单杠结构差分离散系统的振动反问题

Inverse Problems in Vibration for Difference Discrete Systems of a Horizontal Bar Structure

研究组合结构中的杆-梁-杆组合单支结构,或称单杠结构的模态反问题,从数学上证明单杠结构差分离散系统固有振动的刚度矩阵的符号振荡性,并导出其频率和振型的一些定性性质.在此基础上,探讨由两组位移或应变振型及相应频率构造物理参数的条件和方法,给出两个计算实例.讨论结构参数关于其几何对称轴具有对称性的条件下的模态反问题,并给出计算实例.计算结果表明,上述反问题提法合理,解法正确.

Inverse mode problem of a horizontal bar structure, a single branch structure of a rod-beam-rod system, is investigated. Sign-oscillatory properties of inherent vibration stiffness matrix of discrete horizontal bar structure are shown mathematically. In addition, qualitative properties of frequencies and modes are introduced. Physical parameters of horizontal bar structure are constructed from two sets of displacement or strain modes and corresponding circular frequencies. Several numerical examples are given. A particular inverse mode problem is discussed, where structure parameters of horizontal bar are symmetrical for geometrical symmetry axis. It shows that formulation of inverse problems is reasonable and solution method is validated.