复杂载荷作用下功能梯度圆锥壳的非线性动力学研究

发布时间：2018-01-12 16:18

本文关键词：复杂载荷作用下功能梯度圆锥壳的非线性动力学研究　出处：《北京信息科技大学》2015年硕士论文　论文类型：学位论文

【摘要】：功能梯度材料(Functionally Graded Material，简称FGM)是一种非均质新型复合材料，它的材料属性沿厚度方向由一侧向另一侧呈连续梯度变化。在航空航天领域中，圆锥壳结构常常要承受气动载荷和机械荷载的共同作用，这将导致系统的大幅振动，往往会产生很大的噪声，甚至发生严重的故障。因此，对功能梯度圆锥壳的动力学的研究是非常重要的。本文考虑热应力的影响，基于一阶剪切变形理论和von-Karman几何非线性关系，运用Hamilton原理推导出功能梯度截顶圆锥壳的偏微分形式的运动方程，又利用Galerkin法将偏微分方程离散为常微分方程。研究了复杂载荷作用下的功能梯度截顶圆锥壳的非线性动力学行为，主要研究内容包括以下4个方面。（1）研究了面内载荷对热环境下的功能梯度截顶圆锥壳振动响应的影响，并对比了不同温度场下的系统非线性振动响应。（2）研究了在气动载荷和机械荷载共同作用下，陶瓷体积分数指数、气动载荷、半顶角和面内载荷幅值对功能梯度截顶圆锥壳振动响应的影响。（3）在气动载荷和机械荷载共同作用下的情况下，运用多尺度法对常微分方程进行摄动，获得1:1内共振时的平均方程，，研究了马赫数和面内载荷对系统幅频特性和振动响应的影响。（4）考虑带有曲率修正项的气动力和气动热，建立了功能梯度截顶圆锥壳的颤振方程，然后通过求解系统的特征值问题和Runge-Kutta法，对功能梯度截顶圆锥壳的气-热-弹颤振特性进行了研究。
[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.
【学位授予单位】：北京信息科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：V214

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