Line spectra chaotification of the nonlinear vibration isolation system on the flexible foundation based on the open-plus-nonlinear-closed-loop method

Line spectra chaotification is a principal method to weaken or eliminate the line spectra feature of submarines. However, this method is difficult to obtain chaos under the variable working conditions and small amplitudes. Furthermore, there are multistable attractors in the nonlinear vibration isolation system simultaneously. So, the quality of chaos highly depends on initial conditions and systematic parameters. In this study, the attractor entrainment control and line spectra chaotification of a nonlinear vibration isolation system on the flexible foundation have been studied by using the open-plus-nonlinear-closed-loop method. First, the dynamic equation of the nonlinear vibration isolation system on the flexible foundation was formulated, and its exhaustive bifurcation characteristics were analyzed. The regulations of global characteristics and coexistent attractors were found out. Second, the entrainments between the different attractors were carried out under the open-plus-nonlinear-closed-loop control, which can ensure the system always works in the lowest line spectra intensity and the best overall vibration isolation performance. Finally, an open-plus-nonlinear-closed-loop coupling method was used to achieve generalized chaotic synchronization between the driving system and the response system, which effectively obtained sustainable chaos even under variable working conditions and small amplitudes. Simulation results validate the feasibility and validity of the open-plus-nonlinear-closed-loop method, which achieves the dual goals of effective vibration isolation in the low frequency range and line spectra chaotification under variable working conditions.