变质量系统振动分析的两种方法

变质量系统振动特性研究对于航天航空工程具有重要的意义.根据虚位移原理和动量守恒定理,推导了一般变质量动力学系统的变系数控制微分方程,分析了质量变化对系统动特性的影响,给出了适用于变质量系统的改进欧拉中点辛差分格式和模态叠加方法.针对变质量质点、变质量拉压杆和变质量欧拉梁系统,用这两种方法对其动态响应进行了模拟.两种方法数值结果的高度一致性,初步证明了两种方法对于变质量系统振动分析的正确性和有效性.

Two methods for vibration analysis of variable-mass systems

The vibration analysis of variable-mass systems is of great importance in astronautics and aeronautics. The dynamical governing equation of a general variable-mass system was obtained by using the virtual displacement principle in conjunction with the conservation law of momentum, and the effects of mass variation on the dynamic properties of system were also investigated. A modified Euler symplectic midpoint difference method and a modified mode superposition method were proposed and used to solve the equation of variable-mass systems. Regarded as typical variable-mass systems, the variable-mass single particle system, the variable-mass rod and the variable-mass Euler-Bernoulli beam were studied, the numerical results of the proposed two methods agree well. This validates the correctness and feasibility of the developed two methods.