多自由度振动系统的一类凸集响应

对激励用凸集合建模的线性时不变振动系统定义了响应集的概念，将多自由度振动系统的凸集响应问题转化成寻求响应集的问题，从而降低了求解的难度．并提出了求解一类凸集载荷的响应集的支撑超平面法．对有限时刻的响应集，导出了求任意方向边界点的解析解，而对无限时刻的响应集，建议了一种求任意精度的凸多胞形近似的方法．最后给出了一个实例，得到了不同时刻的响应集，并将凸集响应与谐波响应及非平稳随机响应作了对照

THE CONVEX RESPONSE SET OF A CLASS OF MDOF VIBRATION SYSTEM

The response reachable set is defined for a linear time invariant vibration system excitation of which is modeled by a convex set. The problem of resolving the convex responses of MDOF vibration system is transformed into that of finding the response reachable set. A support hyperplane method of finding the response reachable set to the excitation modeled by aspecial convex set is presented. An analytical expression is obtained for the boundary point of the finite time response reachable set at a direction. A convex polytope is proposed to estimate the infinite time response reachable set with any accuracy. An example is given to obtain the response reachable sets at different instants, and the comparison for a convex response with a harmonic response and a non stationary random response is also given.