Nonlinear dynamics of vortex-induced vibration of a nonlinear beam under high-frequency excitation

Abstract

The present article studies the nonlinear dynamics and effects of high-frequency excitations (HFE) on a forced 2-D coupled beam and wake oscillator model ascribing vortex-induced vibrations. Oscillatory strobodynamics (OS) theory is employed for studying the characteristics of the system in slow time-scale. Linear stability analysis is performed near the equilibrium point of the system for both with and without sinusoidal high-frequency excitation. The method of multiple scales (MMS) is implemented to get the approximate periodic solutions of both the beam and wake responses. It is observed that for pure self-excitation the vortex induced instabilities are suppressed by the high-frequency excitation. However, shifting of primary resonance curve and changing of quasi-periodic attractor to periodic attractor are observed under the influence of high-frequency excitation in the simultaneous self-excited and forced excited system. Furthermore, for the existing system the quasi-periodic and transient routes to chaos are discussed. Numerical results show that the chaotic responses are changed into periodic responses for the higher strength of high-frequency (HF) excitation (product of amplitude and frequency of high-frequency excitation). Direct numerical simulations are carried out by MATLAB SIMULINK to validate the analytical results. Overall, an appropriately chosen high-frequency excitation can be beneficial in reducing the response amplitude as well as suppressing the complex instabilities in the system.