Study on chaotic parameters range of nonlinear isolation system with multi-frequency excitations

It is well known that the response of the linear vibration isolation system (VIS) has the same frequency characteristic as that of the external excitation, and thus the warship is easy to be identified by sonar. However, the nonlinear VIS (NVIS) has many advantages in vibration and noise control, such as avoiding the high amplitude at resonant frequency, changing the vibration pattern. It is usually used to isolate vibration and protect precise instruments in the warship. The response of the nonlinear VIS is more complex than that of the linear one including primary, super, sub- ultrasubharmonic resonance, limit cycles, jump phenomena and coexisting multiple responses. When the nonlinear VIS is in a chaotic state, the output has a broadband spectrum characteristic. Linear spectrum of the warship is transformed into a continuous one by the chaotic vibration isolation system, so that the energy of the predominant frequency can be reduced, and its capability of concealing is improved greatly. This paper applies Melnikov's method to study the parameters range of an isolation system with many nonlinear factors under multi-frequency external excitations. Results show that when the system's parameters are in a special range, the stable and unstable manifolds intersect transversely, and the system is in a chaotic state. When the condition of intersection is, broken, the isolation system is in a quasi-periodic or periodic state.