Partitioned schemes of the finite-element method for dynamic problems of acoustoelectroelasticity

A number of schemes which use partitioned forms of the matrices of the finite-element method are proposed for dynamic problems of acoustoelectric elasticity. The features of the solution, specific for electroelasticity, of generalized eigenvalue problems for large sparse matrices, and also of the realization of the method of expansion in eigenforms in harmonic non-stationary problems are pointed out. An explicit-implicit scheme for the integration with respect to time of the equations of the finite-element method of non-stationary acoustoelectroelasticity is proposed and discussed. Approaches to analysing pyroelectric devices at low modulation frequencies are indicated. The ARPACK software packages for solving eigenvalue problems are integrated into the ACELAN specialized finite-element system, for which corresponding partitioned algorithms are realized. Numerical experiments are presented on determining the first eigenfrequencies and forms of the oscillations of an axisymmetric composite piezoelectric radiator in ACELAN and in the well-known ANSYS finite-element software package. The method of expansion in eigenforms in illustrated by the analysis of a longitudinal-longitudinal piezoelectric transformer.