基于切比雪夫里兹法的变厚度锥形环盘三维振动特性分析

Three-dimensional Vibration Analysis of Linearly Tapered,Annular Plates Based on Chebyshev-Ritz Method

为更全面地反映变厚度锥形厚环盘的振动特性以及满足机械加工对其高阶频率的需求,提出基于三维弹性振动理论,应用里兹法,以切比雪夫多项式与相应边界条件的乘积作为容许函数,得到特征值方程,进而求得环盘固有频率。对该方法的计算结果进行了收敛性验证以确保该方法的准确性。并与采用代数多项式与相应边界条件乘积作为容许函数的里兹法的计算结果进行比较,由于切比雪夫相较于代数多项式拥有更好的数值稳定性,切比雪夫里兹法可以求得较为准确的结果。

To reflect the vibration more comprehensively and obtain more accurate high order frequencies for machining,a three-dimensional free vibration analysis of thick,linearly tapered,annular plate is presented through Ritz method.The admissible function is made up of Chebyshev polynomial multiplying boundary functions.The governing eigenvalue equations can be derived through ritz method.The solution procedure is based on three-dimensional elasticity theory.Convergence study is made to ensure the accuracy of Chebyshev-Ritz method.Because the Chebyshev polynomials possesses better numerical stability,the method can obtain more accurate eigenvalues than the Ritz method presented whose admissible function is made up of Algebraic polynomial multiplying boundary function.