Showing papers in "Journal of Vibration and Acoustics in 2021"

Elastic Metasurfaces for Full Wavefront Control and Low-Frequency Energy Harvesting

Abstract: Controlling and manipulating elastic/acoustic waves via artificially structured metamaterials, phononic crystals, and metasurfaces have gained an increasing research interest in the last decades. Unlike others, a metasurface is a single layer in the host medium with an array of subwavelength-scaled patterns introducing an abrupt phase shift in the wave propagation path. In this study, an elastic metasurface composed of an array of slender beam resonators is proposed to control the elastic wavefront of low-frequency flexural waves. The phase gradient based on Snell’s law is achieved by tailoring the thickness of thin beam resonators connecting two elastic host media. Through analytical and numerical models, the phase-modulated metasurfaces are designed and verified to accomplish three dynamic wave functions, namely, deflection, non-paraxial propagation, and focusing. An oblique incident wave is also demonstrated to show the versatility of the proposed design for focusing of wave energy incident from multiple directions. Experimentally measured focusing metasurface has nearly three times wave amplification at the designed focal point which validates the design and theoretical models. Furthermore, the focusing metasurface is exploited for low-frequency energy harvesting and the piezoelectric harvester is improved by almost nine times in terms of the harvested power output as compared to the baseline harvester on the pure plate without metasurface.

Dynamic Characteristic Analysis of Rotating Blade With Transverse Crack—Part I: Modeling, Modification, and Validation

Abstract: This study aims at the systematical improvement and comparative analysis of analytical crack models for the rotating blade. Part I of this study focuses on analytical modeling, model modification, and model validation of transverse crack for the rotating blade. The most widely applied analytical crack models for the rotating blade are reviewed and compared, and then their limitations are discussed. It is indicated that the conventional analytical crack models suffer from low physical interpretability and vibration prediction accuracy. By considering these limitations of conventional analytical crack models, model modification is performed to enhance the physical meaning and improve the accuracy. First, the stress-based breathing crack model is modified by direct calculation of the breathing function based on the theory of linear elastic fracture mechanics and resetting the correction factor of centrifugal stiffening stiffness. Second, the vibration-based breathing crack models, including bilinear breathing crack model and cosine breathing crack model, are modified by introducing the coupling effect between bending stress and centrifugal stress based on the stress state at the blade crack section. The additional bending moment induced by the blade part outside the crack section is considered in all analytical models. The modified crack models’ validity is verified by comparing vibration responses obtained by the modified crack models, the finite element contact crack model, and the conventional crack models. The comparative results suggest that the modified models promote the physical interpretability and improve the vibration prediction accuracy of analytical crack models.

On New Analytic Free Vibration Solutions of Doubly Curved Shallow Shells by the Symplectic Superposition Method Within the Hamiltonian-System Framework

Abstract: This study presents a first attempt to explore new analytic free vibration solutions of doubly curved shallow shells by the symplectic superposition method, with focus on non-Lévy-type shells that are hard to tackle by classical analytic methods due to the intractable boundary-value problems of high-order partial differential equations. Compared with the conventional Lagrangian-system-based expression to be solved in the Euclidean space, the present description of the problems is within the Hamiltonian system, with the solution procedure implemented in the symplectic space, incorporating formulation of a symplectic eigenvalue problem and symplectic eigen expansion. Specifically, an original problem is first converted into two subproblems, which are solved by the above strategy to yield the symplectic solutions. The analytic frequency and mode shape solutions are then obtained by the requirement of the equivalence between the original problem and the superposition of subproblems. Comprehensive results for representative non-Lévy-type shells are tabulated or plotted, all of which are well validated by satisfactory agreement with the numerical finite element method. Due to the strictness of mathematical derivation and accuracy of solution, the developed method provides a solid approach for seeking more analytic solutions.

Effect of In-Plane Load and Thermal Environment on Buckling and Vibration Behavior of Two-Dimensional Functionally Graded Tapered Timoshenko Nanobeam

Abstract: In this work, buckling and vibration characteristics of two-dimensional functionally graded (FG) nanobeam of nonuniform thickness subjected to in-plane and thermal loads have been analyzed within the frame work of Timoshenko beam theory. The beam is tapered by linear variation in thickness along the length. The temperature-dependent material properties of the beam are varying along thickness and length as per a power-law distribution and exponential function, respectively. The analysis has been presented using Eringen’s nonlocal theory to incorporate the size effect. Hamilton’s energy principle has been used to formulate the governing equations of motion. These resulting equations have been solved via generalized differential quadrature method (GDQM) for three combinations of clamped and simply supported boundary conditions. The effect of in-plane load together with temperature variation, nonuniformity parameter, gradient indices, nonlocal parameter, and slenderness ratio on the natural frequencies is illustrated for the first three modes of vibration. The critical buckling loads in compression have been computed by putting the frequencies equal to zero. A significant contribution of in-plane load on mechanical behavior of two-directional functionally graded nanobeam with nonuniform cross section has been noticed. Results are in good accordance.

Hybrid Electromagnetic Shunt Damper for Vibration Control

Abstract: It has been shown that shunting electromagnetic devices with electrical networks can be used to damp vibrations. These absorbers have however limitations that restrict the control performance, i.e., the total damping of the system and robustness versus parameter variations. On the other hand, the electromagnetic devices are widely used in active control techniques as an actuator. The major difficulty that arises in practical implementation of these techniques is the power consumption required for conditioners and control units. In this study, robust hybrid control system is designed to combine the passive electromagnetic shunt damper with an active control in order to improve the performance with low power consumption. Two different active control laws, based on an active voltage source and an active current source, are proposed and compared. The control law of the active voltage source is the direct velocity feedback. However, the control law of the active current source is a revisited direct velocity feedback. The method of maximum damping, i.e., maximizing the exponential time-decay rate of the response subjected to the external impulse forcing function, is employed to optimize the parameters of the passive and the hybrid control systems. The advantage of using the hybrid control configuration in comparison with purely active control system is also investigated in terms of the power consumption. Besides these assets, it is demonstrated that the hybrid control system can tolerate a much higher level of uncertainty than the purely passive control systems. [DOI: 10.1115/1.4048389]

Uncertainty Quantification of Mode Shape Variation Utilizing Multi-Level Multi-Response Gaussian Process

Abstract: Mode shape information play the essential role in deciding the spatial pattern of vibratory response of a structure. The uncertainty quantification of mode shape, i.e., predicting mode shape variation when the structure is subjected to uncertainty, can provide guidance for robust design and control. Nevertheless, computational efficiency is a challenging issue. Direct Monte Carlo simulation is unlikely to be feasible especially for a complex structure with large number of degrees of freedom. In this research, we develop a new probabilistic framework built upon Gaussian process meta-modeling architecture to analyze mode shape variation. To expedite the generation of input dataset for meta-model establishment, a multi-level strategy is adopted which can blend a large amount of low-fidelity data acquired from order-reduced analysis with a small amount of high-fidelity data produced by high-dimensional full finite element analysis. To take advantage of the intrinsic relation of spatial distribution of mode shape, a multi-response strategy is incorporated to predict mode shape variation at different locations simultaneously. These yield a multi-level, multi-response Gaussian process that can efficiently and accurately quantify the effect of structural uncertainty to mode shape variation. Comprehensive case studies are carried out for demonstration and validation.

Modeling of Welded Joints in a Pyramidal Truss Sandwich Panel Using Beam and Shell Finite Elements

Abstract: Pyramidal truss sandwich panels (PTSPs) are widely used in engineering structures and their face sheets and core parts are generally bonded by the welding process. A large number of solid elements are usually required in the finite element (FE) model of a PTSP with welded joints to obtain its accurate modal parameters. Ignoring welded joints of the PTSP can save many degrees of freedom (DOFs), but significantly change its natural frequencies. This study aims to accurately determine modal parameters of a PTSP with welded joints with much fewer DOFs than those of its solid element model and to obtain its operational modal analysis results by avoiding missing its modes. Two novel methods that consider welded joints as equivalent stiffness are proposed to create beam-shell element models of the PTSP. The main step is to match stiffnesses of beam and shell elements of a welded joint with those of its solid elements. Compared with the solid element model of the PTSP, its proposed models provide almost the same levels of accuracy for natural frequencies and mode shapes for the first 20 elastic modes, while reducing DOFs by about 98% for the whole structure and 99% for each welded joint. The first 14 elastic modes of a PTSP specimen that were measured without missing any modes by synchronously capturing its two-faced vibrations through use of a three-dimensional scanning laser vibrometer (SLV) and a mirror experimentally validate its beam-shell element models created by the two proposed methods.

Three-dimensional aeroelastic model for successive analyses of high-aspect-ratio wings

Abstract: Next-generation civil aircraft and atmospheric satellites will have high-aspect-ratio wings. Such a design necessitates successive analysis of static, frequency, and time-domain dynamic responses based on a three-dimensional nonlinear beam model. In this study, a new successive-analysis framework based on an absolute nodal coordinate formulation with mean artificial strains (ANCF-MAS) is developed. While retaining the advantages of other three-dimensional (3D) ANCF approaches, such as constancy of the mass matrix and absence of velocity-dependent terms, ANCF-MAS uses the elastic force of the mean artificial strains to remove cross-sectional deformations that cause locking problems. The equation becomes a differential equation with an easily linearized elastic force that enables not only static and dynamic analyses but also frequency analysis using standard eigenvalue solvers. The solutions converge to the analytical frequencies without suffering from locking problems. A proposed successive-analysis method with model-order reduction reveals that the frequencies vary with the nonlinear static deformation because of the 3D deformation coupling. This reduced-order model agrees well with nonlinear models even when the wing experiences a large nonlinear dynamic deformation.

Comparison Between the Incremental Harmonic Balance Method and Alternating Frequency/Time-Domain Method

Abstract: Two widely used semi-analytical methods: the incremental harmonic balance (IHB) method and alternating frequency/time-domain (AFT) method are compared, and some long-standing discussions on frameworks of these two methods are cleared up. The IHB and AFT methods are proved for the first time to be theoretically equivalent when spectrum aliasing does not occur in the AFT method. Based on this equivalence, the minimal nonaliasing sampling rate for the AFT and fast Fourier transform (FFT)-based IHB methods can be obtained for a system with polynomial nonlinearities. While spectrum aliasing is theoretically inevitable for nonpolynomial nonlinearities, a sufficiently large sampling rate can be usually used with acceptable accuracy and efficiency for many systems. Convergence and efficiency of the IHB method, AFT method, and several FFT-based IHB methods are compared. Accuracy and convergence can be affected when the sampling rate is insufficient. This comparison can provide some insights to avoid misuse of these methods and choose which methods to use in engineering applications.

Three-Dimensional Solid Finite Element Contact Model for Rotordynamic Analysis: Experiment and Simulation

Abstract: Conventional rotordynamic analyses generally treat the rotor as a continuous body without considering effect of clamped joints. However, in modern rotating machines, rotors are often assembled with multiple complex-shaped parts and joints, which may significantly affect rotordynamic behavior. Several authors have proposed methods for implementing contact effects in rotordynamic analysis, but a more general modeling method for handling arbitrary contact geometries with various levels of surface roughness is needed. The present paper suggests a new contact model for rotordynamic analysis of an assembled rotor-bearing system with multiple parts connected by multiple joints. A contact element formulation is presented using solid finite elements and statistics-based contact theories. A test arrangement was developed to validate the proposed contact model for varying interface surface roughness and preloads. An iterative computation algorithm is introduced to solve the implicit relation between contact stiffness and stress distribution. Prediction results, using the contact model, are compared with measured natural frequencies for multiple configurations of a test rotor assembly. A case study is performed for an overhung type rotor-bearing system to investigate the effect of contact interfaces, between an overhung impeller and a rotor shaft, on critical speeds.

Control of Vibratory MEMS Gyroscope With the Drive Mode Excited Through Parametric Resonance

Abstract: In this paper, we present a control strategy for a micro-electro-mechanical gyroscope with a drive mode excited through parametric resonance. The reduced order two degrees-of-freedom model of the device is built, and the drive mode control is implemented using phase-locked loop (PLL) and automatic gain control (AGC) loop. A sense mode vibration control algorithm is developed as well for enhanced sensor performance. The analysis of the drive mode control loops is conducted using the multiple scales method. The robustness of the suggested control loops to parameters perturbation is demonstrated using the model. A simplified linear model of the control loops is shown to predict the device behavior with good accuracy.

Modeling and Analysis of Phononic Crystal With Coupled Lanes for Enhanced Elastic Wave Attenuation

Abstract: Phononic crystals and metamaterials have attractive potential in elastic wave attenuation and guiding over specific frequency ranges. Different from traditional phononic crystals/metamaterials consisting of identical unit cells, a phononic crystal with coupled lanes is reported in this article for enhanced elastic wave attenuation in the low-frequency regime. The proposed phononic crystal takes advantages of destructive interference mechanism. A finitely length phononic crystal plate consisting of coupled lanes is considered for conceptual verification. The coupled lanes are designed to split the incident elastic wave into separated parts with a phase difference to produce destructive interference. Theoretical modeling and finite element method (FEM) analysis are presented. It is illustrated that significant elastic wave attenuation is realized when the phase difference of elastic waves propagating through the coupled lanes approximates π. Besides, multiple valleys in the transmission can be achieved in a broad frequency range with one at a frequency as low as 1.85 kHz with unit cells’ width and length of 25 mm and ten unit cells in one lane.

Online Signal Denoising Using Adaptive Stochastic Resonance in Parallel Array and Its Application to Acoustic Emission Signals

Abstract: Signal denoising has been significantly explored in various engineering disciplines. In particular, structural health monitoring applications generally aim to detect weak anomaly responses (including acoustic emission) generated by incipient damage, which are easily buried in noise. Among various approaches, stochastic resonance (SR) has been widely adopted for weak signal detection. While many advancements have been focused on identifying useful information from the frequency domain by optimizing parameters in a post-processing environment to activate SR, it often requires detailed information about the original signal a priori, which is hardly assessed from signals overwhelmed by noise. This research presents a novel online signal denoising strategy by utilizing SR in a parallel array of bistable systems. The original noisy input with additionally applied noise is adaptively scaled, so that the total noise level matches the optimal level that is analytically predicted from a generalized model to robustly enhance signal denoising performance for a wide range of input amplitudes that are often not known in advance. Thus, without sophisticated post-processing procedures, the scaling factor is straightforwardly determined by the analytically estimated optimal noise level and the ambient noise level, which is one of the few quantities that can be reliably assessed from noisy signals in practice. Along with numerical investigations that demonstrate the operational principle and the effectiveness of the proposed strategy, experimental validation of denoising acoustic emission signals by employing a bistable Duffing circuit system exemplifies the promising potential of implementing the new approach for enhancing online signal denoising in practice.

Damping Mechanisms in Cable-Harnessed Structures for Space Applications: Analytical Modeling

Abstract: Recent developments in the aerospace industry have driven focus toward accurately modeling the effects of the cables and electronic cords on space structures. In the past, researchers have modeled the mass and stiffness effects of these cables but primarily overlooked their damping effects through careful analytical model developments. The objective of the current work is to present analytical models for cable-harnessed structures that also include the damping effects in their vibration response. Obtaining simple, low-order and high-fidelity models are highly advantageous in designing robust vibration real-time control algorithms for structures. Additionally, the analytical models are useful tools in providing insight into and better understanding of the dynamics of space structures as they are often difficult to be tested prior to launch due to their large size and at best only a few components may be tested. Motivated by the space applications, this work considers beam structures wrapped with cables which are modeled using beam and string theory assumptions. Two different damping models namely Kelvin–Voigt and hysteretic damping are considered. The homogenization approach is used as a starting point for structures of periodic wrapping patterns. Using the variational principle, the governing partial differential equation for the transverse coordinate of vibrations is found for three cable patterns and the results are compared to those from the distributed transfer function method (DTFM). Finally, the effects of several structural parameters are studied on the overall system damping.

Nonlinear Coupled Torsion/Lateral Vibration and Sommerfeld Behavior in a Double U-Joint Driveshaft

Abstract: Many driveline systems are designed to accommodate angular misalignment by the use of flexible couplings or Universal Joints (U-Joints) which link individual shaft segments. The Sommerfeld effect is a nonlinear phenomenon observed in some rotor systems being driven through a critical speed when there is not enough power to accelerate the rotor through resonance. Previous studies have shown that rotor speed can become captured when transitioning through natural frequencies due to nonlinear interactions between a non-ideal driving input and rotor imbalance. This paper, for the first time, shows that this type of rotor speed capture phenomena can also be induced by driveline misalignment. During rotor spinup under constant motor torque, it is found that misalignment-induced rotor speed capture phenomena can occur as the shaft speed approaches ½ the first elastic torsional natural frequency. Depending on misalignment level and motor torque, the shaft speed will either dwell near this speed and then pass through, or the speed will become trapped. Here, a nonlinear rotordynamics model of a segmented driveshaft connected by two U-joints including effects of angular misalignment and load torque is developed for the study. This analysis also determines the minimum driveline misalignment angle for which the shaft speed capture phenomena will occur for a given motor torque and load torque condition.

On Design and Analysis of Electrostatic Arch Micro-Tweezers

Abstract: This article provides criteria for the design of electrostatic arch micro-tweezers. The tweezers can be operated in two modes: a traditional quasi-static mode where a direct current voltage commands the tweezers arms along a trajectory to manipulate objects and dynamic mode where a harmonic signal commands release or characterization of objects. While the arms are rigid and move in tandem in the static mode, this is not guaranteed in the dynamic mode. To satisfy this, we carried out modal analysis of the tweezers using a finite element model (FEM) and a reduced-order model (ROM). The results show that the arms kinetic and potential energies divide the beam span into a middle sub-span between the arms and two outer sub-spans and result in significant changes in the relative compliance of the sub-spans. The changes in the platform compliance place limitation on the tweezers dynamic operation, such that only the first symmetrical mode shape of the tweezers satisfies the design criteria. We also investigate the adequacy of an ROM using straight unbuckled beam mode shapes as basis functions to represent the tweezers response by comparing its results with those of FEM. A five-mode ROM is found adequate to represent small motions in the vicinity of the tweezers initial curvature. It is inadequate for larger motions involving snap-though motions between the initial and counter curvatures. To capture larger motions, ROM should be improved by incorporating higher order straight beam modes or using the actual tweezers modes.

The Effects of Gravity on the Response of Centrifugal Pendulum Vibration Absorbers

Abstract: This article describes the effects of gravity on the response of systems of identical, cyclically arranged, centrifugal pendulum vibration absorbers (CPVAs) fitted to a rotor spinning about a vertical axis. CPVAs are passive devices composed of movable masses suspended on a rotor, suspended such that they reduce torsional vibrations at a given engine order. Gravitational effects acting on the absorbers can be important for systems spinning at relatively low rotation speeds, for example, during engine idle conditions. The main goal of this study is to predict the response of a CPVA/rotor system in the presence of gravity. A linearized model that includes the effects of gravity and an order n torque acting on the rotor is analyzed by exploiting the cyclic symmetry of the system. The results show that a system of N absorbers responds in one or more groups, where the absorbers in each group have identical waveforms but shifted phases. The nature of the waveforms can have a limiting effect on the absorber operating envelope. The number of groups is shown to depend on the engine order n and the ratio N/n. It is also shown that there are special resonant effects if the engine order is n = 1 or n = 2, the latter of which is particularly important in applications. In these cases, the response of the absorbers has a complicated dependence on the relative levels of the applied torque and gravity. In addition, it is shown that for N > 1, the rotor response is not affected by gravity, at least to leading order, due to the cyclic symmetry of the gravity effects. The linear model and the attendant analytical predictions are verified by numerical simulations of the full nonlinear equations of motion.

Damping Mechanisms in Cable-Harnessed Structures for Space Applications: Experimental Validation

Abstract: In this technical brief, the experimental study and model validations for the damping mechanisms of cable-harnessed beam structures are presented. The structure consists of cables wrapped around a host beam in a periodic zigzag pattern. A special case of cable attached along the beam length over its centerline is also considered. First, material damping in the cables is characterized using dynamic tests and the relevant cable damping factors are calculated for both the Kelvin–Voigt and hysteretic damping models. Experimental modal testing is then performed on the fabricated cable-harnessed beams to obtain the frequency response functions (FRFs). Finally, the experimental FRFs are compared with the damped analytical models. The test and model results are shown to be in very good agreements in predicting the structural damping induced by the cables.

Investigating Coupled Train-Bridge-Bearing System Under Earthquake- and Train-Induced Excitations

Abstract: The dynamic interaction between a bridge and a moving train has been widely studied. However, there is a significant gap in our understanding of how the presence of isolation bearings influences the dynamic response, especially when an earthquake occurs. Here, we formulate a coupled model of a train-bridge-bearing system to examine the bearings’ dynamic effects on the system responses. In the analysis, the train is modeled as a moving oscillator, the bridge is a one span simply supported beam and one isolation bearing is installed under each support of the bridge. A mathematical model using fractional derivatives is used to capture the viscoelastic properties of the bearings. The vertical response is the focus of this investigation. Dynamic substructuring is used in modeling to efficiently capture the coupled dynamics of the entire system. Illustrative numerical simulations are carried out to examine the effects of the bearings. The results demonstrate that although the presence of bearings typically decreases the bridge seismic responses, there is a potential to increase the bridge response induced by the moving train.

Effect of Uncertainty in the Balancing Weights on the Vibration Response of a High-Speed Rotor

Abstract: This work investigates how uncertainties in the balancing weights are propagating into the vibration response of a high-speed rotor. Balancing data are obtained from a 166-MW gas turbine rotor in a vacuum balancing tunnel. The influence coefficient method is then implemented to characterize the rotor system by a deterministic multi-speed and multi-plane matrix. To model the uncertainties, a non-sampling probabilistic method based on the generalized polynomial chaos expansion (gPCE) is employed. The uncertain parameters including the mass and angular positions of the balancing weights are then expressed by gPCE with deterministic coefficients. Assuming predefined probability distributions of the uncertain parameters, the stochastic Galerkin projection is applied to calculate the coefficients for the input parameters. Furthermore, the vibration amplitudes of the rotor response are represented by appropriate gPCE with unknown deterministic coefficients. These unknown coefficients are determined using the stochastic collocation method by evaluating the gPCE for the system response at a set of collocation points. The effects of individual and combined uncertain parameters from a single and multiple balancing planes on the rotor vibration response are examined. Results are compared with the Monte Carlo simulations, showing excellent agreement.

Graphical Design Methodology of Multi-Degrees-of-Freedom Tuned Mass Damper for Suppressing Multiple Modes

Abstract: The multi-degrees-of-freedom (MDOF) tuned mass damper (TMD) has proven its ability to suppress multiple modes of interest, and it possesses less mounting space than multiple single degree-of-freedom TMDs of equal damping mass. However, it is challenging to implement the exact design of MDOF TMDs having expected vibration modes. The conceptual design of MDOF TMD containing visualized DOFs is first presented by the graphical approach, and the visualization of the quantitative relationship between the freedoms and constraints of TMD is attained. Then, dynamics modeling is analytically formulated by incorporating experimental data, and optimization of MDOF TMD considering background modes is performed. Two scenarios of MDOF TMD (i.e., 2DOFs TMD and 3DOFs TMD) are simulated. Vibration suppression of single dominant mode and multiple modes are achieved, corresponding to the case when the primary structure is subjected to wide and narrow band harmonic excitations, respectively. Afterward, a TMD with one rotational and two translational (1R2 T) DOFs is designed by embodying the geometric constraint patterns by flexible beams, and changeable elastic elements are incorporated. Experiments show that the first, second, and third bending modes of the cantilever beam are suppressed by 80.0%, 67.5%, and 61.2%, respectively, by the 3DOFs TMD for multiple modes suppression.

Wave Propagation in Tapered Periodic Curved Meta-Frame Using Floquet Theory

Abstract: In this work, the elastic wave propagation and dispersion characteristics of a curved tapered frame structure is investigated analytically. Separately, wave propagation through uniform curved and straight tapered beam were reported in the existing literature; however, no literature reports the influence of simultaneous bent and taper on the wave propagation. In particular, the band characteristics for the curved and tapered beam with two types of cross-sections, i.e., rectangular and circular, are presented. The paper elucidates that introducing a small periodic bent angle cross-section produces a complete, viz. axial and flexural band gap in the low-frequency region, and conicity enhances the width of the band. It is also evidenced that a curved tapered frame with a solid circular cross-section induces a wider band gap than the rectangular section. A complete first normalized bandwidth of 159% is achievable for the circular cross-section and 123% in the case of the rectangular section. The complete result is presented in a non-dimensional framework for wider applicability. An analysis of a finite tapered curved frame structure also demonstrates the attenuating characteristics obtained from the band structure of the infinite structure. The partial wave mode conversion, i.e., generation of coupled axial and flexural mode from a purely axial or flexural mode in an uncoupled medium is observed. This wave conversion is perceived in reflected and transmitted waves while this curved tapered frame is inserted between the two uniform cross-section straight frames.

Bifurcation and Chaos of a Spur Gear Transmission System With Non-Uniform Wear

Abstract: In this study, a nonlinear dynamic model of a spur gear transmission system with non-uniform wear is proposed to analyze the interaction between surface wear and nonlinear dynamic characteristics. A quasi-static non-uniform wear model is presented, with consideration of the effects of operating time on mesh stiffness and gear backlash. Furthermore, a nonlinear dynamic model with six degrees-of-freedom is established considering surface friction, time-varying gear backlash, time-varying mesh stiffness, and eccentricity, and the Runge–Kutta method applied to solve this model. The bifurcation and chaos in the proposed dynamic model with the change of the operating time and the excitation frequency are investigated by bifurcation and spectrum waterfall diagrams to analyze the bifurcation characteristics and the dimensionless mesh force. It is found that surface wear is generated with a change in operating time and affects the nonlinear dynamic characteristics of the spur gear system. This study provides a better understanding of nonlinear dynamic characteristics of gear transmission systems operating under actual conditions.

Dynamic Characteristic Analysis of Rotating Blade With Transverse Crack—Part II: A Comparison Study of Different Crack Models

Abstract: This study aims at the comparative analysis and improvement of different analytical crack models for rotating blade. Part II of this study focuses on the comparative analysis of dynamic characteristics based on modified models mentioned in Part I. A nonlinear damage indicator (NDI) and an equivalent energy indicator (EEI) are introduced to characterize the nonlinear effect of crack from different perspectives. EEI offers a physical mechanism explanation of crack closing behavior, which is invisible. Meanwhile, NDI offers an observable indicator to quantify the nonlinearity of crack. It is demonstrated through the numerical study that the variation of NDI and EEI varies the same with each other, which cross-verified the validity of NDI and EEI for quantifying the nonlinear effect of crack. Comparative investigations are performed to analyze the effects of load amplitude, crack depth, and crack location on the nonlinear dynamics of cracked blade, and both NDI and EEI are utilized to quantify the nonlinear effects of crack. The comparative results suggest that NDI of the second-order super-harmonic component increases with the increasing crack depth and excitation load amplitude and decreases with the increasing crack locations, while the variation of EEI follows the variation of NDI. This phenomenon indicates that the crack, which is deeper and closer to blade root under a larger load will be more dangerous. This study’s comparative results may provide some guidance for choosing the analytical crack models when analyzing the nonlinear dynamics of rotating cracked blade and blade health monitoring.

Damping Frame Vibrations Using Anechoic Stubs: Analysis Using an Exact Wave-Based Approach

Abstract: This paper explores the addition of small stubs with anechoic terminations (termed herein “anechoic stubs”) as a means of damping and/or removing vibration modes from planar frame structures. Due to the difficulties associated with representing anechoic boundary conditions in more traditional analysis approaches (e.g., analytical, finite element, finite difference, and finite volume), the paper employs and further develops an exact wave-based approach, incorporating Timoshenko beams, in which ideal and non-ideal anechoic terminations are simply represented by a reflection matrix. Several numerically evaluated examples are presented documenting novel effects anechoic stubs have on the vibration modes of a two-story frame, such as eliminated, inserted, and exchanged mode shapes. Modal damping ratios are also computed as a function of the location and number of anechoic stubs, illustrating optimal locations and optimal reflection ratios as a function of mode number. Forced vibration studies are then carried out, demonstrating reduced, eliminated, and inserted resonance response.

A Novel Accelerometer Mounting Method for Sensing Performance Improvement in Acoustic Measurements From the Knee.

Abstract: In this study, we propose a new mounting method to improve accelerometer sensing performance in the 50 Hz-10 kHz frequency band for knee sound measurement. The proposed method includes a thin double-sided adhesive tape for mounting and a 3D-printed custom-designed backing prototype. In our mechanical setup with an electrodynamic shaker, the measurements showed a 13 dB increase in the accelerometer's sensing performance in the 1-10 kHz frequency band when it is mounted with the craft tape under 2 N backing force applied through low-friction tape. As a proof-of-concept study, knee sounds of healthy subjects (n = 10) were recorded. When the backing force was applied, we observed statistically significant (p < 0.01) incremental changes in spectral centroid, spectral roll-off frequencies, and high-frequency (1-10 kHz) root-mean-square (RMS) acceleration, while low-frequency (50 Hz-1 kHz) RMS acceleration remained unchanged. The mean spectral centroid and spectral roll-off frequencies increased from 0.8 kHz and 4.15 kHz to 1.35 kHz and 5.9 kHz, respectively. The mean high-frequency acceleration increased from 0.45 mgRMS to 0.9 mgRMS with backing. We showed that the backing force improves the sensing performance of the accelerometer when mounted with the craft tape and the proposed backing prototype. This new method has the potential to be implemented in today's wearable systems to improve the sensing performance of accelerometers in knee sound measurements.

Enhancement of Static and Dynamic Performance of Composite Tapered Pretwisted Rotating Blade With Variable Stiffness

Abstract: Composite pretwisted tapered rotating thin-walled beams (TWB) can be used as a load-carrying structural part of a composite helicopter, wind turbine, fan, and turbomachinery blades. In the present study, the variable stiffness concept with curvilinear fiber path is used to achieve improved structural statics and dynamics performance of uniform and asymmetric composite thin-walled rotating beams. A parametric study is performed to investigate the effect of different fiber paths on the structural performance metrics including frequency spacing, coupling factor, and critical buckling load. For this purpose, The Euler–Lagrange governing equations of the dynamic system are derived via Hamilton's principle. To solve the governing set of equations, the extended Galerkin’s method (EGM) is employed. To validate the TWB model with curvilinear fibers, commercial finite element analysis tools abaqus is used. The author believes that the results presented here are likely to provide valuable information to the engineers involved in the design of advanced turbomachinery rotating blades using a variable stiffness concept with curvilinear fiber placement.