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该文提出采用分段转换B3样条插值函数模拟横截面的翘曲位移,利用有限杆元对薄壁曲梁进行振动分析的样条有限杆元法。方法采用静力分析中位移的精确解代替振动时的可能位移,应用Hamilton变分原理导出刚度矩阵,形成有限元列式,进而求出薄壁曲梁的振动频率和相应的振型,并用ANSYS有限元程序进行校核。数值算例表明:方法具有前处理简单、收敛速度快、精度高等特点。
In this paper, a spline finite element method is proposed to simulate the warping displacement of a cross-section using the B3-spline interpolation function and the finite element method for the vibration analysis of the thin-walled curved beam. Methods By using the exact solution of the displacement in static analysis instead of the possible displacement of vibration, the stiffness matrix is derived by using the Hamilton variational principle to form the finite element formulation. Then the vibration frequencies and the corresponding vibration modes of the thin-walled curved beam are obtained and compared with ANSYS Finite element program to check. The numerical example shows that the method has the advantages of simple preprocessing, fast convergence and high accuracy.