中文摘要：

基于非局部弹性理论,研究了弹性边界约束条件下杆结构纵向振动特性。在非局部杆两端引入纵向约束弹簧,通过设置相应弹簧刚度系数,可以得任意经典边界及其组合情况下非局部杆结构纵振问题。非局部弹性杆纵振位移采用一种改进傅立叶级数进行展开,在标准傅立叶级数基础上构造附加函数,以使纵振位移在整个求解域内足够光滑。通过联合求解非局部纵振微分方程与弹性边界约束条件获得系统特征矩阵。通过与现有文献中不同边界条件非局部弹性杆纵振模态数据进行对比,充分验证了所构造模型的正确性。在此基础上讨论了边界约束刚度系数和非局部特征参数对非局部弹性杆纵振特性的影响。与现有方法相比,该方法能够统一考虑任意边界条件,当边界条件改变时不需要对理论推导和计算程序进行重新修改,实现了非局部弹性杆纵振特性分析的最为一般情况。

英文摘要：

Based on the nonlocal elasticity theory, longitudinal vibration characteristics of rod structures with general elastic boundary restraints are studied. Elastic springs are applied to the both ends of a nonlocal rod. All the classical boundary condi- tions as well as their combinations can be easily obtained by setting the spring coefficients accordingly. The displacement of the longitudinal vibration of the nonlocal rod is expanded into an improved Fourier series, in which a supplementary polynomial is introduced to make the constructed functions sufficiently smooth in the whole solution domain. The system characteristic ma- trix is derived by solving the nonlocal longitudinal vibration governing equation and the general elastic boundary condition sim- ultaneously. The accuracy of the proposed model is validated by comparing with the modal parameters of a nonlocal rod with various boundary conditions available in literatures. Based on the established model, the influences of the boundary restraining stiffness and the nonlocal characteristic parameters on the modal characteristics of a nonlocal rod structure are also analyzed. By comparing with other approaches, the proposed method can take the boundary condition into account in the most general case. Therefore, there is no need to reformulate the theoretical model and/or modify the simulation code when the boundary conditions are changed.