Self-adaptive Newmark method of variable-mass beam dynamic system

Variable-mass beam was used to model launch vehicle. Firstly the results of a spring-variable-mass ball system were compared with the analytical solutions. Then by using an example of a constant-mass beam, the parameters of the self-adaptive Newmark method were determined. At last the practical procedure of propellant decreasing and its effects on the transverse vibration were taken into account in a variable-mass beam. The self-adaptive Newmark method whose parameters depend on the inherent frequency of dynamic system, phase error and spectral radius of the method was employed to solve the dynamic responses of a variable-mass beam system, and the obtained results were compared with those of the analytical solutions by mode superposition method, average acceleration method (NMA) and Fox-Goodwin method (NMF). The comparison shows that the self-adaptive Newmark method is applicable to the variable-mass system, and it is more accurate than the methods used for comparison, especially the phase accuracy.