摘要
对热载荷和机械载荷共同作用下的功能梯度圆锥扁壳进行了1:2内共振分析。假设材料属性与温度有关,材料组分沿厚度方向呈幂律梯度变化,基于一阶剪切变形理论和von-Karman几何非线性关系,运用Hamilton原理建立功能梯度圆锥扁壳的非线性动力学方程;采用Galerkin法将运动控制方程离散成一个两自由度非线性动力学系统,采用多尺度法对上述方程进行摄动分析,获得了系统的平均方程,进一步得到频率响应函数和力幅响应函数。研究了材料体积分数指数和面内载荷对幅-频响应特性的影响,结果表明:研究可以得出:改变材料体积分数指数会影响材料中金属的含量及分布,从而引起幅-频响应曲线刚度特性和共振峰带宽的变化;面内载荷的变化不会影响幅-频响应曲线的刚度特性,但是会改变共振峰的带宽。本文还研究了振幅跳跃现象,通过Runge-Kutta法对共振系统进行数值仿真,研究了面内载荷对系统非线性动力学行为的影响,得出:随着面内载荷的变化,系统的运动从周期运动经历概周期运动变成混沌运动。
The 1:2 internal resonance analysis of a FGM shallow conical shell subjected to the thermal load and mechanical load are investigated in this paper. Material properties of the constituents are assumed to be temperature-dependent and the effective properties of FGM shallow conical shell are graded in thickness direction according to a power law distribution. Based on first-order shear deformation theory and von-Karman type nonlinear strain-displacement relationship, the nonlinear governing equations of motion for the shell are obtained by the Hamilton's principle. Galerkin's method is utilized to discrete the governing partial differential equations to a two-degree-of-freedom nonlinear system. Then the averaged equations of the system are obtained by using the method of multiple scales. The frequency-response functions and the force-response functions are derived by the averaged equations. The effects of volume fraction exponent and in-plane load on frequency-response characteristics are investigated, and it is concluded that changing the volume fraction exponent affects the content and distribution of the material, thus make the stiffness characteristics and bandwidth of the frequency-response change. It is found that the stiffness characteristic of frequency-response will not change with the variation of in-plane load, but the bandwidth of formant will change. And amplitude jump phenomenon is studied, too. Runge-Kutta method is applied for numerical simulation, and the influences of the in-plane load are researched. Then in-plane load are changed under certain conditions to get different forms of motion. As the changing of in-plane load, the system experiences from periodic motion, then quasi-periodic motion and finally chaotic motion.
出处
《应用力学学报》
CAS
CSCD
北大核心
2016年第1期36-42,178,共7页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(11272063)
北京市属高等学校高层次人才引进与培养三年行动计划(2013年-2015年)青年拔尖人才培育计划(CIT&TCD201304112)
关键词
功能梯度材料
圆锥扁壳
非线性动力学
1:2内共振
多尺度法
functionally graded materials
shallow conical shell
nonlinear dynamics
1
2 internal resonance
method of multiple scales
作者简介
牛燕，女，1990年生，北京信息科技大学，硕士生；研究方向——非线性动力学与控制。E—mail：niuyanny@163．com
