An asymptotically exact theory of functionally graded piezoelectric shells

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.Comment: 42 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1606.0217