【作者】 吕朋； 杜敬涛； 许得水； 刘志刚；

【Author】 1Lv Peng;Du Jingtao;Xu Deshui;Liu Zhigang;College of Power and Energy Engineering, Harbin Engineering University;

【机构】 哈尔滨工程大学动力与能源工程学院；

【摘要】 本文应用改进傅里叶级数方法建立了弹性边界约束条件下圆环薄板面内振动特性分析模型。基于平面弹性理论,对圆环薄板面内振动采用能量原理进行描述,弹性边界约束以边界存储势能的形式引入系统运动方程。圆环薄板面内振动耦合位移场表示为周向和径向位移乘积形式,为改善径向位移级数解的收敛性,在圆环内外径边界分别构造相应的辅助多项式,以使面内位移函数在边界各阶导数足够连续。随后,结合瑞利-里兹方法,推导出圆环面内振动分析特征方程。求解特征方程得到弹性边界约束圆环薄板面内振动固有频率及相关振型。基于所建立模型,讨论分析了边界约束刚度对圆环板面内振动特性的影响规律。更多还原

【Abstract】 In this paper, an improved Fourier series method is employed for the modeling of in-plane vibration of circular annular panel with elastically restrained edges. Based the plane elasticity theory, in-plane vibration of circular annular panel is described via the energy principle, in which the elastically retrained edges is introduced into the system formulation in the form of potential energy. The in-plane coupled displacement fields are expressed as the product of circumferential and radial components, and the supplementary polynomials are introduced into the standard Fourier series solution of radial displacement on the inner and outer edges with the purpose of make its relevant differential sufficiently smooth. Rayleigh-Ritz procedure is then used to obtain the system characteristic equation. In the numerical simulation section, the correctness and reliability of the proposed model is validated through the comparison with those available in literature and calculated from FEA. All the boundary conditions can be easily realized by adjusting the restraining stiffness on each edge in the current framework. Based on the model established, the influence of boundary restraints on the in-plane modal characteristics of circular annular panel is discussed and analyzed.更多还原