环板结构面内自由振动特性分析
发布时间：2018-08-05 19:09
【摘要】：采用谱几何法(Spectro-Geometric Method,SGM)对弹性边界条件下环板结构的面内自由振动特性进行计算分析,弹性边界条件采用沿各边界均匀分布的法向和切向线性弹簧来模拟。板结构的位移容许函数被不变地描述为一种谱形式的改进三角级数,正弦三角级数项的引入能够有效地克服弹性边界处潜在的不连续或跳跃现象。将位移容许函数的级数展开系数看作广义坐标,并采用瑞利-里兹法对其进行求解,得到一个关于级数展开系数的标准特征值问题。通过求解标准特征值问题而简便地求解环板结构面内自由振动固有频率及其振型。通过不同数值算例,并与现有文献解及有限元法计算结果进行对比,验证了文中方法的正确性。
[Abstract]:The in-plane free vibration characteristics of annular plate structures under elastic boundary conditions are calculated and analyzed by Spectro-Geometric method. The elastic boundary conditions are simulated by normal and tangential linear springs distributed uniformly along each boundary. The displacement-tolerance function of plate structure is described as an improved trigonometric series in spectral form. The introduction of sinusoidal trigonometric series can effectively overcome the potential discontinuity or jump phenomenon at the elastic boundary. The series expansion coefficient of the displacement-admissible function is regarded as a generalized coordinate and solved by Rayleigh-Ritz method, and a standard eigenvalue problem for the expansion coefficient of the series is obtained. By solving the standard eigenvalue problem, the natural frequencies and modes of in-plane free vibration of annular plate structures are solved simply. The correctness of the proposed method is verified by comparing the numerical results with the existing literature and the results of finite element method (FEM).
【作者单位】： 中国工程物理研究院总体工程研究所;哈尔滨工程大学机电工程学院;
【基金】：国家自然科学基金资助项目(51505445) 中国工程物理研究院重点学科项目“计算固体力学”
【分类号】：O327
本文编号：2166721
[Abstract]:The in-plane free vibration characteristics of annular plate structures under elastic boundary conditions are calculated and analyzed by Spectro-Geometric method. The elastic boundary conditions are simulated by normal and tangential linear springs distributed uniformly along each boundary. The displacement-tolerance function of plate structure is described as an improved trigonometric series in spectral form. The introduction of sinusoidal trigonometric series can effectively overcome the potential discontinuity or jump phenomenon at the elastic boundary. The series expansion coefficient of the displacement-admissible function is regarded as a generalized coordinate and solved by Rayleigh-Ritz method, and a standard eigenvalue problem for the expansion coefficient of the series is obtained. By solving the standard eigenvalue problem, the natural frequencies and modes of in-plane free vibration of annular plate structures are solved simply. The correctness of the proposed method is verified by comparing the numerical results with the existing literature and the results of finite element method (FEM).
【作者单位】： 中国工程物理研究院总体工程研究所;哈尔滨工程大学机电工程学院;
【基金】：国家自然科学基金资助项目(51505445) 中国工程物理研究院重点学科项目“计算固体力学”
【分类号】：O327
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