Free-field wave solutions in a half-plane exhibiting a special-type of continuous inhomogeneity

摘要: Abstract This work presents closed-form solutions for free-field motions in a continuously inhomogeneous half-plane that include contributions of incident waves as well reflected from the traction-free horizontal surface. Both pressure and vertically polarized shear are considered. Furthermore, two special types material inhomogeneity studied, namely (a) modulus varies quadratically with respect to depth coordinate (b) one exponentially said coordinate. In all cases, Poisson’s ratio is fixed at one-quarter, while both density profiles vary proportionally. Next, series numerical results serve validate aforementioned models, show differences wave motion patterns developing media compared reference homogeneous background. These clearly influence inhomogeneity, summarized by single parameter, on develop half-plane. It believed this type information useful within context propagation studies non-homogeneous continua, which turn find applications fields diverse laminated composites, geophysical prospecting, oil exploration earthquake engineering.