| Two-stage vibration isolation system with its efficient high frequency vibration isolation efficiency is widely used in ships, generators, air craft, and other fields. In view of the current modeling analysis of Two-stage vibration isolation system is not sound, this paper is based on the point of view of the vibration energy transfer path control, to further improve the theory of two-stage vibration isolation system modeling and analysis. First, two analytical models of a typical two-stage vibration isolation system are established which comprise multidirectional composite disturbance source, rubber vibration isolator, the middle quality (elastic raft or lumped mass), and flexible foundation. Based on the theory of mobility matrix approach, the overall system transfer equation is derived. Combined with examples, the vibration mechanism and vibration isolation effect of the two kinds of two-stage passive vibration isolation system is revealed using the concept of power flow. Secondly, for the problems existing in the study of active vibration isolation, a feedforward adaptive control mathematical model of the two-stage vibration isolation system is established. Considering the limit of actual actuator output threshold, respectively based on five control strategy of minimizing total power, cancellation of axial input velocity to the foundation, cancellation of axial input force to the foundation, minimizing axial power and minimizing axial velocity and axial force to the foundation, the vibration isolation effectiveness of three kinds of actuator layout (source/upper control, foundation/lower control, full control) under the compound source excitation was discussed. Finally, with floating raft isolation system as an example, the applicability of the passive-active control of two-stage distributed parametervibration isolation system analysis model for the system with multi-vibration source, compound source excitation is examined. Details are as follows:Based on the concept of vibration energy transfer, the analytical form of mathematical model of the two kinds of two-stage vibration isolation system with the middle quality (elastic raft or lumped mass) was established. With considering the distributed parameter characteristics of the elastic raft, isolators and the flexible foundation, dynamic equations of eachsubsystem were derived by using of the mobility matrix approach. The mechanism of the vibration transmission was revealed by the concept of power flow. Meanwhile, general rules which should be followed for designing two-stage isolation systems were discussed. It isshown that moment excitations play an important role in the vibration transmission process. Hence, the injection of power caused by moment excitations should be reduced. In the permitting condition of energy efficiency and installation spaces, a better isolation effect will be got when enlarging the intermediate mass appropriately. Using the scheme of dispersion intermediate mass can effectively avoid the impact of flexible raft, and it can also significantly inhibit the interaction between wave effects caused by isolators and modals of the flexible raft which may input amount of power to the installed foundation.In order to improve the low-frequency performance of floating raft systems which are always used in marine ships, a feedforward active control solution is proposed. Mathematical model of the overall system under complex excitations is established for giving analytical solutions. The substructure mobility analysis method is used to derive the dynamic characteristics of the transfer equation. To consider the actual actuator output constraint, the output of the secondary actuator force threshold is as the penalty term to rewrite the finial objective function. Respectively based on five equations of total power, axial input velocity, axial input force, axial power and weighted axial velocity and axial force, the vibration isolation effectiveness of three kinds of actuator layout (source/upper control, foundation/lower control, full control) under the compound source excitation was discussed. It was shown that under the control of total power minimization, the upper active control strategy can achieve good effect during rigid-body modal frequencies, and the prominent advantage of the lower active control strategy was mainly reflected in higher frequencies. However, the full active control strategy can realize the optimal control of vibra-acoustic power among broadband domain.The analytical model which consisted of complex excitations(containing the transverse force, vertical force and moment of motivation), distributed parameter isolators, a flexible floating raft and a non-rigid foundation is established. The general mathematic description of the dynamic transfer characteristics of the overall system is given by using the mobility matrix approach. The influence mechanism of the source excitations, the flexible of raft and the resonance of mounts to the system vibration transfer characteristics is discussed. For unified design and evaluation criteria, choose the total power flow as the optimal cost function, and combine the secondary force vector and the output threshold as a penalty term to the function in order to considering the actual actuator output constraints. To discuss the difference among three kinds of layout of actuators (upper, lower and full) which can impact the vibration isolation efficiency. It is shown that moment excitations played an important role in the vibration transfer process. Coupling interactions between the elastic raft and distribution parameter isolators can lead to a deterioration of performance in the high-frequency domain. The upper active control strategy can achieve good effect during rigid-body modal frequencies, and the prominent advantage of the lower active control strategy is mainly reflected in higher frequencies. However, the full active control strategy can realize the optimal control of vibra-acoustic power among broadband domain. |
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