Stability results for piezoelectric beams with long‐range memory effects in the boundary

Abstract

AbstractIn this paper, a piezoelectric beam is investigated under fully‐dynamic magnetic effects and long‐range dielectric and strain memories. The mathematical model under consideration is for the type of piezoelectric beams which strongly couple the electromagnetic effects with mechanical vibrations. This particular model is highly preferred for complex systems for which the vibrational profile is under the strong influence of the electromagnetic interactions. By a careful analysis, an optimal energy decay result is explicitly established under a wide class of kernel functions of the memory terms. The results are based on the multipliers technique. These results are compared to the widely‐used electrostatic/quasi‐static models which entirely exclude magnetic effects.