复合材料圆柱壳的动力屈曲与混沌行为

发布时间：2018-05-17 11:02

本文选题：复合材料 + 圆柱壳　；参考：《太原理工大学》2015年硕士论文

【摘要】：随着科技的进步和加工工艺的日益革新，复合材料以其优良的力学性能而广泛的应用于各类工程结构中，复合材料圆柱壳在动态载荷作用下的力学行为是人们关注的重点。本文对复合材料圆柱壳在轴向阶跃载荷作用下的力学行为进行了详细的讨论，主要研究了圆柱壳的动力屈曲和混沌行为。这些研究系统地揭示了复合材料圆柱壳在动态载荷作用下的力学本质，为其工程应用提供了理论基础。本文的研究工作主要包括以下几个方面：（1）基于Hamilton原理和Donnell壳理论，考虑应力波在壳中的传播，得到了圆柱壳的动力屈曲控制方程。利用Ritz法进行求解，将动力屈曲问题转化为一组齐次线性方程组的求解，，要使齐次线性方程组有非平凡解，则系数矩阵的行列式等于0，由此给出了屈曲长度与屈曲临界载荷曲线并得到了屈曲模态。利用MATLAB进行编程计算，详细讨论了边界条件、铺层角度、环向模态数与轴向模态数等因素对复合材料圆柱壳的临界屈曲载荷的影响。研究结果表明：圆柱壳在固支边界条件下抵抗屈曲的能力最强，而圆柱壳在自由边界条件下最容易发生屈曲，但是随着应力波的传播，这一差异会逐渐减小；复合材料圆柱壳随着径厚比的增加，圆柱壳将更加容易出现高阶模态。（2）计及结构变形的几何非线性项，采用圆柱壳的非线性大挠度理论，基于应力函数和Hamilton原理，得到了复合材料圆柱壳的大挠度控制方程。利用Ritz法和Galerkin法可得到单自由度的非线性动力学控制方程。利用四阶Runge-Kutta法进行计算得到了系统的分叉图、相平面和Poincaré映射，用此详细的讨论了系统的运动状态，结果表明：复合材料圆柱壳的周期运动和混沌运动是随着侧向载荷幅值的增加而相互交替出现的。
[Abstract]:With the development of science and technology and the innovation of processing technology, composite materials are widely used in various engineering structures because of their excellent mechanical properties. The mechanical behavior of composite cylindrical shells under dynamic loading is the focus of attention. In this paper, the mechanical behavior of composite cylindrical shells under axial step loads is discussed in detail, and the dynamic buckling and chaotic behavior of cylindrical shells are studied. These studies systematically reveal the mechanical nature of composite cylindrical shells under dynamic loading and provide a theoretical basis for its engineering application. The research work of this paper mainly includes the following aspects: 1) based on Hamilton principle and Donnell shell theory, considering the propagation of stress wave in the shell, the governing equations of dynamic buckling of cylindrical shells are obtained. The dynamic buckling problem is transformed into the solution of a group of homogeneous linear equations by Ritz method. Then the determinant of the coefficient matrix is equal to 0, thus the buckling length and critical buckling load curve are obtained and the buckling modes are obtained. The effects of boundary condition, layer angle, toroidal mode number and axial mode number on the critical buckling load of composite cylindrical shells are discussed in detail by using MATLAB. The results show that the cylindrical shell has the strongest ability to resist buckling under the condition of clamped boundary, while the cylindrical shell is most prone to buckle under the free boundary condition, but the difference will gradually decrease with the propagation of stress wave. With the increase of the ratio of diameter to thickness, the higher modes of composite cylindrical shells will occur more easily. Taking into account the geometric nonlinear terms of structural deformation, the governing equations of large deflection of composite cylindrical shells are obtained by using the nonlinear large deflection theory of cylindrical shells and based on the stress function and Hamilton principle. The nonlinear dynamic control equations with single degree of freedom can be obtained by using Ritz method and Galerkin method. The bifurcation diagram, phase plane and Poincar 茅 map of the system are obtained by using the fourth-order Runge-Kutta method. The motion state of the system is discussed in detail. The results show that the periodic motion and chaotic motion of composite cylindrical shells alternate with the increase of lateral load amplitude.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB33

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