Spatial forced oscillations of axisymmetric inhomogeneous systems

Mirziyod Mirsaidov,Ismoil Nasirov,Abdurasul Nosirov,A Zheltenkov,A Mottaeva

doi:10.1051/e3sconf/202016402009

Abstract

The aim of this paper is to develop an adequate mathematical model, methods and algorithms for solving three-dimensional problems for axisymmetric spatial inhomogeneous viscoelastic systems (shells, foundations and bases) and to assess the dynamics of protective shell (containment) of a nuclear power plant (NPP) under resonant modes of vibration. The problem is solved using the semi-analytical finite element method. Firstly, the eigenmodes of vibration of the system are determined in an elastic three-dimensional statement, secondly, the solution to the problem of forced vibrations of viscoelastic systems is constructed using the expansion of these eigenmodes of vibration. Viscoelastic properties of the material are described using the hereditary Boltzmann-Volterra theory. The principle of virtual displacements is used to simulate dynamic processes in inhomogeneous viscoelastic systems. The convergence and accuracy of the solutions obtained are investigated by test problems. The frequency response characteristics (FRC) in various points of the NPP containment are estimated at various viscosity parameters of the material. It was revealed that the highest amplitude of vibrations in resonance modes occurs at close values of the frequency of external effect to the first eigen frequencies of the system; in the presence of dense spectra of eigen frequencies of the system, the highest amplitudes can occur at higher frequencies of external effect.

Highlights

IntroductionThe vibration intensity of real structures during earthquakes significantly depends on the degree of energy dissipation in them
High rates of construction, the erection of unique structures and buildings, the need to fulfill complex industrial orders require further development of the theory of calculating spatial axisymmetric structures under the influence of various loads, taking into account inelastic properties of the material.The vibration intensity of real structures during earthquakes significantly depends on the degree of energy dissipation in them
amplitude-frequency characteristics (AFC) is an indicator of how certain points of the structure react to certain effects at certain viscosity parameters under resonant modes of vibration

Summary

Introduction

The vibration intensity of real structures during earthquakes significantly depends on the degree of energy dissipation in them. It can be expected that the higher the energy dissipation in the structure, the less intense the resonant vibrations at a given level of excitation. For a complete assessment of dissipative properties of a structure, it is necessary to study its natural, steady-state and transient structural vibrations, taking into account internal friction in the material. The difficulty of solving this problem is, firstly, due to the lack of models more or less realistically describing the phenomenon of internal friction in the material. Solving the problem with well-known models leads to a number of tasks that are difficult to implement even on modern computers, due to the lack of computational methods and algorithms that meet a number of requirements for the tasks posed

Objectives

Methods

Results

Conclusion