Exact piezothermoelastic axisymmetric solution of a finite transversely isotropic cylindrical shell

Abstract

This work presents an exact piezothermoelastic solution of a finite transversely isotropic piezoelectric cylindrical shell under axisymmetric thermal, pressure and electrostatic excitation. The general solution of the governing equations is obtained in terms of potential functions which satisfy the boundary conditions at the ends. The axisymmetric loadings are expanded as a Fourier series in the axial coordinate. The coefficients in the infinite set of potential functions are obtained by solving sets of six algebraic equations resulting from the satisfaction of boundary conditions at the inner and outer surfaces of the shell for each Fourier component. The inverse problem of inferring the applied temperature and pressure fields from the given measured distribution of electrical potential difference between the inner and outer surfaces of the shell has also been solved. Numerical results are presented for typical pressure, thermal and electrostatic loadings.