均匀轴对称端面荷载下半无限长杆动力学响应

Dynamic Responses of a Semi-infinite Circular Rod to Homogeneous Axisymmetric End Loads

杆结构的导波检测技术因其高效而受到重视.欲利用导波检测杆结构,首先必须明确杆结构的动力学响应特征.利用本征函数展开法导出均匀轴对称端面荷载下半无限长杆瞬态动力学响应问题的解析解.与利用积分变换法得到的解析解相比,该解形式简洁且物理意义清晰.在该解析解基础上,可定量分析外力对各导波模式激发的影响.以端面冲击载荷作用下半无限长杆瞬态动力学响应为例进行数值研究表明,基于该解析解所得结果与有限元法(FEM)模拟结果一致.

Guided acoustic wave inspection technique for rods has received a plenty of attention because of its high efficiency.To inspect rods using guided waves,the dynamic response of them must be clarified first.The analytical transient dynamic response of a semi-infinite circular rod to homogeneous axisymmetric end loads is obtained using the method of eigenfunction expansion.Compared with the solution obtained using the integral transform technique,that obtained using the method of eigenfunction expansion has concise form and clear physical meaning.The effect of external forces on the excitation of each guided wave mode can be quantitatively evaluated on the basis of the present solution.The response of the semi-infinite circular rod to an impact applied on the end is numerically evaluated.And it is found that the results computed from the present analytical solution agree well with those simulated using the finite element method（FEM）.