The dynamic wave coefficient

Seismic calculations nowadays are carried out without accounting for the wave nature of the problem. All the seismic wave energy is assumed to be transmitted to the structure, but the wave part is reflected. The oscillating structure, in turn, affects the soil and gives back some of the energy to the soil. Thus failure to the wave nature of the problem results in to the excess of the calculated seismic loads over the real loads. Moreover, the magnitude of this excess is unknown. The paper presents a solution of the wave effects determining problem. To account for the wave effects the system consisting of the soil seismic vibrations wave equation and the structure vibrations equation is solved. Thus, the task seems to be very difficult. The purpose of the work is to develop and analyze compact exact solutions of the above task, since compact exact solutions can be put into practice of engineering calculations. In the works of well-known authors an exact solution of the system of equations consisting of a wave equation describing the joint longitudinal seismic vibrations of the earth's crust and the equation of oscillation of the structure in the form of a point insert was obtained. But the numerical calculations for the exact solution were not carried out. The abstract solution analytical calculation from the work [1] for a concrete initial form of a seismic wave was carried out in this paper. The initial seismic wave is selected in the truncated harmonic function form. This choice allowed to derive a new coefficient – a dynamic wave coefficient. Numerical calculation of the wave dynamic coefficient showed that the classical non-wave methods for calculating seismic forces give overstated assessment. The dynamic coefficient depends on the properties of the soil. In general, it also depends on the material of which the structure is made. For example, if the soil passes only high frequency seismic vibrations, it may be useful to select new materials to create a low frequency structure. But the exact solution of the wave seismic stability problem is difficult even in the initial formulation. Therefore, in the present work a detailed analysis of the obtained exact solution was carried out.