Abstract
The escape dynamics of a damped system of two coupled particles in a truncated potential well under biharmonic excitation are investigated. It is assumed that excitation frequencies are tuned to the modal natural frequency of the relative motion and to the modal frequency of the centre of mass on the bottom of the potential well. Although the escape is essentially a non-stationary process, the critical force strongly depends on the stationary amplitude of the relative vibrations within the pair of masses. The characteristic escape curve for the critical force moves up on the frequency-escape threshold plane with increasing relative vibrations, which can be interpreted as a stabilizing effect due to the high-frequency excitation. To obtain the results, new modelling techniques are suggested, including the reduction in the effect of the high-frequency excitation using a probability density function-based convolution approach and an energy-based approach for the description of the evolution of the slow variables. To validate the method, the coupled pair of particles is investigated with various model potentials.
Highlights
Escape from a potential well is a classic problem arising in various fields of natural science and engineering [1–5]
Two bodies of mass m1 and m2 coupled with a linear spring of stiffness k and a linear damper with the damping coefficient c are located in the corresponding potential wells V1(x) and V2(x). m1 is excited by the superposition of two harmonic forces
To concentrate on the effects caused by the coupled bodies in contrast to a single body, the truncated, purely quadratic potential (1) is mainly investigated; most of the calculations are presented in a general form so that the procedure described below is applicable to arbitrary potentials
Summary
Escape from a potential well is a classic problem arising in various fields of natural science and engineering [1–5]. Paper [3] addressed the escape dynamics of harmonically forced and damped particles in three model potential wells. The conjecture was further examined for different model potentials under harmonic forcing in the papers [22,23] These papers addressed the escape dynamics of the forced particle in conditions of 1:1 resonance. The response amplitude drastically grows, and the particle escapes The combination of these two mechanisms provides an understanding and prediction of the sharp minimum on the frequency-amplitude plane without any empirical corrections. This approach somewhat resembles recent studies of transient phenomena in systems of coupled oscillators in terms of limited phase trajectories (LPT) [24,25].
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