Eigenfunction analysis of radially polarized piezoelectric cylindrical shells of finite length

Abstract

An eigenfunction approach is presented to determine the response of radially polarized piezoelectric cylindrical shells of finite length to electrical excitation. The equations of motion of the piezoelectric cylinder are first derived by using the membrane approximation. Then they are solved by expressing the displacement distribution as the sum of the static solution and a weighted sum of a complete set of functions—the eigenfunctions of the short-circuited cylinder. The static solution is necessary to exactly satisfy the boundary conditions of the electrically excited cylinder. Moreover, in some cases, the series solution does not converge to the correct displacement distribution when some other terms, instead of the static solution, are used to satisfy the boundary conditions. The weights or displacement coefficients are determined by using the orthogonal property of the eigenfunctions. Finally, the input electrical admittance is determined by using the equation of state and the displacement distribution. Analyses of cylinders with various boundary conditions are presented to illustrate the approach. Numerical results are used to show that the series solutions converge very rapidly to the closed form solutions.