摘要
当振动系统的参振质量随时间变化时,该系统即为变质量振动系统。采用改进的多尺度方法对变质量振动系统进行近似解析求解,并与四阶Runge-Kutta数值法进行比较,两种方法解得的振动响应一致。由计算结果可知,变质量振动系统的响应具有周期性;参振质量的时变方程中幅值变化系数ε的不同只影响系统振幅的大小,而不改变系统振动响应的周期。ε越大,系统响应的突变性越强;ε越小,振动响应越趋于平稳。
An analytical solution method for solving a nonlinear differential equation with periodically time-varying parameters was developed.The results obtained by the analytical solution are in good agreement with those calculated by Runge-Kutta method of fourth-order,illustrating that the modified multiple scales method is an efficient method.Analyzing the solution,it is shown that the response of the system with time-varying mass is periodic.The variation coefficientεof time-varying mass just relates to the amplitude of the vibration response and is unrelated to the period of vibration system. The amplitude of the response changes much more rapidly as the value ofεincreases.That is,the value of e is smaller, the tendency of the time-response curves is more stable.
出处
《振动与冲击》
EI
CSCD
北大核心
2008年第11期160-162,167,共4页
Journal of Vibration and Shock
基金
国家自然科学基金资助项目(编号:50375100)
关键词
振动
质量时变性
参数激振
多尺度法
vibration
time-varying mass
parametric excitation
multiscale method
