冲击波作用下悬臂梁瞬态响应的传递函数方法

利用传递函数方法对爆炸冲击波作用下的悬臂梁进行分析，得到其瞬态响应的封闭形式的解析解。首先，针对给定的爆炸冲击波载荷和初始条件，对梁的控制方程和边界条件进行Laplace变换，然后通过引入状态向量将其改写成状态空间形式，并利用传递函数方法求得其在频域内的解析解，最后利用Crump方法并结合ε算法进行Laplace逆变换，求得悬臂梁在时域内的瞬态响应。给出数值算例，通过与有限元的比较验证了方法的正确性。

TRANSIENT RESPONSE ANALYSIS OF A CANTILEVER BEAM UNDER BLAST WAVE WITH DISTRIBUTED TRANSFER FUNCTION METHOD

A cantilever beam under blast wave is analyzed with the distributed transfer function method and the analytical solution of its transient response in a closed form is obtained. Firstly, for the given explosive blast wave and the initial conditions, the governing equation of motion of the beam and the boundary conditions are transformed with Laplace transformation, and changed into the state space form after a state vector is introduced. Then, the analytical solution in frequency domain is obtained by using the distributed transfer function method. Finally, by the inversion of Laplace transformation with Crump method and epsilon algorithm, the transient response in time domain of the cantilever beam is obtained. An numerical example is provided and the method proposed is verlified by comparing its results with those by using the finite element method.