变质量振动系统的求解与分析

对变质量碰撞振动系统进行求解分析,研究系统参振质量变化时对系统动力学的影响.采用渐近法对变质量振动方程进行近似解析求解,并运用龙哥库塔法进行数值计算.结果表明,渐近解析法与数值法响应一致,渐近法对于解非线性系统动力行为是有效的;且由计算结果可知,变质量会使系统响应产生一定的突变.振动方程中的参振质量变化系数和质量变化频率分别影响系统突变的振幅和周期.当参振质量变化系数为零时,系统响应平稳;该系数越大,系统响应的突变振幅也越大.激振频率与质量变化频率比值越大,响应突变的周期越大.

Solution and Analysis of Vibration System with Variable Mass

The solution and analysis of a collision vibration system with variable mass were focused and the influence of vibration mass varying with time on the dynamic behaviors of the collision vibration system was discussed.The asymptotic method was used to solve the vibration equations with variable mass,and the method of Runge Kutta was used for numerical calculation.The results show that the responses calculated by the analytical method and the numerical method are in consistency and the asymptotic method is effective for the solution of the dynamic behaviors of nonlinear systems.The calculation also shows that variable mass will make the system response produce a certain mutation.The variation coefficient and the changing frequency of vibration mass will affect the mutation's period and the amplitude of system respectively.When the variation coefficient is zero,the system response is stationary.The greater the variation coefficient is,the greater the mutation is.The greater the ratio of vibration frequency to mass varying frequency is,the longer the cycle of response mutation is.