Dynamics of inhomogeneous elastic half-space under moving load

¹ Department of Theoretical and Constructional Mechanics, Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, 39 KoriNiyoziy str., Tashkent 100000, Uzbekistan
² Department of Building Mechanics and Seismic Resistance of Structures, Tashkent Institute of Architecture and Construction, 13 Navoi str., Tashkent 100000, Uzbekistan

^* Corresponding author: bakhtiyor.yuldashev@bk.ru

Abstract

Wave processes in an elastic half-space covered with an elastic layer and (or) a thin elastic plate are considered in the paper. External load moves along the free surface. In the stationary statement, the waveguide properties of the system are determined. The multiple roots of the dispersion equations are revealed and the critical load velocities, leading to the initiation of resonant processes, are determined. In the case when the load moves with the velocity of the Rayleigh wave, additional resonances determined by the structure can be realized in the structure under consideration. It is revealed that Rayleigh resonance exists for long waves only. Numerical solutions are obtained that make it possible to trace the development of resonant excitations. The models of simple structures that have dispersive properties in the medium wave zone are analyzed, such as a thin plate on an elastic base; a model with an attached inertial medium. Analytical solutions have been obtained for these models. Computer simulations conducted simultaneously allow us to analyze the quantitative features of process throughout the entire time period of the load effect. The numerical and asymptotic solutions are compared.