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首页> 外文期刊>Composite Structures >Parametric instability of functionally graded beams with an open edge crack under axial pulsating excitation
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Parametric instability of functionally graded beams with an open edge crack under axial pulsating excitation

机译：轴向脉动激发下具有开边裂纹的功能梯度梁的参数不稳定性

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摘要

This paper studies the parametric instability of functionally graded beams with an open edge crack subjected to an axial pulsating excitation which is a combination of a static compressive force and a harmonic excitation force. It is assumed that the materials properties follow an exponential variation through the thickness direction. Theoretical formulations are based on Timoshenko beam theory and linear rotational spring model. The governing equations of motion are derived by using Hamilton's principle and transformed into a set of Mathieu equations through Galerkin's procedure. The natural frequencies with different end supports are obtained. The boundary points on the unstable regions are determined by using Bolotin's method. Numerical results are presented to highlight the influences of crack location, crack depth, material property gradient, beam slenderness ratio, compressive load, and boundary conditions on both the free vibration and parametric instability behaviors of the cracked functionally graded beams.
机译：本文研究了具有开放边缘裂缝的功能梯度梁在轴向脉动激励的作用下的参数不稳定性，轴向激励是静态压缩力和谐波激励力的组合。假定材料特性沿厚度方向遵循指数变化。理论公式基于蒂莫申科梁理论和线性旋转弹簧模型。使用汉密尔顿原理导出运动的控制方程，并通过加勒金方法将其转换为一组Mathieu方程。获得具有不同终端支撑的固有频率。不稳定区域上的边界点通过Bolotin方法确定。数值结果表明了裂纹位置，裂纹深度，材料特性梯度，梁的细长比，压缩载荷和边界条件对裂纹的功能梯度梁的自由振动和参数不稳定性行为的影响。

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