Nonlinear transverse vibrations of angle-ply laminated composite piezoelectric cantilever plate with four-modes subjected to in-plane and out-of-plane excitations

Zhang, W.; Yang, Ji-Hou; Zhang, Y.F.; Yang, S.W.

doi:10.1016/j.engstruct.2019.109501

Cited by 25 publications

(19 citation statements)

References 56 publications

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“…In the above equation, U implies strain energy, W is the external work done by the loads and T represents plate kinetic energy in the time interval t 1 to t 2 whereas d denotes the first variation. The partial differential equations of the composite plate exposed to non-uniform in-plane compressive periodic loading are as follows, Nxx;x þ Nxy;y ¼ q g u 0 ;tt (30) Nxy;x þ Nyy;y ¼ q g v 0 ;tt (31)…”

Section: Governing Equations Of Motionmentioning

confidence: 99%

“…Apart from the dynamic buckling, several researchers [23][24][25][26][27][28][29][30] investigated the non-linear dynamic response of the plate and shell subjected to in-plane continuous dynamic forces. In this context, Liu et al 23 investigated the nonlinear dynamic response of a simply supported imperfect functionally graded circular cylindrical shell under complex loads using the 4th order Runge-Kutta method.…”

Section: Introductionmentioning

confidence: 99%

“…In a similar context, Zhang et al 24 investigated the non-linear responses of symmetric cross-ply laminated composite cantilever plate subjected to in-plane and moment excitation using the Galerkin method. Recently, the non-linear dynamic responses of the laminated composite piezoelectric cantilever plate under combined the transverse and in-plane excitations were analyzed by Zhang et al 30 using the Galerkin approach. The authors concluded that the nonlinear dynamic behaviors help us to optimize the structural and physical parameters of the laminated composite piezoelectric cantilever plate under combined the transverse and in-plane excitations.…”

Section: Introductionmentioning

confidence: 99%

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Non-linear response and buckling of imperfect laminated composite plates under in-plane pulse forces

Kumar

Singh

Patel

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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This study presents a semi-analytical solution of the non-linear dynamic response, shock spectrum, and dynamic buckling of an imperfect angle-ply laminated composite plate under various types of in-plane pulse forces. The laminated composite plate is modeled using a higher-order shear deformation theory and von-Kármán geometric nonlinearity. The non-linear governing partial differential equations (PDEs) of imperfect laminated composite plates are derived via Hamilton’s principle. Using Galerkin’s method, the non-linear PDEs are transformed into non-linear algebraic equations for the static stability problems and non-linear ordinary differential equations for the dynamic problem such as dynamic response, shock spectrum, and dynamic buckling. The buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the composite plate is evaluated using the post-buckling analysis based on the Tsai-Wu failure criterion. The dynamic response and shock spectrum of the composite plate are determined via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the Tsai-Wu failure criterion. Dynamic buckling is to be characterized by dynamic load factor (DLF), which is represented as the ratio of the dynamic failure load to the static failure load. Based on the pulse/shock duration time, the pulse forces are divided into three loading regimes known as impulsive, dynamic, and quasi-static. The study revealed that the DLF values are > 1, < 1, and [Formula: see text]1 respectively for the case of impulsive, dynamic, and quasi-static loading regimes of pulse force. The influences of various types of in-plane pulse forces, amplitude and time duration of pulse forces, and amplitude of initial geometric imperfections on the non-linear dynamic response, shock spectrum, and dynamic buckling behavior of the laminated composite plate are addressed in detail. The results will help in the appropriate design of the laminated composite plate against dynamic buckling.

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Section: Governing Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non-linear response and buckling of imperfect laminated composite plates under in-plane pulse forces

Kumar

Singh

Patel

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Smart piezoelectric structures are commonly used for active control in the fields of aerospace engineering [1]. As a type of smart structures, piezoelectric functionally graded plates (PFGPs) refer to using the functionally graded plates (FGPs) [2] as the substrate and using the piezoelectric materials as sensors or actuators.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric Analysis for Active Control of Piezoelectric Functionally Graded Plates in Thermal Environment

Liu

Jiang

et al. 2021

Shock and Vibration

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An isogeometric analysis (IGA) method is proposed for investigating the active shape and vibration control of functionally graded plates (FGPs) with surface-bonded piezoelectric materials in a thermal environment. A simple first-order shear deformation theory (S-FSDT) with four variables is used to describe the displacement field of the plates. To ensure the investigation of smart piezoelectric structure in the thermal environment closer to the actual situation, a modified piezoelectric constitutive equation with consideration of the temperature effect of dielectric and piezoelectric strain coefficients is implemented to replace the traditional linear piezoelectric constitutive equation. Meanwhile, the neutral surface is adopted to avoid the stretching-bending coupling. The accuracy and effectiveness of the proposed S-FSDT-based IGA method are verified by comparing with several existing numerical examples. Then, the static bending and open-loop control of the plates under mechanical and thermal loads are further studied. Finally, the active control including static bending control and vibration control of piezoelectric functionally graded plates (PFGPs) is also investigated by using a displacement-velocity feedback control law.

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“…18 The nonlinear transverse vibration of an arbitrary angle-ply laminated composite piezoelectric cantilever rectangular plate under combined external and parametric excitations by using numerical simulations is studied by Zhang et al. 19 Recently, Keshtegar et al. 20 presented vibration responses of a piezoelectric nanocomposite sandwich structure resting on Kerr foundation.…”

Section: Introductionmentioning

confidence: 99%

Two-frequency parametric excitation and combination resonance of a nanocomposite laminated piezoelectric trapezoidal plate in subsonic airflow

Noroozi

Bakhtiari-Nejad

Dardel

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this study, an analytical approach is presented to analyze the bifurcations and nonlinear dynamics of a cantilevered piezoelectric nanocomposite trapezoidal actuator subjected to two-frequency parametric excitations in the presence of subsonic airflow. The assumption of uniformly distributed single-walled carbon nanotubes along the thickness is taken into the consideration. The governing equations are built by the von-Karman nonlinear strain-displacement relations to consider the geometrical nonlinearity and the linear potential flow theory. The present study focuses on a specific resonance case deals with the occurrence of simultaneous resonances in the principal parametric resonance of the first mode and combination of the parametric resonance of the difference type involving two modes. The multiple scales method is employed to obtain the four nonlinear averaged equations which are solved by using the Runge-Kutta method. Moreover, the frequency-response curves, bifurcation diagrams, time history responses, and phase portrait are obtained to find the nonlinear dynamic responses of the plate. The effects of the amplitude of piezoelectric excitation, piezoelectric detuning parameter, and aerodynamic pressure are also studied. The results indicate that, the chaotic, quasi-periodic and periodic motions of the plate exist under certain conditions and the variation of controlling parameters can change the form of motions of the nanocomposite piezoelectric trapezoidal thin plate.

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Nonlinear transverse vibrations of angle-ply laminated composite piezoelectric cantilever plate with four-modes subjected to in-plane and out-of-plane excitations

Cited by 25 publications

References 56 publications

Non-linear response and buckling of imperfect laminated composite plates under in-plane pulse forces

Non-linear response and buckling of imperfect laminated composite plates under in-plane pulse forces

Isogeometric Analysis for Active Control of Piezoelectric Functionally Graded Plates in Thermal Environment

Two-frequency parametric excitation and combination resonance of a nanocomposite laminated piezoelectric trapezoidal plate in subsonic airflow

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