Random vibrations of a structure modified by damped absorbers

Abstract

Abstract The problem of reducing the level of vibrations in various constructions has been considered for many years. This is an important element of analyzing the technical condition of buildings and the comfort of users. Various ways and means of preventing unacceptable vibrations are known and the search for an optimal absorber is still ongoing. Different kinds of vibration absorbers are applied for reducing the vibration level in various engineering structures. Vibrations caused by traffic do not pose a threat to a structure, but are often a nuisance for people. There is a need to reduce them, especially in cities where there is more traffic. In order to be able to analyze an excited structure, traffic was modeled. A model that is a structure and an absorber system with two degrees of freedom is proposed in the paper. The first eigenfrequency of the structure was included in the analysis. As a result, the authors obtained closed equations of motion. The work examines the problem of the absorber effect on the vibrations of traffic-induced structures. It was assumed that the shocks occurring at random moments, and which form the Poisson process, are determined by random amplitude, a deterministic shape function and two different forms of envelope functions. The problem was discussed in the field of correlation theory and spectral density function. Numerical analysis of the displacement of the two-degree system is considered.