摘要
采用一种改进傅立叶级数方法建立了热环境下弹性边界约束FGM圆环薄板面内振动特性分析模型。基于平面弹性理论应力-应变关系推导了热环境下FGM圆环板面内振动能量原理方程,其中,弹性边界条件通过边界弹簧沿边界分布进行模拟,任意边界条件可以相应设置刚度系数获得。为了改善面内耦合位移场函数在径向边界处连续微分特性,圆环板面内位移径向分量构造为标准傅里叶级数与边界光滑多项式的叠加形式。结合RayleighRitz步骤,热环境下弹性边界约束FGM圆环板结构模态信息可以通过求解一个标准特征值问题而全部得到。随后,通过给出相关数值算例对所建立模型进行了验证,并分析了复杂边界约束情况下圆环板结构面内振动特性的影响。在此基础上,继续探讨并研究了热环境条件、功能梯度材料指数、弹性边界约束刚度等重要参数对FGM圆环薄板面内振动特性的影响规律,为人们全面理解此类复杂结构动力学特性提供了有效的模型基础和分析手段。
In this paper, an improved Fourier series method is employed to establish the theoretical model for investigating the in-plane vibration characteristics of elastically restrained FGM annual panel in thermal environment. Based on the plane stress- strain relation in elasticity theory, the energy equation for in-plane vibration of FGM annual panel in thermal environment is formulated, in which the elastic boundary constraint is introduced in terms of potential energy stored in the springs distributed along the boundary, so that any boundary condition can be easily obtained by setting the stiffness coefficient accordingly. In or-der to improve the continuous differentiability of the radial component of in-plane coupling displacement field functions at the outer boundary, the radial component of the in-plane displacement of the annual panel is constructed as the superposition of Fourier series and the boundary-smooth polynomials. In conjunction with Rayleigh-Ritz procedure, all the modal information of the elastically restrained FGM annual panel in thermal environment can be solved from a standard eigenvalue matrix problem. Then, numerical examples are presented to validate the proposed model, and the in-plane modal characteristics of the annual panel with complicated boundary conditions are analyzed. Based on the established model, the influence of the important pa-rameters , such as the thermal environment condition, FGM power-law exponent and boundary restraints,on the in-plane vi-bration characteristics of FGM circular annular panel is addressed and investigated. It is believed that this work can provide an effective tool for a better understanding of the dynamic characteristics of such complex structures.
出处
《振动工程学报》
EI
CSCD
北大核心
2017年第5期713-723,共11页
Journal of Vibration Engineering
基金
中央高校基本科研基金资助项目(HEUCFP201758)
关键词
弹性振动
FGM圆环板
面内振动
热环境
弹性边界约束
elastic vibration
FGM circular annular panel
in-plane vibration
thermal environment
elastic boundary restraints
