On the Wave Propagation in Elastic Multilayer Periodic Media With Nonlocal Interactions

Abstract

After a brief review of the main concepts of the nonlocal theory of elasticity, the equations of the nonlocal elastic moduli are derived, and the constitutive equations of the nonlocal medium established. Propagation of a longitudinal time-periodic wave normal to the laminae of the layered medium is then analyzed, and the equation of the wave dispersion determined. The dispersion originates from two sources: the configuration (discreteness) of the structure, and the nonlocal constitution of the material of the laminae. A numerical example accompanied by a graph illustrates the dependence of the effective wave velocity on the wave number in the entire Brillouin zone. It is found that for very short waves the wave velocity decreases to about 64 percent of its conventional value established for waves of long wavelength.