功能梯度材料微梁的热弹性阻尼研究

发布时间：2018-03-16 21:14

本文选题：功能梯度材料　切入点：微梁　出处：《力学学报》2017年02期 　论文类型：期刊论文

【摘要】：基于Euler-Bernoulli梁理论和单向耦合的热传导理论,研究了功能梯度材料(functionally graded material,FGM)微梁的热弹性阻尼(thermoelastic damping,TED).假设矩形截面微梁的材料性质沿厚度方向按幂函数连续变化,忽略了温度梯度在轴向的变化,建立了单向耦合的变系数一维热传导方程.热力耦合的横向自由振动微分方程由经典梁理论获得.采用分层均匀化方法将变系数的热传导方程简化为一系列在各分层内定义的常系数微分方程,利用上下表面的绝热边界条件和界面处的连续性条件获得了微梁温度场的分层解析解.将温度场代入微梁的运动方程,获得了包含热弹性阻尼的复频率,进而求得了代表热弹性阻尼的逆品质因子.在给定金属-陶瓷功能梯度材料后,通过数值计算结果定量分析了材料梯度指数、频率阶数、几何尺寸以及边界条件对TED的影响.结果表明:(1)若梁长固定不变,梁厚度小于某个数值时,改变陶瓷材料体积分数可以使得TED取得最小值;(2)固有频率阶数对TED的最大值没有影响,但是频率阶数越高对应的临界厚度越小;(3)不同的边界条件对应的TED的最大值相同,但是随着支座约束刚度增大对应的临界厚度减小;(4)TED的最大值和对应的临界厚度随着金属组分的增大而增大.
[Abstract]:Based on the Euler-Bernoulli beam theory and the unidirectional coupling heat conduction theory, the thermoelastic damping of functionally functionally graded material FGMs microbeams is studied. It is assumed that the material properties of rectangular cross section microbeams vary continuously according to the power function along the thickness direction. Ignoring the temperature gradient in the axial direction, In this paper, one dimensional heat conduction equation with unidirectional coupling coefficient is established. The differential equation of transverse free vibration of thermal coupling is obtained from classical beam theory. The heat conduction equation with variable coefficient is simplified into a series of heat conduction equations by using stratified homogenization method. Differential equations with constant coefficients defined in layers, By using the adiabatic boundary condition of the upper and lower surfaces and the continuity condition at the interface, the layered analytical solution of the temperature field of the micro beam is obtained. The complex frequency containing thermal elastic damping is obtained by substituting the temperature field into the motion equation of the micro beam. The inverse quality factor representing thermoelastic damping is obtained. After given metal-ceramic functionally graded materials, the material gradient index and frequency order are quantitatively analyzed by numerical calculation results. The effect of geometric dimension and boundary conditions on TED. The results show that when the beam length is fixed and the beam thickness is less than a certain value, By changing the volume fraction of ceramic material, the minimum value of TED can be obtained.) the order of natural frequency has no effect on the maximum value of TED, but the higher the frequency order, the smaller the critical thickness of TED, the maximum value of TED corresponding to different boundary conditions is the same. However, with the increase of supporting stiffness, the corresponding critical thickness decreases and the corresponding critical thickness increases with the increase of metal composition.
【作者单位】：扬州大学建筑科学与工程学院;
【基金】：国家自然科学基金资助项目(11272278,11672260)
【分类号】：O326

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