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.