發(fā)布時(shí)間：2018-03-16 21:14

  本文選題：功能梯度材料　切入點(diǎn)：微梁　出處：《力學(xué)學(xué)報(bào)》2017年02期 　論文類型：期刊論文

【摘要】：基于Euler-Bernoulli梁理論和單向耦合的熱傳導(dǎo)理論,研究了功能梯度材料(functionally graded material,FGM)微梁的熱彈性阻尼(thermoelastic damping,TED).假設(shè)矩形截面微梁的材料性質(zhì)沿厚度方向按冪函數(shù)連續(xù)變化,忽略了溫度梯度在軸向的變化,建立了單向耦合的變系數(shù)一維熱傳導(dǎo)方程.熱力耦合的橫向自由振動(dòng)微分方程由經(jīng)典梁理論獲得.采用分層均勻化方法將變系數(shù)的熱傳導(dǎo)方程簡(jiǎn)化為一系列在各分層內(nèi)定義的常系數(shù)微分方程,利用上下表面的絕熱邊界條件和界面處的連續(xù)性條件獲得了微梁溫度場(chǎng)的分層解析解.將溫度場(chǎng)代入微梁的運(yùn)動(dòng)方程,獲得了包含熱彈性阻尼的復(fù)頻率,進(jìn)而求得了代表熱彈性阻尼的逆品質(zhì)因子.在給定金屬-陶瓷功能梯度材料后,通過(guò)數(shù)值計(jì)算結(jié)果定量分析了材料梯度指數(shù)、頻率階數(shù)、幾何尺寸以及邊界條件對(duì)TED的影響.結(jié)果表明:(1)若梁長(zhǎng)固定不變,梁厚度小于某個(gè)數(shù)值時(shí),改變陶瓷材料體積分?jǐn)?shù)可以使得TED取得最小值;(2)固有頻率階數(shù)對(duì)TED的最大值沒(méi)有影響,但是頻率階數(shù)越高對(duì)應(yīng)的臨界厚度越小;(3)不同的邊界條件對(duì)應(yīng)的TED的最大值相同,但是隨著支座約束剛度增大對(duì)應(yīng)的臨界厚度減小;(4)TED的最大值和對(duì)應(yīng)的臨界厚度隨著金屬組分的增大而增大.
[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.
【作者單位】： 揚(yáng)州大學(xué)建筑科學(xué)與工程學(xué)院;
【基金】：國(guó)家自然科學(xué)基金資助項(xiàng)目(11272278,11672260)
【分類號(hào)】：O326

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本文編號(hào)：1621675