An asymptotically exact theory of functionally graded piezoelectric shells

TL;DR

This paper develops a precise two-dimensional theoretical model for functionally graded piezoelectric shells using variational-asymptotic methods, including error estimation and an analytical solution for forced vibrations.

Contribution

It introduces an asymptotically exact 2D theory for functionally graded piezoelectric shells with error bounds and applies it to solve vibration problems analytically.

Findings

The theory provides accurate error estimates in the energetic norm.

An analytical solution for forced vibrations of piezoceramic shells is derived.

The model enhances understanding of piezoelectric shell behavior under harmonic excitation.

Abstract

An asymptotically exact two-dimensional theory of functionally graded piezoelectric shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a functionally graded piezoceramic cylindrical shell with thickness polarization fully covered by electrodes and excited by a harmonic voltage is found.