摘要
采用谱几何法(spectro-geometric method,简称SGM)分析了弹性边界条件下圆板横向自由振动特性。首先,将圆板的振动位移容许函数描述为一种谱形式的改进三角级数,并采用沿边界均匀分布的约束弹簧来模拟弹性边界条件;然后,将未知级数展开系数看作广义变量,应用瑞利-里兹法从能量的角度推导弹性边界条件下圆板结构横向自由振动系统特征矩阵方程;最后,设计搭建了相关实验台架,对圆板结构横向自由振动模态参数进行测试。将文中方法计算结果与文献解、有限元计算结果和实验结果进行对比,验证了谱几何法求解圆板横向自由振动问题的正确性和计算精度。
The free transverse vibration of circular plates with elastic boundary conditions was carried out using the Spectro-Geometric method.First,the displacement admissible function was invariantly expressed in spectral form as an improved trigonometric series expansion.Elastic boundary supports were physically realized by setting restraining springs along the edge with the current method.Then,the unknown series expansion coefficients were treated as the generalized coordinates,and the Rayleigh-Ritz method was employed to derive the characteristic equation for the circular plate with elastic boundary support.Finally,the corresponding experimental setup was constructed,and the experimental study was performed.The numerical results and the comparison between the reference results,finite element software(FEA)results,and test results demonstrated the correctness of the current method.
出处
《振动．测试与诊断》
EI
CSCD
北大核心
2016年第5期984-989,共6页
Journal of Vibration,Measurement & Diagnosis
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资助项目(计算固体力学)
关键词
圆板
横向自由振动
谱几何法
弹性边界条件
circular plates
free transverse vibration
spectro-geometric method(SGM)
elastic boundary conditions
