To the study of the mixed dynamic problems for a limited volume of fluid on an elastic foundation

Abstract

The paper presents the results of analytical studies of the distribution of contact stresses at the interface between a limited pool of liquid and an elastic foundation. A limited amount of an ideal compressible fluid, located on deformable foundation, is considered. An elastic layer and an elastic half-space rigidly coupled with non-deformable base are considered as the latter. In the system “elastic medium - liquid” the oscillations are excited by surface vibrator. The velocity potential that satisfies the wave equation as the characteristic of the wave field in the liquid is being considered. It is assumed that the hydrodynamic pressure on the upper liquid surface is absent. The condition of impermeability is given on vertical borders, on bottom surface the liquid is affected by an elastic foundation. The displacement vector points of the elastic base satisfy the system of Lame differential equations. The interaction of the liquid and elastic medium is determined by the continuity of the vertical speed component in the contact area. It is believed that the system vibrations are of steady character. In this work the integral equation of the first kind with kernel is obtained and solved, depending on both difference and sum of the arguments, the function is also built, that describes the distribution of contact stresses in the area of contact between the liquid and the elastic media with consideration of physical and frequency factors. The relevance of research of dynamic interaction of hydraulic structures with deformable foundation is determined by the high requirements for reliability of their exploitation and the degree of certainty of the forecast of consequences in case of vibroseismic interactions. The results of this study may serve as a foundation for the further development of methods for solving dynamic contact problems of joint oscillations of elastic and liquid mediums.