Harmonic Bursts in Weakly Inhomogeneous Material

Wave motion in a material with weak spacial inhomogeneities described by the nonlinear Murnaghan-type theory of elasticity is studied theoretically. In one-dimensional setting for longitudinal waves a harmonic excitation of finite length and ultrasonic frequency is allowed to propagate through the material and reflect back from a free end. The governing equation of motion is solved making use of the perturbation method and analytical solutions up to the second order are considered. The effects of nonlinearity and inhomogeneity on the wave motion are analysed. These effects permit to clarify the influence of space-dependent material density and elastic properties on the wave motion.