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The present article studies the effects of both tangential and normal high-frequency excitations on a two-degree-of-freedom moving-mass-on-belt which represents a minimal model incorporating both velocity-weakening instability (so-called Stribeck effect) and mode-coupling instability (so-called binary flutter). The method of direct partition of motion 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. It is observed that the instability can be suppressed by the tangential high-frequency excitation only for a specific range of strength of excitation. However, stability does not improve under normal high-frequency excitations, though amplitude of the self-excited oscillation can be controlled to some extent. Direct numerical simulations are carried out in MATLAB SIMULINK to validate the analytical predictions.

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This paper investigates the vibrational resonance and control of the response of a nonlinear tilted cantilever beam under combined multi-harmonic low and high-frequency excitations. The basic system considers the first mode of vibration of a nonlinear tilted beam under parametric and direct base excitation with the frequency components locked in 2:1 ratio. Such a system is susceptible to parametric amplification of resonance, which may be detrimental for structural health in many mechanical systems. The primary objective of the research is to investigate the efficacy of high-frequency excitation in controlling parametric amplification in the system. To the best of the authors' knowledge such a study was not reported previously in the literature. The slow dynamic equations of the system are obtained using the method of direct partition of motion (MDPM), which is then analysed using the harmonic balance method (HBM). It has been shown that the high-frequency base excitation has a considerable influence on the effective damping and stiffness of the system under consideration. The results of the research demonstrate that high-frequency excitation can effectively control the parametric amplification by shifting the resonance curve in the frequency axis and eliminate undesirable bifurcations by increasing the effective damping. The phenomenon of vibrational resonance has been found for certain parameter values in the presence of high-frequency base excitation. Detail parametric studies are performed to reveal the rich nonlinear dynamics of the system, like multiple jumps in response, dual peaks, isolated resonance response (isola), loop formation in frequency response plot, etc. The numerical results reveal that high-frequency excitation transforms chaotic responses into regular periodic responses. Direct numerical simulations are performed in MATLAB SIMULINK to validate the analytical results.

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