基于切比雪夫-里兹法的圆截面锥形杆三维振动特性

为了更全面的反应圆截面锥形杆的振动特性及获得更精确的高阶振动频率,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,进而求得圆截面锥形杆的固有频率,并对该方法的收敛性进行了验证。结果表明,由于切比雪夫多项式具有更好的数值稳定性,对于不同振动模式,切比雪夫-里兹法至少可以确定锥形杆前15阶固有频率,而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,其最多可以确定前3阶固有频率。

Three-dimensional vibration analysis of tapered rods with circular cross-section throughChebyshev-Ritz method

To reflect the vibration more comprehensively and obtain more accurate high order frequencies for machining, a three-dimensional free vibration analysis of thick, tapered rods with circular cross-section is presented through ritz method. The admissible function is made up of Chebyshev polynomial multiplying boundary functions. The governing eigenvalue equationscan be derived through ritz method. The solution procedure is based on three-dimensional elasticity theory.The accuracy was demonstrated by convergence study along with the increase of the number of the admissible functions contained Chebyshev polynomial. The ritz method whose admissible function is made up of Algebraic polynomial multiplying boundary function has three accurate eigenvalues at most for each vibration mode of different mode rods, however, the method presented in this article can ensure fifteen accurate eigenvalues at least.