Abstract

In scope of this study, forced vibration analysis of viscoelastic helical rods with varying cross-section and functionally graded material are investigated. Differential equations governing the dynamic behavior of helical rods are obtained in Laplace domain by the Timoshenko’s beam theory. Material and section geometry are assumed to be varying functionally along the rod axis. Viscoelasticity of the material is implemented via Kelvin’s model. Stiffness and transfer matrix methods are used together in order to obtain dynamic stiffness matrix of the system. Acquired results in Laplace domain are converted to time domain by using Durbin’s inverse Laplace algorithm. A parametric study is carried out for the investigation of the effects of material variation, non-uniformity and damping on the forced vibration of functionally graded viscoelastic rods.

摘要

在本研究范围内，研究了具有不同横截面和功能梯度材料的粘弹性螺旋杆的受迫振动分析。通过 Timoshenko 的梁理论在拉普拉斯域中获得了控制螺旋杆动态行为的微分方程。假定材料和截面几何形状沿杆轴在功能上发生变化。材料的粘弹性通过开尔文模型实现。刚度和传递矩阵方法一起使用以获得系统的动态刚度矩阵。利用杜宾的拉普拉斯逆算法将拉普拉斯域的采集结果转换​​为时域。进行了参数化研究，以研究材料变化、不均匀性和阻尼对功能梯度粘弹性棒的受迫振动的影响。