Dynamic behavior analysis of a spinning Timoshenko beam-rigid disk with nonlinear elastic boundaries under axial loading

In this study, an attempt is made to model and investigate the dynamic behavior of the spinning Timoshenko beam-disk with nonlinear elastic boundaries, in which an unbalanced concentrated mass and axial loads are considered. In order to satisfy the elastic boundary conditions of the spinning beam-disk containing translational and rotational stiffnesses as well as nonlinear stiffnesses, an improved version of Fourier series is employed for the admission function construction. Nonlinear dynamic behavior of the spinning beam-disk and its boundary supporting system are described based on energy principle, and the system governing equations of spinning beam-disk are formulated by the Lagrange equation of the second type. The time-domain response is then obtained by solving the system dynamic equations through Runge–Kutta method, while the reliability of the current model is verified through the comparison with those predicted by harmonic balance method. Then, the effect of sweep direction and nonlinear elastic boundary parameters on system dynamic behavior of the spinning Timoshenko beam-disk is investigated and addressed. The results show that the dynamic responses of the spinning beam-disk with nonlinear elastic boundary are sensitive to the initial values of calculation, and the nonlinear elastic boundary parameters make the spinning beam-disk exhibit complex dynamic behavior. Analysis of Poincare points in the phase diagram can better determine the dynamic behavior of spinning beam-disk, and a set of suitable nonlinear elastic boundary parameters can suppress the complex dynamic response of the spinning beam-disk.