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 uncontrolled controlled static vibration responses smart multi-layered laminated composite plates with integrated piezoelectric layers, acting as actuators sensors. A non-polynomial higher-order plate theory zigzag kinematics involving a trigonometric function local segmented is adopted first time modeling deformation supported an foundation. model has only five independent primary variables like that first-order shear theory, yet it considers realistic parabolic behavior transverse stresses across thickness composites plates, also maintains continuity conditions at interfaces plates. two-parameter foundation model, namely Pasternak’s foundation, used to interactions The governing set equations derived by implementing Hamilton’s principle variational calculus. Two different solution methods, namely, generalized closed-form Navier-type, C 0 isoparametric (FE) formulation, are developed solving equations. in domain obtained Newmark’s average acceleration method. Comprehensive parametric studies presented investigate influence parameters, loading, boundary dynamic layers. control coupling actuator sensor feedback controller. Several benchmark results show various material geometrical parameters significant effect structures. very good agreement available literature, can be concluded proposed FE formulation efficiently electro-elastic foundations.