一维非均匀变截面结构瞬态响应的传递函数渐近解法

分析了具有单结构参数变化的一维非均匀变截面结构。引入状态变量将运动微分方程及边界条件写成状态空间形式。定义小参数，通过Laplace变换并利用摄动方法，得到常系数微分方程，从而得到问题的摄动解。通过反Laplace变换得到时域的响应。给出了数值算例，验证了方法的可行性。

The Asymptotic Solution for Transient Response Analysis of Non-uniform Beam-like Structure by Distributed Transfer Function Method

The transient response analysis of non-uniform beam-like structure is presented in thispaper. The linear partial differential equation and the inhomogeneous boundary conditions have been cast intoa state space form in the Laplace domain. Choosing the small parameter E as a perturbation parameter, theasymptotic solutions of the dynamics response are determined by the state space technique and the transferfunction method. By the inversion of Laplace transform, the structure response with respect to time can beachieved. Numerical examples are provided to illustrate the efficiency of the method and the results arecompared with that of the finite element method.