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Large-amplitude free vibrations of functionally graded beams by means of a finite element formulation

机译：功能梯度梁的大振幅自由振动通过有限元公式表示

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摘要

The large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The Von-Karman type nonlinear strain-displacement relationships are employed where the ends of the beam are constrained to move axially. The effects of the transverse shear deformation and rotary inertia are included based upon the Timoshenko beam theory. The material properties are assumed to be graded in the thickness direction according to the power-law distribution. A statically exact beam element which devoid the shear locking effect with displacement fields based on the first order shear deformation theory is used to study the geometric nonlinear effects on the vibrational characteristics of functionally graded beams. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law exponent, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible. Some new results for the nonlinear natural frequencies are presented in both tabular and graphical forms which can be used for future references.
机译：利用有限元公式研究了功能梯度梁的大振幅自由振动分析。在梁的端部被约束轴向移动的情况下，采用了Von-Karman型非线性应变-位移关系。根据Timoshenko梁理论，包括了横向剪切变形和旋转惯性的影响。假定材料特性根据幂律分布在厚度方向上分级。基于一阶剪切变形理论的静态精确梁单元在位移场中没有剪切锁定效应，用于研究几何非线性对功能梯度梁振动特性的影响。采用有限元方法离散化非线性控制方程，然后通过直接数值积分技术对其求解，以获得具有不同边界条件的功能梯度梁的非线性振动频率。研究了幂律指数，振动幅度，梁的几何参数和端支撑对自由振动频率的影响。在可能的情况下，本数值结果与文献中提供的结果进行了很好的比较。非线性固有频率的一些新结果以表格和图形形式给出，可用于将来的参考。

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