On Nonlinear Lateral Vibrations of Rotating Rods Under the Effect of Initial Stress

In this paper, we study nonlinear lateral vibrations of a simply supported rotating rod under the effect of initial stress and external loadings. The foundations of Novozhilov’s nonlinear theory of elasticity and Biot’s general theory for initially stressed solids are used when deriving a generalized elastic potential, based on which the nonlinear mathematical model is developed. The Bubnov-Galerkin approach and Wolfram Language built-in numerical method are utilized to find a solution of the model. The effect of the initial stress field on the rod spatial vibrations is analyzed and graphs for various values of the initial stress are plotted. Accounting for the tensile initial stresses allowed reducing the amplitude of the rod vibrations, whereas the compressive stresses resulted in their increase with retaining stability of the oscillatory process at optimal system parameters. The assessment of the influence of the initial stress field on the oscillatory process showed the need to take them into account when studying rotating rods under the influence of external loadings.