Showing papers on "Rotary inertia published in 2019"

Robustness of the Active Rotary Inertia Driver System for Structural Swing Vibration Control Subjected to Multi-Type Hazard Excitations

Abstract: In traditional structural disaster prevention design, the effects of various disasters on structures are usually considered separately, and the effects of multi-type hazards are rarely considered. The traditional Tuned Mass Damper (TMD) and Active Mass Damper/Driver (AMD) are ineffective for the control of swing vibration. The Tuned Rotary Inertia Damper (TRID) system has the problems of being ineffective under multi-type hazard excitation and exhibiting a limited robustness. The Active Rotary Inertia Driver (ARID) system is proposed to solve these problems and the robustness of such an active control system is investigated in this paper. Firstly, the equations of motion corresponding to the in-plane swing vibration of the suspended structure with the ARID/TRID system are established. The control algorithm for the ARID system is designed based on the Linear Quadratic Regulator (LQR) algorithm. Next, numerical analyses carried out using Simulink are presented. Then, numerical analyses and experimental investigations corresponding to five working conditions, i.e., free vibration, forced vibration, sweep excitation, earthquake excitation, and sea wave excitation, are introduced. Lastly, the numerical analyses and experimental results of the ARID system, and numerical results of the TRID system, are compared to demonstrate the effectiveness and robustness of the ARID control system. It can be concluded that the ARID system is effective and feasible in structural swing vibration control and it exhibits a better control robustness than the TRID system. Furthermore, the feasibility of applying the ARID control system to multi-type hazard excitations is validated.

Swing Vibration Control of Suspended Structure Using Active Rotary Inertia Driver System: Parametric Analysis and Experimental Verification

Abstract: The Active Rotary Inertia Driver (ARID) system is a novel vibration control system that can effectively mitigate the swing vibration of suspended structures. Parametric analysis is carried out using Simulink based on the mathematical model and the effectiveness is further validated by a series of experiments. Firstly, the active controller is designed based on the system mathematical model and the LQR (linear quadratic regulator) algorithm. Next, the parametric analysis is carried out using Simulink to study the key parameters such as the coefficient of the control algorithm, the rotary inertia ratio. Lastly, the ARID system control effectiveness and the parametric analysis results are further validated by the shaking table experiments. The effectiveness and robustness of the ARID system are well verified. The dynamic characteristics of this system are further studied, and the conclusions of this paper provide a theoretical basis for further development of such unique control system.

Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT

Abstract: In this work, the thermal buckling characteristics of zigzag single-walled boron nitride (SWBNNT) embedded in a one-parameter elastic medium modeled as Winkler-type foundation are investigated using a nonlocal first-order shear deformation theory (NFSDT). This model can take into account the small scale effect as well as the transverse shear deformation effects of nanotubes. A closed-form solution for nondimensional critical buckling temperature is obtained in this investigation. Further the effect of nonlocal parameter, Winkler elastic foundation modulus, the ratio of the length to the diameter, the transverse shear deformation and rotary inertia on the critical buckling temperature are being investigated and discussed. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the thermal buckling properties of boron nitride nanotubes.

Large amplitude free flexural vibrations of functionally graded graphene platelets reinforced porous composite curved beams using finite element based on trigonometric shear deformation theory

Abstract: In this paper, the large amplitude free flexural vibration characteristics of fairly thick and thin functionally graded graphene platelets reinforced porous curved composite beams are investigated using finite element approach. The formulation includes the influence of shear deformation which is represented through trigonometric function and it accounts for in-plane and rotary inertia effects. The geometric non-linearity introducing von Karman’s assumptions is considered. The non-linear governing equations obtained based on Lagrange’s equations of motion are solved employing the direct iteration technique. The variation of non-linear frequency with amplitudes is brought out considering different parameters such as slenderness ratio of the beam, curved beam included angle, distribution pattern of porosity and graphene platelets, graphene platelet geometry and boundary conditions. The present study reveals the redistribution of vibrating mode shape at certain amplitude of vibration depending on geometric and material parameters of the curved composite beam. Also, the degree of hardening behaviour increases with the weight fraction and aspect ratio of graphene platelet. The rate of change of nonlinear behaviour depends on the level of amplitude of vibration, shallowness and slenderness ratio of the curved beam.

Wave propagation in smart laminated composite cylindrical shells reinforced with carbon nanotubes in hygrothermal environments

Abstract: Wave propagation problem is solved in smart laminated carbon nanotube (CNT)-reinforced composite cylindrical shells coupled with piezoelectric layers on the top and bottom surfaces in hygrothermal environments for the first time. The motion equations are derived based on the first-order shear deformation shell theory considering the transverse shear effects and rotary inertia. The hygrothermal effects are also included in the mathematical modeling and the effective material properties of a CNT-reinforced composite shell are estimated through the Mori-Tanaka micromechanical model. Dispersion solutions are obtained by solving an eigenvalue problem. Parametric studies are carried out to investigate the effects of temperature/moisture variation, CNT volume fraction and orientation, piezoelectricity, shell geometry, stacking sequence, and material properties of the host substrate laminated composite shell at different axial and circumferential wave numbers. The results show that the temperature/moisture variation influences moderately on the dispersion solutions of smart laminated CNT-reinforced composite shells. The presented methodology and results can be used in wave propagation analysis of smart laminated CNT-reinforced composite shells affected by hygrothermal environmental conditions.

Wave propagation in piezoelectric cylindrical composite shells reinforced with angled and randomly oriented carbon nanotubes

Abstract: Wave propagation behavior in piezoelectric cylindrical composite shells reinforced with angled and randomly oriented, straight carbon nanotubes (CNTs) is analytically investigated for the first time via the first-order shear deformation shell theory including the transverse shear effects and rotary inertia. The Mori-Tanaka method is used for micromechanical modeling. Dispersion solutions are computed by solving an eigenvalue problem. The effects of CNT orientation, CNT volume fraction, and shell geometry on the dispersion solutions are examined. Various orientations of CNTs lead to different dispersion behaviors; the variation of wave phase velocities is more significant at lower axial wave numbers; and the effects of CNT volume fraction and shell geometry on wave dispersion behaviors are more obvious at higher circumferential wave numbers. The presented model and analytical results of this study can be utilized in the wave propagation analysis of piezoelectric shells reinforced with CNTs for the design of new smart structures used in structural health monitoring and/or energy harvesting applications.

Free and forced analysis of perforated beams

Abstract: This article presents a unified mathematical model to investigate free and forced vibration responses of perforated thin and thick beams. Analytical models of the equivalent geometrical and material characteristics for regularly squared perforated beam are developed. Because of the shear deformation regime increasing in perforated structures, the investigation of dynamical behaviors of these structures becomes more complicated and effects of rotary inertia and shear deformation should be considered. So, both Euler-Bernoulli and Timoshenko beam theories are proposed for thin and short (thick) beams, respectively. Mathematical closed forms for the eigenvalues and the corresponding eigenvectors as well as the forced vibration time response are derived. The validity of the developed analytical procedure is verified by comparing the obtained results with both analytical and numerical analyses and good agreement is detected. Numerical studies are presented to illustrate effects of beam slenderness ratio, filling ratio, as well as the number of holes on the dynamic behavior of perforated beams. The obtained results and concluding remarks are helpful in mechanical design and industrial applications of large devices and small systems (MEMS) based on perforated structure.

Free vibration analysis of a spinning piezoelectric beam with geometric nonlinearities

Abstract: The linear and non-linear free vibrations of a spinning piezoelectric beam are studied by considering geometric nonlinearities and electromechanical coupling effect. The non-linear differential equations of the spinning piezoelectric beam governing two transverse vibrations are derived by using transformation of two Euler angles and the extended Hamilton principle, wherein an additional piezoelectric coupling term and different linear terms are present in contrast to the traditional shaft model. Linear frequencies are obtained by solving the standard eigenvalues of the linearized system directly, and the non-linear frequencies and non-linear complex modes are achieved by using the method of multiple scales. For free vibrations analysis of a spinning piezoelectric beam, the non-linear modal motions are investigated as forward and backward precession with different spinning speeds. The responses to the initial conditions for this gyroscopic system are studied and a beat phenomenon is found, which are then validated by numerical simulation. The influences of some parameters such as electrical resistance, rotary inertia and spinning speeds to the non-linear dynamics of a spinning piezoelectric beam are investigated.

The static and dynamic analyses of warping included composite exact conical helix by mixed FEM

Abstract: The objective of this study is to investigate the combined influence of two important topics on the precision of static and dynamic analyses of non-circular composite helical bars, namely, exact helix geometry and the warping effect. Sometimes a conical helix over logarithmic spiral planar curve is formed by a degenerated plane curve. The most important goal of this study is to determine the range of the geometric parameters in which the degenerated plane curve lacks the precision necessary for the structural analysis of the conical helix compare to using an exact logarithmic spiral function. Another important topic on the precision of the results is the warping of non-circular composite sections. In this study, first, a parametric analysis is carried out in order to determine the maximum influence of warping on the torsional rigidity of non-circular sandwich/composite cross-sections. Then, some benchmark examples are employed to consider the combined influence of the two topics mentioned above. The analysis is performed over a curved mixed finite element formulation based on Timoshenko beam theory by considering the shear influence, rotary inertia and the warping included torsional rigidity. The curved element consists of two nodes and 24 degrees of freedom in total.

Free vibration of arbitrary thick FGM deep arches using unconstrained higher-order shear deformation theory

Abstract: Natural frequencies of circular deep arches made of functionally graded materials (FGMs) with general boundary conditions are obtained in this research based on the unconstrained higher-order shear deformation theory taking into account the depth change, complete effects of shear deformation, and rotary inertia. The material properties are assumed to vary continuously through the thickness direction of the arch. Displacement field within the arch is obtained through expansion up to an arbitrary order. Governing differential equations of the in-plane vibration are derived using Hamilton's principle. These equations are solved numerically utilizing the differential quadrature method (DQM) formulation. In order to illustrate the validity and accuracy of the presented results, results are compared with the available data in the open literature. Afterwards, novel numerical results are given for free vibration behaviour of the FGM deep arches with various boundary conditions.

Incorporating the Havriliak–Negami model in wave propagation through polymeric viscoelastic core in a laminated sandwich cylinder

Abstract: This paper presents the fundamental problem of three-dimensional acoustic wave transmission through a sandwich structure with viscoelastic core excited by an obliquely plane wave. The structure consists of a functionally graded shell as an outer layer, an isotropic layer as an inner layer and also a viscoelastic core. This work considers Havriliak-Negami model for description of complex modulus of viscoelastic core. The Havriliak-Negami model is a new mathematical method for the simulation of polymeric relaxation behavior in the frequency domain. In this model, both of complex Young’s and shear moduli are frequency dependent. Moreover, considering the effective roles of shear deformation and rotary inertia, dynamic governing equations of the functionally graded cylinder, viscoelastic core and isotropic shell are derived within the frameworks of the three-dimensional theory of elasticity. Furthermore, analytical model of acoustic wave transmission based on transfer matrix method is composed of a set of fluid and structural equations which taking into account the frequency dependency of mechanical characterization for the viscoelastic core. A good agreement can be observed, comparing the present results with those of other authors. Besides, the results show that a double-walled cylinder with viscoelastic core has a better acoustic insulation in comparison with isotropic shell with the same mass. Contrary to elastic material, by thickening the viscoelastic layer, sound transmission loss decreases in mass-controlled region due to shear deformation and rotary inertia. It has been also proved that polymer with a larger loss factor has good performance in energy dissipation.

Improvement of the dynamic instability of shallow hybrid composite cylindrical shells under impulse loads using shape memory alloy wires

Abstract: In the present paper, the prevention of a probable instability after a sudden change in deformation of thin shallow cylindrical composite panels under impulse loads is pursued using embedded super-elastic SMA wires. A novel and practical framework is proposed to analyze these panels according to the precisely determined super-elastic function of the shape memory alloys. The suggested phase transformation algorithm can deal with the existing deficiencies in the modeling of the super-elastic behaviors. The governing equations of motion are obtained based on a matrix form of the energy equilibrium, using Sanders’ shell theory, and including the in-plane and rotary inertia effects. The resulting nonlinear finite element formulation is programmed in FORTRAN language to solve the time-dependent equations by the Newmark-beta numerical time-integration approach. The Budiansky-Roth criterion is used to determine the stability thresholds of the structures by detecting the abrupt and unexpected deformations under the suddenly imposed transverse concentrated load. Effects of imposing loads with different time durations, types, and characteristics, various amounts of the pre-tension, different viscous damping and volume fractions of the SMA are examined in order to determine the dynamic instability strength of the hybrid composite cylindrical shells and the resulting deformations in a fully non-linear solution. The large magnitudes of the pre-tension loads can change the instability performance of the structures under even small loads. In this study, the viscous damping of the host composite panels is ignored in comparison to the energy absorption due to the hysteresis loops of the stress-strain transformation diagrams of the SMA wires.

Parametric Investigation of Dual-Mass Flywheel Based on Driveline Start-Up Torsional Vibration Control

Abstract: This paper is aimed to investigate the influence of dual-mass flywheel (DMF) kinetic parameters on driveline torsional vibration in engine start-up process, which prescribes the design requirements under start-up condition for DMF matching. On the basis of driveline excitation analysis during engine start-up, the analytical model of DMF driveline torsional vibration system is built and simulated. The vehicle start-up test is conducted and compared with the simulation results. On account of the partial nonstationary characteristic of driveline during start-up, the start-up process is separated into 3 phases for discussing the influence of DMF rotary inertia ratio, hysteresis torque, and nonlinear torsional stiffness on attenuation effect. The test and simulation results show that the DMF undergoes severe oscillation when driveline passes through resonance zone, and the research model is verified to be valid. The DMF design requirements under start-up condition are obtained: the appropriate rotary inertia ratio (the 1st flywheel rotary inertia-to-the 2nd flywheel rotary inertia ratio) is 0.7∼1.1; the interval of DMF small torsion angle should be designed as being with small damping, while large damping is demanded in the interval of large torsion angle; DMF should be equipped with low torsional stiffness when working in start-up process.

Viscoelastically coupled dynamics of FG Timoshenko microbeams

Abstract: Viscosity effects on the mechanical behaviour of functionally graded (FG) Timoshenko microbeams are investigated; the model possesses both linear nonlinear viscous terms. The Mori–Tanaka homogenisation method is used for the continuous variations of the material properties of the microsystem along the thickness; the Kelvin–Voigt scheme is employed for the internal damping; the shear deformation and rotary inertia are modelled for the viscoelastic microbeam via the Timoshenko theory; the modified couple stress theory is used for size influences. An energy loss/balance via Hamilton’s principle is used for obtaining the equations of motion. Galerkin’s approach together with a continuation method is employed for the mechanical responses. The simultaneous effects of viscosity, being small, and FG materials on the mechanical behaviour are investigated.

Size dependent vibration analysis of micro-milling operations with process damping and structural nonlinearities

Abstract: Micro-milling is one of the micro-manufacturing techniques used for creating micro-scale features. In this article, a size-dependent formulation based on the strain gradient elasticity theory is developed to analyze the micro milling tool vibration. A new cutting forces formulation in rotating frame is presented in this paper. Considering structural nonlinearities , gyroscopic moment, rotary inertia , process damping and size effect, nonlinear equations of tool motion are derived using non-classical Timoshenko beam theory and Hamilton's principal. Partial differential governing equations of the tool are converted to ordinkary differential equations by using assumed modes method. Then the method of multiple scales is used to obtain the analytical solution for tool vibrations. The proposed approach is applied to investigate the chatter instability observed in micro-milling operations. To verify the presented model, simulated stability lobe diagrams are compared with the results obtained from experimental tests and literature. According to the results, neglecting size effect, gyroscopic and rotary terms in the tool model causes significant errors in prediction of the chatter in micro-milling process.

Modeling and Performance Investigation of a Piezoelectric Vibrating Gyroscope

Abstract: An improved mathematical model of a piezoelectric vibrating gyroscope is constructed with the effects of electromechanical coupling and rotary inertia taken into account. The gyroscope consists of a cantilever beam with tip mass attached to its free end. The piezoelectric materials are adhered to the four surfaces of the rectangular beam. By using two Euler angles and extended Hamilton’s principle, the electromechanical coupled partial differential equations governing the flexural-flexural motions of the piezoelectric gyroscope are obtained. The accuracy and effectiveness of the comprehensive mathematical model are validated by the existing models in literature. The necessity of taking rotary inertia into account is discussed. The natural frequencies of the rotating piezoelectric beam in both drive and sense directions have been investigated by considering the effects of the tip mass, angular speed, and external impedance. The dynamic behaviors of the piezoelectric gyroscope with different parameters, such as the tip mass, the lengths of piezoelectric materials and beam, and the external impedance, have been studied. In particular, the optimal combination of the external excitation frequency and the external impedance for the best calibration curve of the piezoelectric gyroscope is identified. Finally, the dynamic performance of the piezoelectric gyroscope under varying boundary conditions has been investigated for the potential practical applications.

Analytical Approach for Thermo-electro-mechanical Vibration of Piezoelectric Nanoplates Resting on Elastic Foundations based on Nonlocal Theory

Abstract: In the present work, thermo-electro vibration of the piezoelectric nanoplates resting on the elastic foundations using nonlocal elasticity theory are considered. In-plane and transverse displacements of the nanoplate have been approximated by six different modified shear deformation plate theories considering transverse shear deformation effects and rotary inertia. Moreover, two new distributions of transverse shear stress along the thickness of the nanoplate were introduced for the first time. The equations of motion were derived by implementing Hamilton’s principle and solved using analytical method for various boundary conditions including SSSS, CSSS, CSCS, CCSS and CCCC. Based on a comparison with the previously published results, the accuracy of the results was confirmed. Finally, the effects of different parameters such as boundary conditions, variations of the thickness to length ratio, aspect ratio, increasing temperature, external voltage, foundation coefficients and length scale on the natural frequency of the plate were shown and discussed in details.

Transient response of rhombic laminates

Abstract: In the present study, a suitable mathematical model considering parabolic transverse shear strains for dynamic analysis of laminated composite skew plates under different types of impulse and spatial loads was presented for the first time. The proposed mathematical model satisfies zero transverse shear strain at the top and bottom of the plate. On the basis of the cubic variation of thickness coordinate in in-plane displacement fields of the present mathematical model, a 2D finite element (FE) model was developed including skew transformations in the mathematical model. No shear correction factor is required in the present formulation and damping effect was also incorporated. This is the first FE implementation considering a cubic variation of thickness coordinate in in-plane displacement fields including skew transformations to solve the forced vibration problem of composite skew plates. The effect of transverse shear and rotary inertia was incorporated in the present model. The Newmark-beta scheme was adapted to perform time integration from step to step. The C0 FE formulation was implemented to overcome the problem of C1 continuity associated with the cubic variation of thickness coordinate in in-plane displacement fields. The numerical studies showed that the present 2D FE model predicts the result close to the analytical results. Many new results varying different parameter such as skew angles, boundary conditions, etc. were presented.

Vibration attenuation of rotor-bearing systems using smart electro-rheological elastomer supports

Abstract: Nowadays, capability of safe operation sufficiently away from the critical speeds is one of the most important design requirements of rotating machineries. The focus of this paper is the application of smart electro-rheological (ER) elastomers to rotor dynamics field to reduce the vibration level of a rotor system. A Jeffcott rotor, supported via two bearings at both ends augmented with ER elastomers, is considered. A finite element approach, based on the Rayleigh beam theory, is used to model the dynamics of the system, and the proposed model accounts for the rotary inertia, gyroscopic effects and shaft’s internal damping. The ER elastomer supports are simulated with four-parameter viscoelastic model. The simulation results reveal that the use of ER elastomer in the conventional bearing supports leads to downshifting of the critical speeds and a considerable reduction in its corresponding vibration amplitude. Also, the stability limit speed of the system is improved by employing the ER elastomer technology. To extend the stability region of the rotor system to higher operating rotational speeds, a simple on–off control strategy is employed. The proposed control scheme determines the required real-time voltage to be applied at ER elastomers and guarantees low vibration amplitude over a wide frequency range. The novel idea of using ER elastomers for vibration suppression of rotor systems can be fairly extended to other applications which suffer from unwanted high amplitude vibrations.

Active rotary inertia driving and controlling system

Abstract: The invention relates to the field of vibration abatement in systems, in particular to an active rotary inertia driving and controlling system. The active rotary inertia driving and controlling systemincludes an output carrier , a driving assembly and a rotary inertia disc; the output carrier includes a separating plate and a shell body, wherein the separating plate is fixed to the inner wall ofthe shell body, and the shell body is connected to the end part of a controlled structure; one end of the driving assembly is fixed to the shell body, the other end of the driving assembly is fixed tothe separating plate, the end part of the driving assembly is connected with an output shaft, the output shaft extends outside the shell body, and the other end of the output shaft is connected withthe rotary inertia disc; and the rotary inertia disc is a ring disc or a ring with a certain mass . The active rotary inertia driving and controlling system solves the problems that in the prior art,the control of a translational TMD on rotary shimmy motion is failed; the control efficiency of the translational AMD is low, and the control effect of the translation AMD is poor; passive tuning rotary inertia damper control is low in application robustness, complex in frequency modulation technology and small in application range.