Maysel's formula generalized for piezoelectric vibrations - Application to thin shells of revolution

Either some or each of the layers of a composite shell made of piezoelectric materials behave as distributed actuators so that the shell becomes an intelligent or smart structure. To effectively suppress the vibrations of the shell, an electrical field with a proper control must be applied. The most efficient calculation of thermoelastic deformations is performed by Maysel's formula, i.e., within a multiple-field analysis in the isothermal background. By generalizing Maysel's formula, it becomes possible to include both the piezoelectric effects and inertia. A version is presented that allows the construction of the best auxiliary problem in the background, particularly preserving all kinds of symmetries present in the actual coupled problem. Applications of the three-dimensional formulation are illustrated for the special case of thin-layered shells of revolution, and, in addition, for a circular cylindrical shell with the piezoelectric influence function being presented. Because solutions of the auxiliary problem are more easily obtained in frequency space, the time convolution is replaced by a Fourier integral, which is eventually subjected to fast Fourier transform.