Abstract

The aim of the current study is to investigate torsional vibrations of bi-directional functionally graded (FG) small-scale tubes. The size effect is captured using the modified couple stress theory (MCST). Through-the-thickness distribution profile of material properties are characterized by employing a power-law function, which incorporates a gradation index, β, and longitudinal varation in material properties is featured by an exponential function which employs a gradient parameter, α. Similar to other material properties, continuous spatial variation of the length scale parameter is also incorporated into the analysis of two-dimensionally FG tubes. The model, including governing equations of motion and boundary conditions, is developed through the utilization of Hamilton’s principle. By employing differential quadrature method (DQM) numerical results regarding torsional vibrations are provided. Accuracy of the proposed model and procedures are verified through verification comparisons made to limiting cases available in the literature. Numerical results reveal effects of various material and geometric parameters on natural frequencies and indicate that torsional free vibration characteristics of small-sized tubes are sensitive to distribution profile of constituents, geometric aspect ratios and effective length scale parameter. Results also demonstrate that length scale parameter variation has significant influence on natural frequencies which justifies the necessity of its consideration in analyses.

摘要

本研究的目的是研究双向功能梯度 (FG) 小型管的扭转振动。使用修正的耦合应力理论 (MCST) 来捕捉尺寸效应。材料特性的全厚度分布曲线通过采用幂律函数来表征，该函数包含渐变指数β，材料特性的纵向变化由采用梯度参数α的指数函数来表征. 与其他材料特性类似，长度尺度参数的连续空间变化也被纳入二维 FG 管的分析中。该模型，包括运动控制方程和边界条件，是通过利用汉密尔顿原理开发的。通过采用微分求积法 (DQM)，提供了关于扭转振动的数值结果。所提出的模型和程序的准确性通过与文献中可用的限制案例进行验证比较来验证。数值结果揭示了各种材料和几何参数对固有频率的影响，并表明小型管的扭转自由振动特性对成分的分布分布很敏感，几何纵横比和有效长度尺度参数。结果还表明，长度尺度参数的变化对固有频率有显着影响，这证明了在分析中考虑它的必要性。