具有附加弹性支承的圆形薄板结构振动分析

Vibration Analysis of a Thin Circular Plate with Additional Elastic Supports Attached

采用瑞利-里兹法对采用附加弹性铰支承的圆形薄板结构进行振动分析,研究不同约束边界条件下,支承的刚度、数量、位置对圆板结构振动特性(频率、振型)的影响。采用正交梁多项式作为圆板的径向试函数,用傅里叶级数作为圆板的周向试函数,保证了振动特征参数计算结果的完备性和准确性。通过一些经典算例分析附加支承的数量、刚度和位置等对圆板结构固有频率的影响规律,揭示圆形薄板附加支承对称布局的重要性。

The Rayleigh-Ritz method is employed to analyze the vibration properties of a thin circular plate structure with additional elastic pin supports.The influences of stiffness,number and position of the supports on the vibration performance(frequency and modal) of the thin circular plate under different constraint boundary conditions are analyzed.The orthogonal polynomials are exploited for the admissible functions in the radial direction,while the full Fourier series is chosen as the trial functions in the circumferential direction,so as to ensure the completeness and correctness of the computation results of the characteristic parameters.The feasibility and accuracy of the method are verified by the simulation of several typical thin circular plates with additional supports under conventional boundary restraint conditions.Moreover,the influences of the stiffness,number and positions of the supports on the frequencies and modes of the circular plate are explored.The importance of the symmetric layout of the additional supports is revealed.