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首页> 外文期刊>Applied Mathematical Modelling >Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials
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Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials

机译：由轴向功能渐变材料制成的锥形Euler-Bernoulli梁的自由振动和稳定性

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摘要

The free vibration and stability of axially functionally graded tapered Euler-Bernoulli beams are studied through solving the governing differential equations of motion. Observing the fact that the conventional differential transform method (DTM) does not necessarily converge to satisfactory results, a new approach based on DTM called differential transform element method (DTEM) is introduced which considerably improves the convergence rate of the method. In addition to DTEM, differential quadrature element method of lowest-order (DQEL) is used to solve the governing differential equation, as well. Carrying out several numerical examples, the competency of DQJEL and DTEM in determination of free longitudinal and free transverse frequencies and critical buckling load of tapered Euler-Bernoulli beams made of axially functionally graded materials is verified.
机译：通过求解运动的控制微分方程，研究了轴向功能梯度锥形Euler-Bernoulli梁的自由振动和稳定性。考虑到传统的差分变换方法（DTM）不一定会收敛到令人满意的结果，引入了一种基于DTM的新方法，称为差分变换元素方法（DTEM），该方法大大提高了该方法的收敛速度。除DTEM外，还使用最低阶微分正交元素法（DQEL）求解控制微分方程。通过几个数值算例，验证了DQJEL和DTEM在确定轴向，梯度自由轴向频率和由轴向功能梯度材料制成的锥形Euler-Bernoulli梁的临界屈曲载荷方面的能力。

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