Abstract:
Modal impedances are found by solving the equations of motion of a thin spherical shell in terms of nonaxisymmetric modes of vibration. These mechanical impedances relate the modal expansion coefficients of the applied force per unit area and the velocity of the shell. The application and interpretation of these modal impedances require an awareness of the lack of orthogonality of certain modes. In proper combinations, the modal impedances in the nonaxisymmetric case are found to be identical to known modal impedances in the axisymmetric case. The analysis is restricted to extensional effects of a thin shell with radial forcing. An application of the modal impedances is given in the prediction of the radiation pattern of a three-dimensional array of closely spaced interacting spherical shells.