Wave propagation in isotropic elastic bodies

AbstractThis chapter briefly considers wave propagation in isotropic linear elastic solids. During wave propagation inertial effects must be accounted for, which results in the so-called elastodynamic problem. This problem admits plane harmonic waves as an important class of solutions. A plane wave possesses a direction of travel and an amplitude, which gives the magnitude and direction of particle motion, a wave speed, and a wavelength. The wave is called a longitudinal wave if the amplitude is parallel to the direction of propagation, and a shear wave if the amplitude is perpendicular to the travel direction. Longitudinal and shear waves are shown to travel at different speeds that depend on the elastic moduli and the mass density of the material.