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Metamaterial is a designed material, having some exotic phenomena in resonating frequency range,such as negative properties. This is often achieved through resonant electromagnetic, acoustic ormechanical structures inside the metamaterial. Mechanical metamaterials have a comprehensiverange of applications in sound, vibration and seismic engineering. However, the effectiveness ofmetamaterials is limited to a relatively narrow frequency band as they are generally based on linearresonance mechanisms. These linear metamaterials do not perform well under the broadbandexcitation spectra that are common in real life applications. Towards the first step to widen thebandwidth of the metamaterial, different classes of nonlinear oscillations, namely Duffing typemonostable and bistable, and piecewise linear, are studied in non-dimensional way and comparedwith each other, to identify the best one according to resonating bandwidth increment. A straightforwardtime history based iterative methodology FRSFTI is developed to get the frequencyamplitude plot of a nonlinear system without employing any approximate perturbation method. Thefrequency-amplitude plot from this method shows a good agreement with the conventionalperturbation method at the resonating frequency range; moreover, this method enables to computethe response away from the resonating range. From the analysis it can be concluded that thebandwidth increment of bistable Duffing type oscillator is largest compared to others.

 

Nonlinear metamaterial; Mechanical metamaterial; Nonlinear oscillation; Chaos; Multi-stability; Steady state response