British Columbia Institute of Technology
Burnaby, British Columbia, Canada
The investigated problem belongs to Solid Deformable Body mechanics' field and is described by a mathematical model of a real phenomenon, such as an earthquake. Different analytical methods and also the method of Factorization were applied to solve similar problems with mixed boundary conditions.
The crux of these problems is the necessity to consider the integral equations, which have kernels possessive oscillations and particular behavior. In addition, semi-limited continuum requires the correct definition at the infinity.
The similar problems with mixed boundary conditions in the strict mathematical description and the proof of only-one-solution existing were presented in the papers of well-known scientists, such as: Academicians I. I. Vorovich, V. A. Babeshko, Professors Seymov, V. A. Alexandrov, and others.
In the present paper the distribution of contact stresses on the boundary ``fluid - elastic semispace'' is investigated.
A limited fluid volume is located on the elastic semispace boundary. A time-periodical force is acting in a remote point of the boundary. It is necessary to investigate the force influence on the distribution of contact stresses under the fluid volume.
The problem is described by a mathematical model where the fluid is considered ideal and compressive. Displacements of elastic continuum points are given by differential equations of Theory of Elasticity - Lame Equations, displacements of fluid volume - by the Wave Equation. Thus there are two problems - for both the elastic semispace and the fluid volume.
Using the equation that states vertical components of speed for the elastic semispace and the fluid are equaled at the contact area, we have Fredgolm Integral Equation of 1 type, depending on the pressure at the contact area. The special method combining two methods: one of them is to obtain to the system of functional equations, another is to solve the system using the factorization method.
The contact pressure function is investigated under different parameters.
Based on the numerical results, conclusions are made.