An analytical investigation on large post-buckling behavior of a drilling shaft modeled as a rotating beam with various boundary conditions. (November 2018) - Yu, Yongping; Chen, Lihui; Sun, Weipeng; Zeng, Baihui; Sun, Youhong
Highlights: Large post-buckling of a rotating beam with various boundary conditions is studied. Analytical solutions are obtained with improved harmonic balance and Galerkin method. Expressions of analytical approximate solutions are explicit and brief. Compared to numerical solution, accuracy of the approximate one is substantiated. Effects of system parameters on post-buckling of a rotating beam are surveyed. Abstract: Post-buckling behavior of a drilling shaft modeled as a rotating beam subjected to terminal force is investigated in this paper. Three boundary conditions: clamped-clamped, clamped-free, and clamped-hinged are considered. Classical Bernoulli-Euler beam model including shear force is applied to depict the problem. In particular, for clamped-hinged ends boundary condition, the analytical approximate solutions are more difficult to construct, due to asymmetric boundary and configuration. Unlike numerical results in the existing literatures, analytical approximate solutions of the problem above are established via combining the Maclaurin series expansion, orthogonal Chebyshev polynomials, Galerkin and Harmonic balance method in this paper. Compared with numerical solutions obtained by using the shooting method on the exact governing equation, the approximate analytical solutions here show excellent accuracy and rapid convergence. The effect of the system parameters on the dynamic response and stability of system can conveniently be investigated via the present analytical approximate solutions. In conclusion, the analytical approximate solutions presented here are sufficiently precise for a wide range of the maximum angle of the rotating beam. Graphical abstract: Analytical approximate solutions of large post-buckling behavior of a drilling shaft modeled as a rotating beam subjected to terminal force with various boundary conditions are established via combining the Maclaurin series expansion, orthogonal Chebyshev polynomials, Galerkin and Harmonic balance method.