Finite element analysis of smart composite plate structures coupled with piezoelectric materials: Investigation of static and vibration responses

Abstract

This research presents a generalized-energy-based finite element modeling of smart composite plates with distributed piezoelectric materials for the static and vibration responses under electrical and mechanical loading. The zigzag kinematics in conjunction with a non-polynomial higher-order shear deformation theory is used to derive the model. The plate theory accounts for the non-linear variations of the transverse shear strains across the thickness of the plates and also accommodates the inter-laminar continuity effects of transverse shear stresses at the interfaces. Eight noded isoparametric serendipity elements are used to discretize the physical domain. The solutions in the time domain are obtained from the discretized system of ordinary differential equations with Newmark’s time integration scheme. Several numerical examples are solved for different types of smart composite plates with various piezoelectric materials, boundary conditions, static and dynamic loadings. The classical negative feedback controller is used for deriving the suppressed and controlled vibration responses of the smart composite plates with distributed actuators and sensors. A comparison of the present FE solutions with the elasticity and other analytical and numerical solutions shows good agreement, thereby ensures the applicability of the present finite element model for studying the coupled electromechanical problems of piezoelectricity.

Keywords:

• Finite element method
• smart composites
• piezoelectric materials
• non-polynomial higher-order theory
• Newmark’s time integration
• static
• vibration control

Acknowledgment

The support of Science and Engineering Research Board (SERB), Department of Science and Technology (DST), India under grant no. ECR/2016/001926 is acknowledged.