Three-dimensional solution for simply-supported piezoelectric cylindrical shell for axisymmetric load

This work presents a three-dimensional solution for simply-supported piezoelectric cylindrical shell subjected to axisymmetric electromechanical load. The variables are expanded in Fourier series to satisfy the boundary conditions at the ends. The solution of the governing differential equations with variable coefficients is constructed as a product of an exponential function and a power series in the thickness coordinate. The coefficients of terms of all degrees in the governing equations are set to zero. This yields a linear eigenvalue problem for the exponent and recursive relations for the coefficients of the power series. The arbitrary constants in the general solution are determined from the boundary conditions. The solution of the inverse problem of inferring the applied pressure field from the measured electrical potential difference between the surfaces of the shell is also presented. Numerical results are presented showing the effect of nature of loading and the geometrical parameters on the response. These results would enable development and assessment of two-dimensional piezoelastic shell theories.