Laminated Timoshenko beams with interfacial slip and infinite memories

TL;DR

This paper investigates the mathematical well-posedness and stability of laminated Timoshenko beams with interfacial slip and infinite memory effects, providing conditions for solution existence, uniqueness, and decay rates.

Contribution

It establishes the well-posedness and stability of the system with a broad class of kernels, including decay rates, without parameter restrictions.

Findings

Unique solutions with regularity properties

Solutions decay to zero at infinity

Decay rate depends on kernel growth

Abstract

We study in this paper the well-posedness and stability of three structures with interfacial slip and two infinite memories effective on the transverse displacement and the rotation angle. We consider a large class of kernels and prove that the system has a unique solution satisfying some regularity properties. Moreover, without restrictions on the values of the parameters, we show that the solution goes to zero at infinity and give an information on its speed of convergence in terms of the growth of kernels at infinity. A numerical analysis of the obtained theoretical results will be also given.