Oscillations of a rod carrying a small attached mass


DOI: 10.34759/trd-2020-110-2

Аuthors

Dobryshkin A. Y.

Komsomolsk-na-Amure State University, 27, Lenina str., Komsomolsk-on-Amur, 681013, Russia

e-mail: wwwartem21@mail.ru

Abstract

In this paper, the oscillation of a rod carrying a small attached mass in a nonlinear setting is considered. The basis for the development of a new mathematical model is the general equation of oscillations. The mounting location and the influence of the small attached mass on the frequency characteristics of the natural frequency are taken into account. The first and second eigenfrequency characteristics of the oscillations of the rod carrying the attached mass are determined. It is also determined that the presence of a small attached mass is a factor that triggers the interaction of internal forms of vibration, which can lead the structure to a state of resonance. The obtained values of the wave-forming parameter above zero refer to the solid, and below zero to the weak parameter of the damping force. The presence of several components of the internal oscillatory process is a feature of the system in which the splitting of the frequency spectrum is possible. The small attached mass is one of the inclusions that deviate from the ideal mechanism of harmonic vibrations. The solution of an infinite system of nonlinear algebraic equations uses a new asymptotic approach based on the introduction of an artificial small parameter μ. The case when the system is close to the state of internal resonance is considered. As a result of the study, it was found that the mathematical model specified in the course of the study is better than the existing ones and is consistent with the available data.

Keywords:

rod, vibrations, small attached mass

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