有碰撞存在的多体振动系统的周期运动和稳定条件

有碰撞存在的多体振动系统在工程中应用甚广,但由于运动过于复杂,过去一般限于研究和利用个别特殊系统.本文考虑任意多个串联质体在多个正弦力的激励下振动,并和多个自由体碰撞(弹性或塑性碰撞)的一般情况,提出振动和稳定的统一解法.首先按工程需要选择周期运动的界点(碰撞点与脱离点),以避免解非线性方程.然后采用矩阵迭代方法求得周期运动的简便条件及其若干推论(如界点的最多个数、周期运动的存在唯一条件等).再用差分方程和矩阵迭代确定周期运动的稳定条件.文末讨论了多体系统的多种功能,如参数稳定区域大、优化程度高、自动消振和隔振等,可以充分加以利用.

Periodic Motion and Stability Condition of Multimass System Vibrating with Impact

Multimass systems vibrating with impacts are much used in engineering,But in the past,the studies and applications were always limited to some individual objeets and special cases because the motion of the system is very complicared.In this paper,a system that is composed of any number of masses connected in series,excited by many sinusoidal forces and collides with many free bodies is dealt with.A general method for the analysis of vibration and stability of the system is proposed.Firstly,according to the needs of an engineering,we properly choose the all boundary points(impact and separation points)of a periodic motion within a period in order to avoid solving a great number of nonlinear equaitons,and then to apply an iteration method of matrixes we obtain a simple condition for determining the periodic motion and some corllaries(e.g.,the maximum number of the boundary points within a period,the existenc and uniqueness condition of the periodic motion,etc.).Next to use difference equations of disturbances and the iteration method of matrixes we get a condition to determine the stability of the periodic motion.At last,discuss variform functions the system possesses,such as,the stability region of parameters is wider,the standatd of the optimization of parameters is higher,may achieve self-absorption and selfisolation of vibration,etc.,which may be sufficiently used by us.