The Stability Condition and Energy Estimate for Nonstationary Problems of Coupled Electroelasticity

Abstract

In this article, a coupled problem of dynamic electroelasticity is investigated using the variational approach and the concept of generalized solutions. The author derives a numerical procedure directly from the definition of the generalized solution of the problem and proves the convergence of the numer- ical scheme (with the second order in space-time) to the solution of the original problem from a class of generalized solutions. The stability condition is obtained from an energy estimate. It is shown that such a condition is the Courant-Friederichs-Lewy-type stability condition, being dependant of the velocity mixed electroelastic waves. Coupling effects are discussed with a numerical example.