Analysis of the interaction of finite-dimensional surface vibrators with a compacted linear-viscous-elastic medium

Abstract

This paper develops an approach to solving problems about the excitation of vibrations/vibrations by sources of waves in linear-viscous-elastic media modeling compacted concrete/building mixtures with depth-variable mechanical characteristics. An analysis of contact stresses and forces occurring under the oscillating stamp, the types of waves generated in the medium and on its surface, and the energy carried by each type of wave for different vibration sources are discussed. The previously described but unspecified for such problems, phenomena of resonance in deep layers of the medium of great thickness and the eigenmovement of the vibration stamps themselves are proposed. We present the technique of reducing the problem of dynamic interaction of finite-dimensional surface vibrosources with compacted linear-viscous-elastic medium to the possible ways of its solution. It is important to comprehensively investigate the peculiarities of vibrations of the stamp-elastic/linear-viscous-elastic medium system, but the integral equations arising here are a serious obstacle to research. Attempts to circumvent these difficulties give rise to a number of approximate, "engineering" approaches, within which the response of the medium (compacted by the vibrating field of the concrete/concrete mixture) is modeled by elastic and viscoelastic (damping) links with some "attached mass". The characteristics of elastic elements and the value of the attached mass are selected, as a rule, from experimental data. The oscillations of the finite-dimensional system resulting from this approach are determined by the usual theoretical methods of mechanics. Such an approach is especially widely used in construction calculations. It gives the possibility to determine the static settlement of structures with a sufficient accuracy and provides satisfactory results at a certain, fixed frequency. When analyzing vibrations in a wide range of frequencies, the linear-viscous-elastic medium is substantially infinitely measurable system with its own resonances and complex dispersion properties, and therefore cannot be approximated by a finite set of springs. In order to identify the characteristic features of the dynamics of massive stamps on a linear viscoelastic basis in this paper we carried out: calculations using methods of solving integral equations; analysis of numerical results and identified qualitative effects.