Exact piezoelastic solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending

Abstract

This work presents an exact piezoelastic solution of an infinitely long, simply-supported, orthotropic, piezoelectric, radially polarised, circular cylindrical shell panel in cylindrical bending under pressure and electrostatic excitation. The general solution of the governing differential equations is obtained by separation of variables. The displacements and electric potential are expanded in appropriate trigonometric Fourier series in the circumferential coordinate to satisfy the boundary conditions at the simply-supported longitudinal edges. The governing equations reduce to Euler Cauchy type of ordinary differential equations. Their general solution involves six constants for each Fourier component. These are solved from the algebraic equations obtained by satisfying the boundary conditions at the lateral surfaces. The solution of the inverse problem of inferring the applied pressure field from the given measured distribution of electrical potential difference between the lateral surfaces of the shell has also been presented. Numerical results are presented for typical pressure and electrostatic loadings for various values of radius to thickness ratio