On the Nonlocal Theory of Wave Propagation in Elastic Plates

TLDR: In this article, the propagation of longitudinal waves in isotropic homogeneous elastic plates is studied in the context of the linear theory of nonlocal continuum mechanics, and the dispersion equation obtained for the plane longitudinal wave in an infinite medium is matched with the parallel equation derived in the theory of atomic lattice dynamics.

Abstract: Propagation of longitudinal waves in isotropic homogeneous elastic plates is studied in the context of the linear theory of nonlocal continuum mechanics. To determine the nonlocal moduli, the dispersion equation obtained for the plane longitudinal waves in an infinite medium is matched with the parallel equation derived in the theory of atomic lattice dynamics. Using the integroalgebraic representation of the stress tensor and the Fourier transform, the system of two coupled differential field equations is solved in the standard manner giving the frequency equations for the symmetric and antisymmetric wave modes. It is found that the short wave speed in the Poisson medium differs by about 13 percent from the speed established in the classical theory. A numerical example is given.