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首页> 外文期刊>Composite Structures >Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment
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Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment

机译：在嵌入弹性矩阵中的裂缝FG微观的自由振动并在热环境中暴露于磁场

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A mathematical model is developed, though this article, to investigate a vibrational behaviour of functionally graded (FG) cracked microbeam rested on elastic foundation and exposed to thermal and magnetic fields. The model includes a size scale effect and temperature dependent material properties, for the first time. The crack is modelled as a rotating spring, that is connecting the two parts of the microbeam at the crack's position. The equation of motion of the FG microbeam is obtained by using the Euler-Bernoulli beam theory for kinematic assumption and nonlocal elasticity theory for size- dependency effects. The transverse Lorentz force induced from the magnetic field is derived using Maxwell's equations. By adding the effects of thermal loading and foundation parameters on the cracked micro beam, the motion equation of the entire system is obtained using the Hamilton's principle and then solved with a Navier type solution method. Eight constraints equations are used to derived the frequency equation, which are boundary conditions at the end points and the displacement, slope, bending moment and transverse force continuity in the section where the crack is located. The resulting system of equations is solved sequentially, and natural frequencies and vibration modes of the cracked microbeam are obtained. The model is verified with previous published work. Numerical results are presented to illustrate influences of temperature, material composition, foundation parameters and magnetic field on the dynamics of the cracked FG microbeam.
机译：尽管本文开发了一种数学模型，以研究功能梯度（FG）裂纹的微观区域的振动行为，靠在弹性基础上并暴露于热和磁场。该模型首次包括尺寸比例效应和温度依赖性材料特性。该裂缝被建模为旋转弹簧，其在裂缝位置将微沟的两部分连接。通过使用Euler-Bernoulli光束理论获得FG MicroBeam的运动方程，用于运动学假设和非识别弹性理论，用于大小依赖性效应。从磁场引起的横向洛伦兹力使用Maxwell等式导出。通过在裂纹微束上添加热负荷和基础参数的影响，使用Hamilton的原理获得整个系统的运动方程，然后用Navier型解决方法解决。八个约束方程用于导出频率方程，该频率方程是在裂缝所定位的部分中的端点和位移，斜面，弯矩和横向力连续性的边界条件。所得到的等式系统顺序求解，得到裂纹微沟的自然频率和振动模式。该模型通过以前发布的工作进行了验证。提出了数值结果，以说明温度，材料组成，基础参数和磁场对裂纹FG微沟动力学的影响。

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