Vibration monitoring of cylindrical shells using piezoelectric sensors

From linear vibration theory for beams and plates, one can express the response as a linear combination of its natural modes. For beams, these eigenfunctions can be shown to be mutually orthogonal for any boundary conditions. For plates, orthogonality of the modes is not guaranteed, but can be proven for various boundary conditions. Modal analysis for beams and plates allows the system response to be broken down into simpler vibration models, due to the orthogonality of the modes. Here the modal analysis approach is extended to the vibration of thin cylindrical shells. The longitudinal, radial, and circumferential displacements are coupled with each other, due to Poisson's ratio and the curvature of the shell. As will be shown, the mode shapes can be solved analytically with numerically determined coefficients. The immediate application of this work will be for modal sensing of cylindrical shell vibrations using thin piezoelectric films.