Abstract The main purpose of this study is to investigate free vibrations of cylindrical helical rods with variable cross-section, composed of functionally graded materials, which may be used to model environmental effects. The material variation is considered to be along the rod axis. Governing differential equations of the free vibration are obtained via Timoshenko's beam theory, where axial and shear deformations and rotary inertia are taken into consideration. The governing equations are solved numerically by using the transfer matrix method. The effects of cross-section variation ( β s e c ) , material gradient index ( β m a t ) , helix pitch angle ( α ) , and number of active coils ( n ) on the frequencies are investigated. All results are compared with the ANSYS solutions, in which a very well approximation is achieved.

中文翻译：

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具有可变截面的功能梯度圆柱螺旋的自由振动分析

摘要 本研究的主要目的是研究由功能梯度材料组成的可变截面圆柱螺旋杆的自由振动，可用于模拟环境影响。材料变化被认为是沿着杆轴的。自由振动的控制微分方程是通过 Timoshenko 的梁理论获得的，其中考虑了轴向和剪切变形以及旋转惯性。通过使用传递矩阵方法对控制方程进行数值求解。研究了横截面变化 (βsec)、材料梯度指数 (βmat)、螺旋桨距角 (α) 和有源线圈数 (n) 对频率的影响。所有结果都与 ANSYS 解决方案进行了比较，其中实现了非常好的近似。