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基于傅里叶级数法的开孔板振动固有特性分析

王旻昊 李凯 邱永康 李天匀 朱翔

王旻昊, 李凯, 邱永康, 李天匀, 朱翔. 基于傅里叶级数法的开孔板振动固有特性分析[J]. 中国舰船研究, 2017, 12(4): 102-109. doi: 10.3969/j.issn.1673-3185.2017.04.016
引用本文: 王旻昊, 李凯, 邱永康, 李天匀, 朱翔. 基于傅里叶级数法的开孔板振动固有特性分析[J]. 中国舰船研究, 2017, 12(4): 102-109. doi: 10.3969/j.issn.1673-3185.2017.04.016
Minhao WANG, Kai LI, Yongkang QIU, Tianyun LI, Xiang ZHU. Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method[J]. Chinese Journal of Ship Research, 2017, 12(4): 102-109. doi: 10.3969/j.issn.1673-3185.2017.04.016
Citation: Minhao WANG, Kai LI, Yongkang QIU, Tianyun LI, Xiang ZHU. Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method[J]. Chinese Journal of Ship Research, 2017, 12(4): 102-109. doi: 10.3969/j.issn.1673-3185.2017.04.016

基于傅里叶级数法的开孔板振动固有特性分析

doi: 10.3969/j.issn.1673-3185.2017.04.016
基金项目: 

国家自然科学基金资助项目 51379083

国家自然科学基金资助项目 51579109

详细信息
    作者简介:

    王旻昊, 男, 1992年生, 硕士生。研究方向:结构振动噪声, 机械结构静、动力学仿真分析。E-mail:710959552@qq.com

    通讯作者:

    李天匀(通信作者), 男, 1969年生, 教授, 博士生导师。研究方向:结构振动噪声分析。E-mail:ltyz801@hust.edu.cn

  • 中图分类号: U661.44

Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method

  • 摘要:   目的  开口板结构普遍存在于各类工程结构中,对其振动特性的研究直接关系到整体结构的减振降噪和稳定性分析。为研究针对弹性薄板在任意位置开与板平行的矩形口的自由振动特性研究问题,  方法  通过改进傅里叶级数形式表示开口矩形板的位移容许函数,用区域划分思想将开口板沿开口延伸线划分为多个区域板,采用沿边界均匀分布的线性模拟弹簧模拟经典边界条件和区域板间连续边界条件,将边界表达为弹性势能的形式,从而将有约束问题转化为无约束问题,并结合位移连续条件和能量泛函变分方法,对未知傅里叶展开系数一次变分求极值以求解标准特征值方程。然后将得到的开口矩形板的固有频率值及其对应振型与有限元软件(ANASYS)计算结果进行对比,最后分析不同边界条件、开口尺寸和开口位置对开口板自振特性的影响。  结果  结果验证了方法的有效性和精确性,  结论  所得结果可为相关实际工程应用提供理论参考。
  • 图  1  开口矩形板示意图

    Figure  1.  Rectangular plate with a rectangular opening

    图  2  开口板物理模型描述图

    Figure  2.  Physical model of rectangular plate with an opening

    图  3  开口板前4阶振型对比图

    Figure  3.  Comparison of the first four order modes of rectangular plate with a rectangular opening

    图  4  不同边界下开口板前6阶固有频率对比图

    Figure  4.  Natural frequencies of rectangular plate with square opening in different boundaries

    图  5  SS-SS边界下开口板前6阶固有频率对比图

    Figure  5.  Natural frequencies of rectangular plate with different rectangular openings in SS-SS boundary

    图  6  F-F边界下开口板前6阶固有频率对比图

    Figure  6.  Natural frequencies of rectangular plate with different rectangular openings in F-F boundary

    图  7  开口位置分布描述图

    Figure  7.  The opening position of rectangular plate

    图  8  C-F边界下开口板前3阶固有频率对比图

    Figure  8.  Natural frequencies of rectangular plate with different opening positions in C-F boundary

    表  1  C-F边界下开口板固有频率

    Table  1.   Natural frequencies of rectangular plate with a rectangular opening in C-F boundary

    截断项 模态阶数
    1 2 3 4 5 6
    M=N=7 4.18 6.63 10.16 11.99 13.35 16.78
    M=N=8 3.95 6.39 9.76 11.4 12.71 15.88
    M=N=9 3.94 6.38 9.74 11.39 12.7 15.85
    M=N=10 3.94 6.37 9.73 11.37 12.69 15.82
    M=N=11 3.93 6.37 9.72 11.37 12.68 15.81
    M=N=12 3.93 6.37 9.72 11.37 12.68 15.80
    M=N=13 3.93 6.37 9.72 11.37 12.68 15.80
    M=N=14 3.93 6.37 9.72 11.37 12.68 15.80
    M=N=15 3.93 6.37 9.72 11.37 12.68 15.80
    FEM 3.93 6.37 9.72 11.37 12.69 15.80
    下载: 导出CSV

    表  2  不同位移约束弹簧刚度K′的开口板固有频率

    Table  2.   Natural frequencies of rectangular plate with a rectangular opening in different K

    K'/(N·m-1 模态阶数
    1 2 3 4 5 6
    F-F(FEM) 1.24 1.48 2.60 3.18 3.82 4.41
    0 1.24 1.48 2.60 3.18 3.82 4.42
    101 1.24 1.49 2.60 3.18 3.82 4.42
    103 1.33 1.26 2.65 3.22 3.86 4.44
    106 1.95 3.88 5.43 7.15 7.76 9.25
    109 2.04 4.14 5.83 8.04 8.65 10.40
    1010 2.04 4.14 5.83 8.04 8.65 10.40
    1011 2.04 4.14 5.83 8.04 8.65 10.40
    1012 2.04 4.14 5.82 8.04 8.65 10.40
    SS-F(FEM) 2.04 4.13 5.82 8.03 8.65 10.38
      注:FEM为ANSYS有限元软件计算结果。
    下载: 导出CSV

    表  3  SS-SS边界条件下不同开口尺寸开口板固有频率表

    Table  3.   Natural frequencies of rectangular plate with different rectangular openings in SS-SS boundary

    ξ 模态阶数
    1 2 3 4 5 6
    0.1 5.89 5.92 7.93 8.87 11.07 13.3
    0.3 8.81 8.81 11.58 11.85 13.69 15
    0.5 14.88 14.88 19.64 19.64 23.24 23.8
    0.7 36.22 36.22 41.94 41.95 49.9 49.9
    0.9 308.72 308.72 313.33 313.33 320.99 320.99
    下载: 导出CSV
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出版历程
  • 收稿日期:  2017-01-03
  • 网络出版日期:  2017-07-27
  • 刊出日期:  2017-08-04

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