Longitudinal vibrations of a cylindrical bar from the action of harmonic forces

Abdukakhkhar Abduvaliev,Abdulaziz Abdulkhayzoda,D Bazarov

doi:10.1051/e3sconf/202126404091

Abstract

The longitudinal vibration of a cylindrical rod has been studied in an elastic medium from the action of axial harmonic forces in a state of compression tension. The consideration took into account the damping of vibration of the rod according to the theory of E.S. Sorokin. Taking into account, internal friction made it possible to approach the real state of the rod as a source of wave radiation. The amplitude-frequency characteristic of the structure is built, taking into account changes in the parameters of the environment and the rod. The possibilities of the emergence of the resonance state of the rod are established. At the same time, cases were considered with and without inelastic properties of the rod material. The analysis of the influence of the properties of the environment and the rod on the amplitude of the displacement of the latter is carried out.

Highlights

Wave problems are relevant for underground structures, so transverse vibrations of an underground cylindrical structure and vibrations of an elastic half-space with a cylindrical cavity under the action of Rayleigh waves are considered in [1, 2], and the vibrations of a hard disk in elastic space are studied in [3]
Consider the longitudinal vibrations of an extended cylindrical rod located in an elastic space from the action of axial harmonic forces
It is necessary to protect the structure by preventing it from entering the resonance zone

Summary

Introduction

Wave problems are relevant for underground structures, so transverse vibrations of an underground cylindrical structure and vibrations of an elastic half-space with a cylindrical cavity under the action of Rayleigh waves are considered in [1, 2], and the vibrations of a hard disk in elastic space are studied in [3].To reduce the movement of structures, dynamic vibration dampers are used. Wave problems are relevant for underground structures, so transverse vibrations of an underground cylindrical structure and vibrations of an elastic half-space with a cylindrical cavity under the action of Rayleigh waves are considered in [1, 2], and the vibrations of a hard disk in elastic space are studied in [3]. The possibility of damping vibrations of underground pipelines from the action of Rayleigh waves using a single-mass damper and damping of vibrations of an underground structure using a three-mass damper is considered in [4, 5]. Nonlinear vibrations of an axisymmetric body under the action of impulse loads, forced axisymmetric vibrations of a viscoelastic cylindrical shell, natural vibrations of structurally inhomogeneous multiply connected shell structures with viscoelastic elements are considered [12, 13, 14]. The method of compensating loads applied to the problems of equilibrium, vibrations and stability of plates and membranes is presented in [15]

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