In previous work, Lo and Tatar studied the exponential decay for a laminated beam with viscoelastic damping acting on the effective rotation angle in the case of equal-speed wave propagations. In this paper, we continue consideration of the same problem in the case of non-equal wave speeds. In this case, the main difficulty is how to estimate the non-equal speed term. To overcome this difficulty, the second-order energy method introduced in Guesmia and Messaoudi seems to be the best choice for our problem. For a wide class of relaxation functions, we establish the general decay result for the energy without any kind of internal or boundary control.
"General decay for a laminated beam with structural damping and memory: The case of non-equal wave speeds." J. Integral Equations Applications 30 (1) 95 - 116, 2018. https://doi.org/10.1216/JIE-2018-30-1-95