Abstract
In present paper, the problem of the vibration of a viscoelastic dam-plate of a hydro-technical structure is investigated, based on the Kirchhoff-Love hypothesis in the geometrically nonlinear statement. This problem is reduced to a system of nonlinear ordinary integro-differential equations by using the Bubnov-Galerkin method. The resulting system with a weakly-singular Koltunov-Rzhanitsyn kernel is solved using a numerical method based on quadrature formulas. The behavior of the viscoelastic dam-plate of hydro-technical structure is studied for the wide ranges of physical, mechanical, and geometrical material parameters.
Highlights
When solving energy and water management problems in Uzbekistan, one of the main tasks is creating economic and reliable structures of mountain hydro-technical structures, taking into account the fact that the construction site presents a zone of high seismicity
The design of hydro-technical structures subject to potential earthquakes significantly depends on their dynamic characteristics and the vibration processes over time
Hypotheses and linear models of frequency-independent internal friction [1, 2] are widely used to solve the dynamics of structures
Summary
When solving energy and water management problems in Uzbekistan, one of the main tasks is creating economic and reliable structures of mountain hydro-technical structures, taking into account the fact that the construction site presents a zone of high seismicity. The design of hydro-technical structures subject to potential earthquakes significantly depends on their dynamic characteristics and the vibration processes over time. The intensity of structures vibrations under dynamic influences substantially depends on the degree of energy dissipation in them. Theoretical description of the processes of strain during vibrations of rigid bodies and structures, taking into account internal friction, is often limited to studying the general laws of the external manifestation of the dissipation mechanism. Hypotheses and linear models of frequency-independent internal friction [1, 2] are widely used to solve the dynamics of structures. These hypotheses, reflecting the manifestation of elastic imperfections in the materials, do not describe the creep of strains and relaxation of stresses, called “hereditary properties”
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