The stability of rotating machinery is a major challenge for the floating production storage and offloading (FPSO) units such as steam turbines or centrifugal compressors. The use of active magnetic bearings (AMBs) in turbomachines enables high operating speeds, active mechatronic system for the diagnostics, and the control and enables downsizing of the whole installation footprint. In case of strong base motions, the rotor can contact its touchdown bearings (TDBs) which are used as emergency and landing bearings. The aim of this study is to assess the stability of a rotating machine supported on AMBs during severe foundation excitation. The combined effect of unbalance forces, base motion excitation, and contact non-linearity on a rotor–AMB system response is analyzed focusing on the capacity of an augmented proportional-integral-derivative controller to maintain the system stable. An academic scale test rig was used for the experimental investigations. The controller was efficient and able to maintain the system stable during and after the application of the excitation, but the dynamic capacity of the AMBs was largely oversized with respect to the studied system. In order to check the capacity of the AMBs, when they are designed as a function of the rotor weight and expected excitation, numerical simulations were carried out (downsized). A finite element (FE) model was developed to model the on-board rotor–AMB system. Predicted and measured responses due to impulse excitation applied on the foundations were compared. The capacity of the controller to maintain the system stability is then discussed.

Journal ArticleDOI
TL;DR: In this paper, the dynamics of a coupled three-blade-rotor system with parametric stiffness, which is similar to a horizontal-axis wind turbine, is studied. But the rotor speed is not constant and the cyclic variations cannot be expressed as explicit functions of time, therefore, it is more convenient to use the rotor angle as the independent variable.
Abstract: Coupled blade-hub dynamics of a coupled three-blade-rotor system with parametric stiffness, which is similar to a horizontal-axis wind turbine, is studied. Blade equations have parametric and direct excitation terms due to gravity and are coupled through the hub equation. For a single degree-of-freedom blade model with only in-plane transverse vibrations, the reduced-order model shows parametric resonances. A small parameter is established for large blades, which enables us to treat the effect of blade motion as a perturbation on the rotor motion. The rotor speed is not constant, and the cyclic variations cannot be expressed as explicit functions of time. Therefore, it is more convenient to use the rotor angle as the independent variable. By expressing the system dynamics in the rotor angle domain and assuming small variations in rotor speed, the blade equations are decoupled from the rotor equation. The interdependent blade equations constitute a three-degree-of-freedom system with periodic parametric and direct excitation. The response is analyzed by using a first-order method of multiple scales (MMS). The system has a superharmonic and a subharmonic resonances due to direct and parametric effects introduced by gravity. Amplitude-frequency relations and stabilities of these resonances are studied. The MMS solutions are compared with numerical simulations for verification.

Journal ArticleDOI
TL;DR: In this paper, a deployment-scale array of locally resonant membrane-type acoustic metamaterials (MAMs) is fabricated, and the acoustic performance of the array is measured in a transmission loss chamber, and a complex interaction between the individual cell and the array length scales is shown.
Abstract: A deployment-scale array of locally resonant membrane-type acoustic metamaterials (MAMs) is fabricated. The acoustic performance of the array is measured in a transmission loss chamber, and a complex interaction between the individual cell and the array length scales is shown to exist. Transmission behavior of both the membrane and the array are independently studied using analytical models, and a method for estimating transmission loss through the structure that combines vibroacoustic predictions from both length scales is presented and shown to agree with measurements. Degradation of transmission loss performance often associated with scaling individual MAM cells into arrays is explained using analytical tools and verified using laser vibrometry. A novel design for hierarchical locally resonant acoustic metamaterials is introduced, and experimental and analytical data confirm this approach offers an effective strategy for minimizing or eliminating the efficiency losses associated with scaling MAM structures. [DOI: 10.1115/1.4045789]

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TL;DR: In this paper, a pre-optimization procedure was developed to exclude all those cross-sectional shapes that will bring the damper to roll and thus limit the amount of dissipated energy.
Abstract: Underplatform dampers are used to limit the resonant vibration of turbine blades. In recent years, various strategies have been implemented to maximize their damping capability. Curved-flat dampers are preferred to ensure a predictable bilateral contact, while a pre-optimization procedure was developed to exclude all those cross-sectional shapes that will bring the damper to roll and thus limit the amount of dissipated energy. The pre-optimization bases its predictions on the assumption that the effective width of the flat contact interface corresponds to the nominal one. It is shown here that this hypothesis cannot be relied upon: the energy dissipated by two nominally identical dampers, machined according to the usual industrial standards, may differ by a factor up to three due to the morphology of the flat-to-flat contact interface. Five dampers have been tested on two dedicated test rigs, available in the AERMEC laboratory, specially designed to reveal the details of the damper behavior during operation. Their contact interfaces are scanned by means of a profilometer. In each case, the mechanics, the kinematics, and the effectiveness of the dampers in terms of cycle shape and dissipated energy are correlated to the morphology of the specific contact surface. To complete the picture, a state-of-the-art numerical simulation tool is used to show how this tribo-mechanic phenomenon, in turn, influences the damper effect on the dynamic response of the turbine.

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TL;DR: In this article, a general approach for the free vibration analysis of curvilinearly stiffened rectangular and quadrilateral plates using the Ritz method by employing classical orthogonal Jacobi polynomials is presented.
Abstract: This paper presents a general approach for the free vibration analysis of curvilinearly stiffened rectangular and quadrilateral plates using the Ritz method by employing classical orthogonal Jacobi polynomials. Both the plate and stiffeners are modeled using first-order shear deformation theory (FSDT). The displacement and rotations of the plate and stiffeners are approximated by separate sets of Jacobi polynomials. The ease of modification of the Jacobi polynomials enables the Jacobi weight function to satisfy geometric boundary conditions without loss of orthogonality. The distinctive advantage of Jacobi polynomials, over other polynomial-based trial functions, lies in that their use eliminates the well-known ill-conditioning issues when a high number of terms are used in the Ritz method, e.g., to obtain higher modes required for vibro-acoustic analysis. In this paper, numerous case studies are undertaken by considering various sets of boundary conditions. The results are verified both with the detailed finite element analysis (FEA) using commercial software msc.nastran and with those available in the open literature. New formulation and results include: (i) exact boundary condition enforcement through Jacobi weight function for FSDT, (ii) formulation of quadrilateral plates with curvilinear stiffeners, and (iii) use of higher order Gauss quadrature scheme for required integral evaluations to obtain higher modes. It is demonstrated that the presented method provides good numerical stability and highly accurate results. The given new numerical results and convergence studies may serve as benchmark solutions for validating the new computational techniques.

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TL;DR: In this paper, the authors focused on the dynamics of the rotating system when angular misalignment is induced, using the structural analysis of the flexible coupling, with the consequent use of cyclic restoring forces and moments exerted by this component on the coupled shafts.
Abstract: Modeling of the dynamic behavior of the rotating system when subject to misaligned shafts is an interesting subject, aiming either the selection of appropriate couplings from early stages of project or the monitoring and model-based diagnosis of such machines. This research is focused on the dynamics of the system when angular misalignment is induced. The methodology to take into account this fault is based on the structural analysis of the flexible coupling, with the consequent use of cyclic restoring forces and moments exerted by this component on the coupled shafts. Structural analysis of metallic disc coupling is conducted by means of the finite element method, in which the flexible disc component is modeled using thin shell formulation. Once misalignments are applied, the cyclic nature of coupling efforts is captured by the application of consecutive shaft spin angles. Steady-state response is simulated and then displacements spectrum are analyzed in order to highlight harmonic components rising due to misalignment. Test rig measurements are performed, and the theoretical model is discussed in terms of locus, frequency response function (FRF), orbit shape, and spectrum information. Disc coupling is regarded, as limited literature in vibration spectrums is available for this type of coupling.