非局部杆纵向振动的特性研究

基于非局部理论,研究弹性杆在任意边界约束条件下的纵向振动特性.根据Chebyshev谱级数建立非局部弹性杆的纵向位移形式.在杆的两端引入纵向约束弹簧,通过设置弹簧刚度系数,模拟经典边界及弹性边界.建立非局部杆的能量表达式,由瑞利-里兹法得到齐次线性方程组,求解对应的矩阵特征值与特征向量问题获得非局部杆的固有频率和振型.通过数值仿真计算,研究非局部特征系数与边界约束条件对非局部杆振动频率的影响.结果表明本文方法合理简便,具有良好的精度,且适用于任意弹性边界条件.

Study of Longitudinal Vibration Characteristics of a Nonlocal Rod

The longitudinal vibration of a nonlocal rod with elastic boundary condition is analyzed. The form of the displacement function of the rod is established based on Chebyshev-Spectro method series. At the both ends, longitudinal springs are arranged, and the values of the spring’s stiffness are chosen to simulate the boundary conditions of rod. A linear homogeneous equation set is obtained by Rayleigh-Ritz method to get the natural frequencies and vibration modes by solving eigenvalue and eigenvector problems. The influence of nonlocal parameters and boundary constraint conditions on the vibration characteristics is studied by several cases numerically. The results show that the proposed method is reasonable and has good accuracy, and can also be applied to rods with arbitrary boundary conditions.