功能梯度夹层双曲抛物壳非线性动力学研究

项目名称： 功能梯度夹层双曲抛物壳非线性动力学研究

项目编号： No.11472056

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 郝育新

作者单位： 北京信息科技大学

项目金额： 82万元

中文摘要： 功能梯度夹层结构由于其在芯层和表层材料之间的梯度变化，可以有效地避免夹层结构的脱层、裂纹和应力集中等现象，增强夹层结构的力学性能。功能梯度夹层壳体结构常处于复杂的工作环境中，会受到多种载荷耦合作用等各种负面影响，往往会引起系统复杂的非线性动力学现象，现已成为工程实际应用中非常重要的关键性技术问题。本项目将在Reddy高阶剪切变形理论的基础上，构建一个不仅考虑横向剪切变形，同时还考虑横向拉伸/压缩影响的功能梯度夹层结构的、运算简便的新的位移场。在此基础上，分别以具有功能梯度芯层和表层结构的双曲抛物壳为研究对象，建立其几何非线性动力学方程，深入研究系统几何和物理参数对系统非线性动力学行为的影响、分析该类非线性动力学系统的全局分叉和发生混沌运动的规律。通过近似解和数值计算相结合的方法研究其共振响应特性，给出系统在自由振动和外载荷作用的强迫振动幅-频响应曲线。

中文关键词： 非线性动力学；功能梯度；夹层；分岔与混沌；双曲抛物壳

英文摘要： Because of the gradual variation of the material properties at the facesheet-core interface, Functionaly graded materials (FGM) sandwich structures can alleviate the phenomenon of stress concentration at the face sheet-core interface, interfacial debonding and crack, and can enhanced their mechanical properties. It is known that FGM sandwich structures are always in complicated environment. When we take some coupled force into account, the nonlinear dynamic responses of these structures are very complex. It has been very important technical problems in engineering application. The aim of this term focuses on research of nonlinear dynamics of FGM sandwich doubly curved parabolic shells whose structures are the homogeneous facesheet with FGM core and FGM facesheet with homogeneous core, respectively. Based on the Reddy's third shear deformation theory, a new theory is presented which not only takes the transverse shear deformation into account but also the transverse normal stress and strain. The geometrically nonlinear dynamic governing equations are derived in the framework of shear deformation shell theory considering the effect of transverse normal stress. We study influence of the geometry and physical parameters of on the nonlinear dynamics of the FGM sandwich doubly curved parabolic shells. The results of numerical simulations will be used to analyze the global bifurcation and chaotic motions. Perturbation techniques combined the numerical simulations are performed to study the internal resonance.

英文关键词： nonlinear dynamics;functionally graded;sandwich;bifurcations and chaos;doubly curved parabolic shells