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
WANG Minhao, LI Kai, QIU Yongkang, LI Tianyun, ZHU Xiang. 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: WANG Minhao, LI Kai, QIU Yongkang, LI Tianyun, ZHU Xiang. 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

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。

     

    Abstract: Plate structures with openings are common in many engineering structures. The study of the vibration characteristics of such structures is directly related to the vibration reduction, noise reduction and stability analysis of an overall structure. This paper conducts research into the free vibration characteristics of a thin elastic plate with a rectangular opening parallel to the plate in an arbitrary position. We use the improved Fourier series to represent the displacement tolerance function of the rectangular plate with an opening. We can divide the plate into an eight zone plate to simplify the calculation. We then use linear springs, which are uniformly distributed along the boundary, to simulate the classical boundary conditions and the boundary conditions of the boundaries between the regions. According to the energy functional and variational method, we can obtain the overall energy functional. We can also obtain the generalized eigenvalue matrix equation by studying the extremum of the unknown improved Fourier series expansion coefficients. We can then obtain the natural frequencies and corresponding vibration modes of the rectangular plate with an opening by solving the equation. We then compare the calculated results with the finite element method to verify the accuracy and effectiveness of the method proposed in this paper. Finally, we research the influence of the boundary condition, opening size and opening position on the vibration characteristics of a plate with an opening. This provides a theoretical reference for practical engineering application.

     

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