Dynamics of a single mass vibrating system impacting into a deformable support

K Ragulskis,L Ragulskis

doi:10.21595/mme.2020.21398

K Ragulskis, L Ragulskis

Open Access

https://doi.org/10.21595/mme.2020.21398

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Abstract

The investigated system comprises a mass attached by a deformable link to a fixed foundation, and an elastic-dissipative limiter of motion of that mass. Such types of systems are widely used in different technological devices and machines. This paper is devoted for the improvement of dynamical qualities of such systems. Free and forced stationary harmonic vibrations as well as the qualitative parameters of motions of the system are analyzed in this paper. Characteristics of vibrations are determined using analytical and numerical techniques. It is determined that for the case of zero fastening the values of eigenfrequencies of the system do not depend on the amplitude of excitation. Then the system has an infinite number of multiple eigenfrequencies. In the case of forced harmonic excitation single valued stable motions exist in the vicinity of the resonance. This gives rise to some qualities of the system which are useful in practical applications.

Highlights

This paper is focused on a nonlinear system which is characterized by two following features: first – the values of eigenfrequencies do not depent on the amplitude of excitation, and the second – an infinite number of eigenfrequencies does exist
The dynamics of such kind of systems has not been investigated in the existing literature
Nonlinear vibro-impact systems may have a number of various regimes of motion in steady state regimes under harmonic excitation

Summary

Introduction

This paper is focused on a nonlinear system which is characterized by two following features: first – the values of eigenfrequencies do not depent on the amplitude of excitation, and the second – an infinite number of eigenfrequencies does exist The dynamics of such kind of systems has not been investigated in the existing literature. Nonlinear systems, two-dimensional transmissions, their dynamics and vibrations are analysed in [1]. Resonances in nonlinear vibrating systems are investigated in [3]. DYNAMICS OF A SINGLE MASS VIBRATING SYSTEM IMPACTING INTO A DEFORMABLE SUPPORT. 2. Free damped vibrations, that is when xs = f = 0 Case x = x , that is according to Eq (1) it is assumed that this takes place in the interval:. (2) and (5) are valid: into Eq (2) solutions Eqs.

Vibrations of the conservative system

Numerical investigation of the damped system

Numerical investigation of the conservative system

Conclusions