弹性板中柱面Lamb波问题的哈密顿体系方法

A method of Hamiltonian system for cylinder Lamb waves in elastic plates

针对柱面Lamb波问题,引入哈密顿体系并利用辛本征值和本征解及其辛共轭正交关系,得到柱面Lamb波解析解.采用表面载荷激励的柱面Lamb波,分析Lamb波传播特点.研究结果表明:数值模拟结果与文献实验结果吻合,说明在分析柱面Lamb波问题中哈密顿体系方法是可靠和准确的.研究结论可用于对含损伤板的响应分析,并为结构健康监测和检测提供依据.

For the cylindrical Lamb wave problem,the Hamiltonian system is introduced and the symplectic eigenvalues,eigensolutions and their symplectic conjugate orthogonal relations are used to obtain the analytical solution of Lamb cylindrical wave.The characteristics of Lamb cylindrical wave propagation are analyzed under the excitation of surface load.The research results show that the numerical simulation results are in agreement with the experimental results of others,indicating that the Hamiltonian system method is reliable and accurate.The research conclusion can be used for the response analysis of plates with damage and provide the basis for structural health monitoring.