Development of analytical and FEM solutions for static and dynamic analysis of smart piezoelectric laminated composite plates on elastic foundation

Abstract

This paper proposes new analytical and finite element solutions for studying the effects of elastic foundations on the uncontrolled and controlled static and vibration responses of smart multi-layered laminated composite plates with integrated piezoelectric layers, acting as actuators and sensors. A non-polynomial higher-order plate theory with zigzag kinematics involving a trigonometric function and a local segmented zigzag function is adopted for the first time for modeling the deformation of a smart piezoelectric laminated composite plate supported on an elastic foundation. This model has only five independent primary variables like that of the first-order shear deformation theory, yet it considers the realistic parabolic behavior of the transverse shear stresses across the thickness of the laminated composites plates, and also maintains the continuity conditions of transverse shear stresses at the interfaces of the laminated plates. A two-parameter foundation model, namely Pasternak’s foundation, is used to model the deformation and shear interactions of the elastic foundation. The governing set of equations is derived by implementing Hamilton’s principle and variational calculus. Two different solution methods, namely, a generalized closed-form analytical solution of Navier-type, and a C0 isoparametric finite element (FE) formulation, are developed for solving the governing set of equations. The solutions in the time domain are obtained with Newmark’s average acceleration method. Comprehensive parametric studies are presented to investigate the influence of elastic foundation parameters, piezoelectric layers, loading, and boundary conditions on the static and dynamic responses of the smart composite plates with piezoelectric layers. The effects of the elastic foundations on the vibration control of the smart composite plates are also presented by coupling the piezoelectric actuator and sensor with a feedback controller. Several benchmark results are presented to show the influence of the various material and geometrical parameters on the controlled and uncontrolled responses of the smart plates, and also the significant effect of the elastic foundations on the static and dynamic responses of the smart structures. The results obtained are in very good agreement with the available literature, and it can be concluded that the proposed analytical solution and FE formulation can be efficiently used to model the static and dynamic electro-elastic behavior of smart laminated plates supported on elastic foundations.

Analysis of Laminated Composite Porous Plate under Sinusoidal Load with Various Boundary Conditions

“…Table 1 shows the results of the validation study; the obtained results are compared with those obtained by (Sheikh and Chakrabarti [35], Reddy [36], and Pagano [37]) due to the applied sinusoidal load. Using a three-layer laminated plate with a thickness ratio of 10 to 100, deflection and stresses are examined.…”

“…Algül and Oktem [35] examined the flexural analysis of symmetric and antisymmetric laminated plates using a double Fourier series. Chanda et al [36] studied the static and dynamic behavior of a multilayered smart piezoelectric plate resting on an elastic base. Assie et al [37] developed a mathematical model for the static analysis of a bi-directional pervious plate resting on elastic foundation, with the help of an efficient mathematical approach including a differential integral quadrature technique.…”

Analysis of Laminated Composite Plates: A Comprehensive Bibliometric Review

“…The SSM technique provides a new analytical solution to the buckling response of thin rectangular plates. Chanda et al [197] presented a non-polynomial, higher-order plate theory with zigzag kinematics, involving a trigonometric function and a local segmented zigzag function, for modeling the deformation of a smart piezoelectric laminated composite plate supported on an elastic foundation. This model has only five independent primary variables, like that of the FSDT, yet it considers the realistic parabolic behavior of the transverse shear stresses across the thickness of the laminated composites plates and also maintains the continuity conditions of transverse shear stresses at the interfaces of the laminated plates.…”

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

“…In this context many authors shows interested in implementing analytical solution for analyzing FV behavior of CPs. Chanda et al [281] accomplished an analytical study and FEM solutions to investigate the impact of EL on the controlled and uncontrolled FV, forced vibration, and static responses of smart multi-layered laminated composite (SMLLC) plates by implementing the non-polynomial HZZPT kinematics as well as HP for driving the GE. The GEs were solved by NvS and C 0 isoparametric finite element (IFE).…”