Abstract:

A theoretical model for the multi-span spinning beams with elastic constraints under an axial compressive force is proposed. The displacement and bending angle functions are represented through an improved Fourier series, which ensures the continuity of the derivative at the boundary and enhances the convergence. The exact characteristic equations of the multi-span spinning beams with elastic constraints under an axial compressive force are derived by the Lagrange equation. The efficiency and accuracy of the present method are validated in comparison with the finite element method (FEM) and other methods. The effects of the boundary spring stiffness, the number of spans, the spinning velocity, and the axial compressive force on the dynamic characteristics of the multi-span spinning beams are studied. The results show that the present method can freely simulate any boundary constraints without modifying the solution process. The elastic range of linear springs is larger than that of torsion springs, and it is not affected by the number of spans. With an increase in the axial compressive force, the attenuation rate of the natural frequency of a spinning beam with a large number of spans becomes larger, while the attenuation rate with an elastic boundary is lower than that under a classic simply supported boundary.

Key words: multi-span spinning beam, elastic constraint, improved Fourier series, free vibration, semi-analytical solution