【摘要】 许多工程结构中存在着非线性边界，而非线性边界会对结构振动产生一定的影响。对非线性刚度弹簧固定的杆梁结构进行了动力学特性研究。对于杆结构，分别采用了行波法和分离变量法进行分析，并通过比较得到了两种方法之间的联系。对于梁结构，分别考虑了入射传递波和入射近场波，应用谐波平衡法得到了无量纲频率、位移、反射系数及相位等参数之间的关系。最后，应用相位闭合原理与分离变量法得到了杆和梁的骨架与频响曲线。为了验证理论计算的准确性与有效性，对杆梁模型进行了有限元数值仿真。结果表明，理论解与仿真解基本吻合。更多还原

【Abstract】 Nonlinear boundaries exist in many engineering structures and significantly influence the vibration of systems. The dynamic characteristics of a rod or beam structure with nonlinear stiffness boundaries were studied. The traveling wave method and the variable separation method were used to analyze the dynamic characteristics of the rod, and the relationship between the two approaches was investigated. For the beam, the incident propagating and nearfield waves were considered, respectively. The relationships between the dimensionless frequency, displacement, reflection coefficient, and phase were discussed by using the harmonic balance method. Finally, the backbone and frequency response curves of the rod and beam structures were obtained by using the phase closure principle and the variable separation method. In order to verify the accuracy and effectiveness of the theoretical calculations, a finite element numerical simulation was carried out for the rod and beam models. The results show that the theoretical solutions compare well with the numerical simulation results.更多还原