Exact piezothermoelastic solution of simply-supported orthotropic flat panel in cylindrical bending

Abstract

Exact piezothermoelastic solution is presented for infinitely long, simply-supported, orthotropic, piezoelectric, flat panel in cylindrical bending under pressure, thermal and electrostatic excitation. The displacements, electric potential and temperature are expanded in Fourier series to satisfy the boundary conditions at the longitudinal edges. The governing equations reduce to ordinary differential equations with constant coefficients. The six constants in their general solution for each Fourier component are obtained from the boundary conditions at the lateral surfaces. The solution of the inverse problem of inferring the applied temperature from the measured electrical potential difference between the lateral surfaces of the panel is also presented. Results are presented for sinusoidal thermal and electrostatic loadings and the effect of width to thickness ratio has been investigated.