弹性边界约束圆环薄板面内振动特性分析
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- 英文论文题名：In-plane vibration characteristics analysis of circular annular plate with elastically restrained edges
- 论文作者：吕朋 ; 杜敬涛 ; 许得水 ; 刘志刚
- 英文论文作者：1Lv Peng ; Du Jingtao ; Xu Deshui ; Liu Zhigang ; College of Power and Energy Engineering ; Harbin Engineering University
- 年：2016
- 作者机构：哈尔滨工程大学动力与能源工程学院;
- 论文关键词：圆环薄板 ; 面内振动 ; 傅里叶级数 ; 弹性边界约束
- 英文论文关键词：circular annular plate ; in-plane vibration ; Fourier series ; elastic restraint edges
- 会议召开时间：2016-07-28
- 会议录名称：第二十七届全国振动与噪声应用学术会议论文集
- 语种：中文
- 分类号：O327
- 学会代码：ZDZD
- 会议名称：第二十七届全国振动与噪声应用学术会议
- 会议地点：中国黑龙江哈尔滨
- 主办单位：中国振动工程学会振动与噪声控制专业委员会
- 学会名称：中国振动工程学会振动与噪声控制专业委员会
- 页数：4
- 文件大小：1163k
- 原文格式：D
- 会议级别：全国
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。
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.
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.
引文
[1]A.W.Leissa.The free vibration of rectangular plates[J].Journal of Sound and Vibration,1973,31:257-293
[2]K.M.Liew,K.Y.Lam,S.T.Chow.Free vibration analysis of rectangular plates using orthogonal plate function[J].Computers and Structures,1990,34:79-85
[3]W.L.Li.Vibration analysis of rectangular plates with general elastic boundary supports[J].Journal of Sound and Vibration,2004,273:619-635
[4]A.W.Leissa.Vibration of plates.Acoustical Society of America,1993
[5]钱民刚.扇形板自由振动的Fourier-Bessel级数解[J].北京建筑工程学院学报,2006,22(3):61-64,79
[6]R.H.Lyon.In-plane contribution to structural noise transmission[J].Noise Control Engineering Journal,1986,26(1):22-27.
[7]G.Wang,N.M.Wereley.Free in-plane vibration of rectangular plates[J].AIAA journal,2002,40(5):953-959.
[8]刘剑,赵淳生.基于矩形薄板面内振动的直线型超声电机的研究[J].声学学报,2003,28(1):86-90
[9]A.N.Bercin,Application of the dynamic stiffness technique to the in-plane vibrations of plate structures[J].Computers and Structures,1996,59(6):869-875
[10]N.S.Bardell,On the free in-plane vibration of isotropic rectangular plates[J].Journal of Sound and Vibration,1996,191(3),459-467
[11]K.Hyde,Parameter studies for plane stress in-plane vibration of rectangular plates[J].Journal of Sound and Vibration,2001247(3),471-487
[12]Y.F.Xing,B.Liu,Exact solutions for the free in-plane vibrations of rectangular plates[J].International Journal of Mechanical Sciences,2009,52:246-255
[13]Jingtao Du,Wen L.Li,Guoyong Jin.An analytical method for the in-plane vibration analysis of rectangular plates with elastically restrained edges[J].Journal of Sound and Vibration,2007,306:908-927
[14]G.Ambati.In-plane vibration of annular rings[J].Journal of Sound and Vibration,1976,47(3):415-432
[15]T Irie,G Yamada,Y Muramoto.Natural frequencies of in-plane vibration of annular plates[J].Journal of Sound and Vibration,1984,97(1):171-175
[16]S Bashmal.In-plane free vibration of circular annular disks[J].Journal of Sound and Vibration,2009,322:216-226
[17]蒲育,滕兆春,房晓林.圆环板面内自由振动的DQM求解[J].振动与冲击,2013 32(24):152-156
[2]K.M.Liew,K.Y.Lam,S.T.Chow.Free vibration analysis of rectangular plates using orthogonal plate function[J].Computers and Structures,1990,34:79-85
[3]W.L.Li.Vibration analysis of rectangular plates with general elastic boundary supports[J].Journal of Sound and Vibration,2004,273:619-635
[4]A.W.Leissa.Vibration of plates.Acoustical Society of America,1993
[5]钱民刚.扇形板自由振动的Fourier-Bessel级数解[J].北京建筑工程学院学报,2006,22(3):61-64,79
[6]R.H.Lyon.In-plane contribution to structural noise transmission[J].Noise Control Engineering Journal,1986,26(1):22-27.
[7]G.Wang,N.M.Wereley.Free in-plane vibration of rectangular plates[J].AIAA journal,2002,40(5):953-959.
[8]刘剑,赵淳生.基于矩形薄板面内振动的直线型超声电机的研究[J].声学学报,2003,28(1):86-90
[9]A.N.Bercin,Application of the dynamic stiffness technique to the in-plane vibrations of plate structures[J].Computers and Structures,1996,59(6):869-875
[10]N.S.Bardell,On the free in-plane vibration of isotropic rectangular plates[J].Journal of Sound and Vibration,1996,191(3),459-467
[11]K.Hyde,Parameter studies for plane stress in-plane vibration of rectangular plates[J].Journal of Sound and Vibration,2001247(3),471-487
[12]Y.F.Xing,B.Liu,Exact solutions for the free in-plane vibrations of rectangular plates[J].International Journal of Mechanical Sciences,2009,52:246-255
[13]Jingtao Du,Wen L.Li,Guoyong Jin.An analytical method for the in-plane vibration analysis of rectangular plates with elastically restrained edges[J].Journal of Sound and Vibration,2007,306:908-927
[14]G.Ambati.In-plane vibration of annular rings[J].Journal of Sound and Vibration,1976,47(3):415-432
[15]T Irie,G Yamada,Y Muramoto.Natural frequencies of in-plane vibration of annular plates[J].Journal of Sound and Vibration,1984,97(1):171-175
[16]S Bashmal.In-plane free vibration of circular annular disks[J].Journal of Sound and Vibration,2009,322:216-226
[17]蒲育,滕兆春,房晓林.圆环板面内自由振动的DQM求解[J].振动与冲击,2013 32(24):152-156