Dispersion relations and mode shapes for waves in laminated viscoelastic composites by variational methods

Generalized Spatial Aliasing Solution for the Dispersion Analysis of Infinitely Periodic Multilayered Composites Using the Finite Element Method

“…In order to overcome the challenges in the analytical investigations, researchers have been employing various numerical techniques such as continuum power series method [24,25], the effective stiffness method [26,27], the mixture theory [28][29][30], the plane wave expansion method [31], the finite difference method [32], the variational method [33,34], and the finite element (FE) method [35][36][37][38][39]. In particular, the FE method offers a remarkable framework to efficiently investigate the effect of material and geometric nonlinearity on phononic dispersion relations [38,[40][41][42][43], which can be hardly done using other numerical techniques.…”

Harmonic wave propagation in an infinite viscoelastic medium with a periodic array of cylindrical elastic fibers

“…Demiray and Eringen [6] developed a two-dimensional lattice dynamics model to study harmonic wave propagation in a fibrous material, in which they assumed that the viscoelastic matrix carries the shear and the fibers carry the tensile forces. Mukherjee and Lee [7,8] used finite difference and variational methods to examine one-dimensional wave propagation in a viscoelastic laminated composite. Sutherland [9] presented some experimental studies on dispersion in fiber reinforced viscoelastic materials.…”