变质量梁的自适应Newmark法

用变质量梁来模拟推进剂减少的液体火箭.先以一弹簧-变质量小球系统为例，用其求解结果与解析解进行比较.再以时不变的简支梁为算例，确定多自由度系统下与结构动特性协同的自适应Newmark方法中的参数选取.最后用时变的简支梁模型模拟贮箱质量的实际变化方式，运用与结构动特性协同的自适应Newmark方法、模态叠加法、Newmark平均加速度方法（NMA法）和Fox-Goodwin方法（NMF法）对其求解.比较结果证明自适应Newmark算法对于时变系统的适用性，尤其具有高精度特性. 

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.