Свободные колебания осциллятора линейно-переменной массы с сухим трением

Abstract

Модернизированным методом энергетического баланса выведены приближенные формулы для расчета амплитуд малых затухающих колебаний осциллятора переменной массы при действии силы сухого трения. Рассмотрены варианты колебаний при постоянном значении силы трения и переменном, когда сила трения пропорционально массе осциллятора. Проведено сравнение численных результатов, к которым приводят полученные формулы и известные более точные решения. Показано, что выведенные компактные приближенные формулы имеют хорошую точность и удобны для инженерных расчетов.

In this paper was carried out a brief overview of the current state of the problem and analysis of publications on it. The aim of this article is to adapt the method to calculate the energy balance oscillators with variable mass under the action of dry friction force. First we considered the problem of the oscillator at a constant value of dry friction force. The problem is reduced to the integration of non-linear differential equations with variable coefficients. With the modified method of energy balance were obtained approximate formulas for the calculation of the amplitude and the mass of the oscillator at the end of the k-th magnitude. We also obtain estimates for the limited number of ranges oscillator with variable mass. Exact, but one-sided estimates of scale were constructed by comparing oscillator variable and constant mass. The second was considered problem of the oscillator with a variable frictional force. Here, based on the energy balance method, formulas for calculating the amplitude of the oscillations at the end of the k-th magnitude were obtained. The conditions are investigated under which the process of the oscillator are complete. The work carried out numerical calculations in which a comparison of oscillation amplitudes obtained by the method of energy balance and the WBK method. A good agreement between the values in the amplitude calculated in different ways. Review the adequacy of two-sided estimates for the number of oscillation amplitudes. Also was compared the values of the amplitudes obtained by approximate formulas with the results of numerical integration of initial differential equations. Calculations were confirmed that received an upgraded energy method are quite suitable formula for calculating the amplitude damped oscillator linearly variable mass under the action of dry friction force.