Decay of the timoshenko beam with thermal effect and memory boundary conditions

In this paper, we study the general decay of solutions for a Timoshenko beam with thermal effect and memory conditions working at the boundary. We show that the dissipation produced by the memory effect is independent of the present values of temperature gradient, and is sufficiently strong to produce a general decay result obtained without imposing the condition of equal-speed propagation. The usual exponential and polynomial decay rate are only special cases of the obtained result. This result improves earlier one in the literature on the stability of Timoshenko beam with or without thermal effect obtained under the condition of equal-speed propagation.