Vibrational Resonance in a Damped Bi-harmonic Driven Mathews-Lakshmanan Oscillator

BackgroundDue to its counter-intuitive nature, understanding the dynamics of nonlinear systems has given rise to many challenges to overcome. This has brought about so many quests to answer because most engineering systems are ubiquitously nonlinear in nature. Vibration analysis is found to be one of the dominant and predictive maintenance techniques. It ranges from budding problems to catastrophic failure of the rotating machinery. It leads to acceptance testing, quality control, loose part detection, noise control, leak detection, machine design and engineering.For example, vibration analysis is found to be a significant approach in the industries for analyzing the performance of rotating machinery.PurposeThe study of vibrational resonance is important in many branches of engineering. For example, in mechanical and civil engineering design, vehicle design, the design of steam-turbine rotor-bearing systems, and bridge design, and the design of vibration controllers and isolators. Understanding vibrational resonance is important to ensure an appropriate running condition, increase the effiency of machines and a desired behavior of the systems.MethodIn this work,vibrational resonance for a class of velocity-dependent potentials and nonpolynomial type oscillator is studied. By using the method of separation of motions (MSM) an analytical equation for the slow oscillations of the systems is obtained in terms of the parameter of the fast signal. The analytical computations are verified by fourth order Runge-Kutta method.ResultThe analytical findings concure well with numerical studies. The response amplitude (Q) of the system depending on the amplitude of high-frequency drive forcing strength. The effects of damping and strength of nonlinearity on the emergence of vibrational resonances and resonant frequencies are analyzed. It is intresting to note that decreasing the strength of the nonlinearity significantly contributies to the emergence of VR in the lower values of amplitude of high-frequency drive forcing strength. When the damping term is increseaed the response amplitude (Q) is reduced.ConclusionIn this paper, we have proposed the new avenue in a broad class of velocity-dependent potential systems and nonpolynomial oscillators, which are typically found in physical and mechanical situations. The results are useful for the study of energy transfer phenomena for this class of nonlinear systems and for investigating the effects of damping on the nonlinear behaviour. These results are important for the design and fault diagnosis of mechanical systems and structures which can be described by this nonlinear model. As a result, the study of the dynamics of nonlinear systems has drawn the attention of researchers in various fields such as for instance, engineering and cognitive sciences.

Automated summary

Vibration analysis is a dominant technique in predictive maintenance for analyzing the performance of engineering systems. The study of vibrational resonance is important for engineering design and ensuring desired system behavior.