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。
In this study,the free in-plane vibrations of annular plates with elastic boundary supports are investigated with spectro-geometric method(SGM).The elastic boundary conditions can be physically simulated by setting tangential and normal constraining springs along each boundary edge in this approach.The displacement admissible functions are invariantly expressed in spectral form as an improved trigonometric series expansion,where the sine series is introduced to eliminate all the relevant discontinuities or jumps of elastic boundary conditions.The series expansion coefficients are taken as the generalized coordinates and are determined using the Rayleigh-Ritz technique.A standard eigenvalue problem concerning the unknown series expansion coefficients is derived,from which the natural frequencies and mode shapes can be solved readily.Various numerical examples are presented and compared with the results published in literatures and of finite element method to demonstrate the effectiveness and validity of the current method.
出处
《振动工程学报》
EI
CSCD
北大核心
2016年第3期465-471,共7页
Journal of Vibration Engineering
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"
关键词
环板
面内振动
谱几何法
弹性边界条件
annular plates
in-plane vibration
spectro-geometric method(SGM)
elastic boundary conditions
