# Nonlinear Dynamics of an Elastic Stop System and Its Application in a Rotor System
## 5 Conclusions  
In this paper, a novel vibro-impact system with an elastic stop present by piecewise-type nonlinearities is promoted, and its vibration behaviors are studied in detail. From the results, some useful conclusions can be drawn, which can give some guidance on predicting resonance frequencies and amplitudes, analyzing frequency components, detecting faults, and suppressing vibration.  
1. As for the frequency amplitude response, the amplitude-frequency curve of a system with an elastic stop is similar to the system with a hardening spring showing the resonance peak bending to the right. As for the \"bending\" curves, the periodic solution is unstable, and there can be more than one steady-state response for a given excitation frequency, and jumps occur in the process of speed-up and speed-down. In engineering, it is important to be concerned about the jumping phenomenon in a system with gaps.
2. When the gap becomes small gradually, the resonance peak shifts from a low frequency to a high frequency, and the amplitude of the resonance peaks decreases. Thus, it is feasible to use an elastic stop for suppressing vibration in practical applications. However, the stiffness of the elastic stop will influence the efficiency of suppression, and the characteristics of the elastic stop should be designed properly.
3. In addition, at the unstable point, the frequency spectrum includes 0.5X, (\(n+0.5\))X and \(n\)X, in addition to the fundamental frequency 1X; and investigating frequency components is an effective method for detecting vibration faults induced by gaps.
4. The amplitudes of super-harmonic components are relatively smaller compared with the fundamental frequency, and are less than 10%. Moreover, the relative amplitudes of high-order components are larger when the gap is smaller. Thus, in most cases of engineering problems, it will be useful to focus on the fundamental frequency component if excess vibration occurs and vibration suppression is required.
5. The application of the elastic stop to a specific rotor support system is investigated. A new pedestal loosening rotor with an overhanging disk and three supports is promoted and investigated. The dynamic responses of the rotor with an elastic stop are similar to that of the two-Dof model with piecewise linear functions. In the meantime, the feasibility of vibration suppression of a flexible rotor by using an elastic stop has been verified in this paper.  
Therefore, the results of this paper can not only explain some dynamic behaviors of the system with an elastic stop, but also provide some guidance for the design of impact dampers in engineering.  
Conceptualization, [PERSON]; Formal analysis, L.J.; Investigation, [PERSON]; Resources, J.H. and Z.S.; Validation, [PERSON]; Writing--original draft, L.J.; Writing--review & editing, Y.W. All authors have read and agreed to the published version of the manuscript.  
This study is supported by the National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant 2017-IV-0011-0048 and J2019-VIII-0008-0169), and the Science Center for Gas Turbine Project (P2021-A-I-002-002).  
Not applicable.  
The authors declare no conflict of interest.