Abstract
An assessment of the dynamic behavior of a plane earth structure with account of its foundation is considered in the paper. A structure with a foundation is considered as an inhomogeneous system, the material of its certain parts is considered elastic or viscoelastic. To assess the effect of the foundation on dynamic behavior of the structure, a finite domain is cut from the foundation and conditions are set at the boundary of this domain that provide energy entrainment from the structure to infinity in the form of the Rayleigh wave. To describe the internal dissipation in material, a linearly hereditary theory of viscoelasticity with the Rzhanitsin kernel is used. A mathematical model, method and algorithm have been developed to assess the dynamic behavior of the structure-finite foundation system. To ensure the adequacy of the mathematical model and to assess the accuracy of the calculation, model problems have been solved when describing the process under consideration. Dynamic behavior of inhomogeneous viscoelastic system of earth dam-foundation with non-reflecting boundary conditions on the boundary of the final domain of the foundation is investigated. In the process of studying the dynamic behavior of inhomogeneous viscoelastic “structure-foundation” systems, a number of mechanical effects.
Highlights
When assessing the dynamics of a structure, the effect of earth foundation on the dynamic behaviour of a structure is often not taken into account, despite the fact that the effect of the foundation may in some cases be significant
The tasks of determining the natural frequencies and amplitude-frequency characteristics (AFC) of longitudinal forced oscillations of a viscoelastic rod of finite length with A.R.Rzhanitsin kernel (3) and the oscillations of piecewise homogeneous semi-infinite elastic rod are considered in the paper
Analysis of the results has shown that the presence of an infinite domain in an elastic oscillatory system leads to the occurrence of dissipation related to the wave entrainment of energy
Summary
When assessing the dynamics of a structure, the effect of earth foundation on the dynamic behaviour of a structure is often not taken into account, despite the fact that the effect of the foundation may in some cases be significant. When taking into account the structure-foundation interaction, the Winkler foundation model is used, which, despite its simplicity in calculation, does not take into account a number of physical effects associated with the inertia properties of earth foundation. The final model of the foundation, cut out from the half-space, is widely used to account for the joint operation of a structure-foundation system. On the border of the final domain of the foundation, the conditions are set that ensure energy entrainment from the structure to infinity, i.e. wave entrainment of energy. Many existing models of the “structure-finite foundation” system do not allow one to adequately describe the dynamic process of energy entrainment to infinity
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