Based on the Euler–Bernoulli beam theory, the natural vibration behavior of functionally graded nonuniform multiple beams has been investigated. It is assumed that the beams are joined by elastic translational springs, and the properties of the beams vary along the axial direction. The Chebyshev spectral collocation method has been used to convert the governing differential equations of transverse motion into a system of algebraic equations that are put in the matrix–vector form. Then, the dimensionless transverse frequencies are obtained by solving the eigenvalue problem. The influence of several factors, such as the stiffness parameters of the coupling translational springs, the properties of the cross section of the beams, and the boundary conditions on the frequencies, has been carried out. The results generated from the Chebyshev spectral collocation method have been verified by comparing them with those reported in other studies and references from the literature. Several numerical examples have been presented and discussed to analyze the system under consideration. The authors hope that the findings of the current study are helpful in designing and characterizing multiple nonuniform thin engineering structures.

基于欧拉-伯努利梁理论，研究了功能梯度非均匀多梁的自然振动行为。假定梁由弹性平移弹簧连接，并且梁的特性沿轴向方向变化。Chebyshev频谱搭配方法已用于将横向运动的控制微分方程转换为代数方程组，并以矩阵-矢量的形式。然后，通过求解特征值问题获得无因次横向频率。已经执行了几个因素的影响，例如耦合平移弹簧的刚度参数，梁的横截面特性以及边界条件对频率的影响。通过将Chebyshev光谱搭配方法产生的结果与其他研究报告和文献参考相比较，已得到验证。已经提出并讨论了几个数值示例来分析所考虑的系统。作者希望当前的研究结果有助于设计和表征多个非均匀的薄工程结构。