Parametric instability of a spinning pretwisted beam under periodic axial force
The authors deal with the parametric instability of a cantilever pretwisted Bernoulli-Euler beam rotating around its longitudinal axis under a time-dependent conservative and axial force which contains a steady-state part and a small periodically fluctuating component. Using Hamilton's principle, the equation of motion governing transverse vibrations is derived taking into acount rotation inertia, viscous damping and conservative end axial forces. Applying the Galerkin method, associated finite element equations of motion are obtained, which are then transformed into a system of first-order differential equations solved by method of multiple scales. Numerical results demonstrating the effects of pretwist angle, spinning speed and steady-state part of the end axial force on instability regions are plotted into a great number of diagrams.
scientific article; zbMATH DE number 762329