An asymptotically exact theory of smart sandwich shells

TL;DR

This paper develops an asymptotically precise two-dimensional elastic-piezoceramic sandwich shell theory using variational-asymptotic methods, including error estimation and an analytical solution for vibration problems.

Contribution

It introduces a new asymptotic shell theory with rigorous error bounds and applies it to solve vibration issues in piezoceramic-covered elastic plates.

Findings

The theory provides accurate predictions with quantified error margins.

An analytical solution for forced vibrations of piezoceramic-covered plates is derived.

The approach enhances understanding of piezoceramic shell behavior.

Abstract

An asymptotically exact two-dimensional theory of elastic-piezoceramic sandwich 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 circular elastic plate partially covered by two piezoceramic patches with thickness polarization excited by a harmonic voltage is found.