本文關鍵詞：復雜載荷作用下功能梯度圓錐殼的非線性動力學研究　出處：《北京信息科技大學》2015年碩士論文　論文類型：學位論文

  更多相關文章： 功能梯度材料 截頂圓錐殼 非線性動力學 混沌 顫振

【摘要】：功能梯度材料(Functionally Graded Material，簡稱FGM)是一種非均質(zhì)新型復合材料，它的材料屬性沿厚度方向由一側向另一側呈連續(xù)梯度變化。在航空航天領域中，圓錐殼結構常常要承受氣動載荷和機械荷載的共同作用，這將導致系統(tǒng)的大幅振動，往往會產(chǎn)生很大的噪聲，甚至發(fā)生嚴重的故障。因此，對功能梯度圓錐殼的動力學的研究是非常重要的。 本文考慮熱應力的影響，基于一階剪切變形理論和von-Karman幾何非線性關系，運用Hamilton原理推導出功能梯度截頂圓錐殼的偏微分形式的運動方程，又利用Galerkin法將偏微分方程離散為常微分方程。研究了復雜載荷作用下的功能梯度截頂圓錐殼的非線性動力學行為，主要研究內(nèi)容包括以下4個方面。 （1）研究了面內(nèi)載荷對熱環(huán)境下的功能梯度截頂圓錐殼振動響應的影響，并對比了不同溫度場下的系統(tǒng)非線性振動響應。 （2）研究了在氣動載荷和機械荷載共同作用下，陶瓷體積分數(shù)指數(shù)、氣動載荷、半頂角和面內(nèi)載荷幅值對功能梯度截頂圓錐殼振動響應的影響。 （3）在氣動載荷和機械荷載共同作用下的情況下，運用多尺度法對常微分方程進行攝動，獲得1:1內(nèi)共振時的平均方程，，研究了馬赫數(shù)和面內(nèi)載荷對系統(tǒng)幅頻特性和振動響應的影響。 （4）考慮帶有曲率修正項的氣動力和氣動熱，建立了功能梯度截頂圓錐殼的顫振方程，然后通過求解系統(tǒng)的特征值問題和Runge-Kutta法，對功能梯度截頂圓錐殼的氣-熱-彈顫振特性進行了研究。
[Abstract]:Functionally graded Graded material (FGM) is a new heterogeneous composite material. Its material properties change continuously from one side to the other along the thickness direction. In the field of aerospace, the conical shell structure is often subjected to the combined action of aerodynamic load and mechanical load. This will lead to the large vibration of the system, which will often produce a lot of noise and even serious failure. Therefore, it is very important to study the dynamics of the functionally gradient conical shell. In this paper, the effect of thermal stress is considered, based on the first-order shear deformation theory and von-Karman geometric nonlinear relationship. The equation of motion of the functionally gradient truncated conical shell in the form of partial differential is derived by using the Hamilton principle. The partial differential equation is discretized into ordinary differential equation by Galerkin method. The nonlinear dynamic behavior of the functionally gradient truncated conical shell under complex loads is studied. The main research contents include the following four aspects. 1) the effect of in-plane loading on the vibration response of the functionally gradient truncated conical shell in thermal environment is studied, and the nonlinear vibration response of the system under different temperature fields is compared. The effects of ceramic volume fraction exponent, aerodynamic load, half top angle and in-plane load amplitude on the vibration response of functionally gradient truncated conical shell under the combined action of aerodynamic load and mechanical load are studied. 3) under the action of aerodynamic load and mechanical load, the ordinary differential equation is perturbed by multi-scale method, and the average equation of 1: 1 internal resonance is obtained. The effects of Mach number and in-plane load on the amplitude-frequency characteristic and vibration response of the system are studied. (4) considering aerodynamic force and aerodynamic heat with curvature correction, the flutter equation of functionally gradient truncated conical shell is established, and then the eigenvalue problem of the system and Runge-Kutta method are solved. The flutter characteristics of a functionally gradient truncated cone shell are studied.
【學位授予單位】：北京信息科技大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：V214

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