Abstract

This study is in investigation of free vibration behavior of functionally graded hyperboloidal and barrel helices with variable cross section. Material and geometric variations of noncylindrical helices are assumed to be along the rod axis. Governing differential equations of motion, including rotatory inertia, axial and shear deformations are derived by the Timoshenko beam theory. Then, transfer matrix and stiffness matrix methods are employed for the numerical solution of obtained ordinary differential equations. Effects of material gradient index $({\beta }_{\mathrm{mat}}),$ diameter variation parameter $({\beta }_{\text{sec}}$), and ratio of helix radius at end section and middle section $R_2/R_1$ on the natural frequencies are investigated through a parametric study considering barrel and hyperboloidal geometries. Comparisons with available literature studies and ANSYS solutions are made regarding obtained results.

摘要

本研究旨在研究具有可变截面的功能梯度双曲面和桶形螺旋的自由振动行为。假设非圆柱螺旋的材料和几何变化沿杆轴。运动的控制微分方程，包括转动惯量、轴向和剪切变形是由 Timoshenko 梁理论推导出来的。然后，采用传递矩阵和刚度矩阵方法对得到的常微分方程进行数值求解。材料梯度指数的影响$({\beta }_{\mathrm{垫}}),$直径变化参数$({\beta }_{\text{秒}}$), 端部与中部的螺旋半径之比$R_2/R_1$通过考虑桶形和双曲面几何形状的参数研究来研究自然频率。与现有的文献研究和 ANSYS 解决方案进行比较以获得结果。