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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.
The study on vibration characteristics of variable mass system is of great significance to aerospace engineering.According to the principle of virtual displacement and the law of conservation of momentum, the variable coefficient governing differential equation of general variable mass dynamics system is deduced, the influence of mass change on the dynamic characteristics of the system is analyzed, The modified Eulerian midpoint symplectic scheme and modal superposition method are given for the variable mass system. For the variable mass point, variable mass tension bar and variable mass Euler beam system, the dynamic response The simulation results show that the two methods are highly consistent with the numerical results, which proves the correctness and validity of the two methods for the vibration analysis of the variable mass system.