Exact solution of the problem of acoustics in an arbitrary multilayer medium during contact interaction with a wedge shaped stamp

This paper is the first to study the behavior of the exact solution of the contact problem for a wedge-shaped stamp in terms of shape in an anisotropic layered medium. We consider the contact problem of the action of a wedge-shaped, right-angled, rigid stamp on the surface of a multilayer anisotropic medium. The case of a sharp-angled stamp in terms of some transformation is reduced to the one under consideration. The stamp is assumed to act on a multilayer medium without friction. There may be cases of static and dynamic effects caused by harmonic oscillations of the stamp. The main attention is paid to analyzing the surface behavior of an anisotropic layered medium outside the contact zone. Formulas describing the behavior of the surface in the far zone are constructed and an example of calculating the necessary parameters for their application is given. The considered mixed problem is reduced to solving the two-dimensional Wiener - Hopf integral equation, the Fourier transform of the kernel of which represents the ratio of two analytical functions. The isotropic case of the presence of the ratio of two integer functions in the representation of the kernel has recently been investigated by a universal modeling method, which prompted the transition to the little-studied anisotropic case. In spatial contact problems, the study is carried out by numerical methods that are ineffective for anisotropic media. The exact solution could be constructed only in cases of one-dimensional or integral equations reducible to them. Along with static tasks, the method developed in the article allows studying the acoustic properties of the surface outside the contact zone of the stamp with the medium in thedynamic case, which have little-studied specifics of behavior by sectors. The two-dimensional Wiener-Hopf integral equation solved for the first time can be used in problems of radio wave propagations, in the design of the element base of radio electronics, in the problem of strength in mechanics, and in numerous other important areas.