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首页> 外文期刊>Advances in Aircraft and Spacecraft Science >An inverse hyperbolic theory for FG beams resting on Winkler-Pasternak elastic foundation
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An inverse hyperbolic theory for FG beams resting on Winkler-Pasternak elastic foundation

机译：基于Winkler-Pasternak弹性地基的FG梁的反双曲理论

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摘要

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distributioa In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.
机译：使用新的反双曲梁理论研究了基于两个参数（Winkler-Pasternak）弹性基础的功能梯度（FG）高阶梁的弯曲，屈曲和自由振动响应。根据幂定律分布，沿厚度方向对梁的材料特性进行分级。在本理论中，轴向位移是反双曲分布，横向剪应力满足顶部和底部的无牵引边界条件。梁的底面。汉密尔顿原理被用来导出运动的控制方程。针对弯曲，弯曲和振动问题获得了Navier型解析解。获得了数值结果，以研究幂律指数，长厚比和基础参数对位移，应力，临界屈曲载荷和频率的影响。通过使用Reddy的抛物线束理论和Timoshenko的一阶束理论得出的数值结果是专门为比较当前结果而得出的，彼此之间有着非常好的一致性。

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