Spectral finite-element modeling of the longitudinal wave propagation in rods treated with active constrained layer damping

A spectral finite-element model (SFEM) is developed to describe the propagation of longitudinal waves in rods treated with active constrained layer damping (ACLD) treatments. The model is formulated in the frequency domain using dynamic shape functions that capture the exact displacement distributions of the different ACLD layers. In this manner, a small number of elements is needed to accurately model the wave propagation dynamics, particularly in rods with discontinuities and partial ACLD treatments. Numerical examples are presented to illustrate the accuracy of the SFEM as compared to the exact solutions. Application of the SFEM to beams, plates and shells treated with ACLD treatments is a natural extension of the present work.