Study on Mechanism for Line Spectrum Reduction in Nonlinear Vibration Isolation system

The chaotic response and mechanism for line spectrum reduction in nonlinear vibration isolation system are studied and the harmonic balance method is applied to uncover the interaction between different harmonics. Since the loss of stability of sub- or super-harmonic resonances leads to the occurrence of chaos, the periodic and chaotic responses are closely related. From the amplitude frequency response curves obtained by the numerical integration of the nonlinear system, a lot of strange phenomena can be observed near the resonant frequency. When the driving frequency is near the natural frequency of the associated linear system, the fundamental harmonic resonance occurs. When the excitation is increased, the amplitude of the third super-harmonic resonance is larger than that of the fundamental harmonic. The case corresponds to a strong resonance region, and the strong nonlinear interaction between different harmonics occurs. It is clear that the considerable energy transfers from the fundamental harmonic to the others by the nonlinear interactions, and thus the energy at the dominant frequency is reduced greatly. When the nonlinear vibration isolation system is in a chaotic state, the response is characteristic of the broadband spectrum, and thus the energy is distributed to all the frequency components. The most important characteristic of chaos is the sensitive dependence on initial conditions. There are many different routes to chaos, such as period-doubling, quasi-periodic and intermittency route etc. Lyapunov exponent λ is usually applied to characterize the chaos quantitatively. When λ is positive, two trajectories in phase space move exponentially away from each other on average. If λ is negative, the nearby trajectories converge. Because the trajectories stretch and fold in different directions, chaotic attractor is different from the point, limit cycle and so on, and the fractal dimension can be applied to describe its characteristic. Furthermore, the chaotic signal is distinguished from the random one by the saturation of the correlation dimension. The former approaches to saturation with the increasing embedding dimension, but the latter does not. The phase space reconstruction based on wavelet transform can achieve the study of both the geometry and frequency characteristics of the chaos, so that provides a new way to study chaotic response.