Dynamical and structural systems are susceptible to sudden excitations and loadings such as wind gusts, blasts, earthquakes, and others which may cause destructive vibration amplitudes and lead to catastrophic impact on human lives and economy. Therefore, various vibration absorbers of linear and nonlinear coupling dynamics have been widely studied in plenty of publications where some have been applied in real-world practical applications. Firstly, the tuned-mass-damper (TMD), the first well-known linear vibration absorber that has been well-studied in the literature and applied with various structural and dynamical systems, is discussed. The linear vibration absorbers such as TMDs are widely used in real-life small- and large-scale structures due to their robust performance in vibration suppression of the low natural frequency structural modes. However, the TMD performs efficiently at narrowband frequency range where its performance is deteriorated by any changes in the frequency content in the structure and the TMD itself. Therefore, the targeted-energy-transfer mechanism which is found to be achieved by nonlinear energy sinks (NESs) has ignited the interest in passive nonlinear vibration suppression. Unlike TMDs, the NESs are dynamical vibration absorbers that achieve vibration suppression for wide range of frequency-energy levels. Given the very rapid growth in this field and the extensive research studies supporting the robustness of the NESs, this paper presents the different types of NESs and their applications with main emphasis on the rotary-based and impact-based NESs since they are of high impact in the literature due to their strong nonlinear dynamical behavior and robust targeted energy transfer.

Rotordynamical systems are usually exposed to recurrent transition through their resonance rotational speeds during runup and coast-down operations. As a result, a nonsynchronous whirl between the shaft rotation and its lateral whirling occurs at the neighborhood of the critical resonance speeds. This nonsynchronous whirl has a significant impact on the system when a breathing crack starts to propagate. The horizontal Jeffcott rotor model with a breathing crack is considered here to study the combined effect of the gravity force vector and the nonsynchronous whirl on post-resonance backward whirl (Po-BW) excitation. The numerical simulation results show that the gravity further intensifies the excitation of the Po-BW in the horizontal cracked rotor compared with the vertical one at relatively small crack depths. In addition, the unbalance force vector orientation has been found to significantly affect the Po-BW excitation and its recurrence.

It has been indicated in the literature to many factors that contribute to faults in rotor dynamical systems such as rubbing impact at stator-rotor contact. Accordingly, the appearance of rubbing impact is investigated here as one of the major factors that could excite the post-resonance backward whirl (Po-BW) phenomena in rotors. Therefore, the effect of rotor-stator rub impact on Po-BW excitation is numerically studied here with a Jeffcott rotor model. Accordingly, vertical and horizontal rotor configurations are considered here with rub-impact. The rubbing between the stator and the rotor is modeled by using both Heaviside function and the exact time calculation during the numerical simulation for comparison and to guarantee whirl results convergence. It is found that at a time step of order 10−6 in the numerical integration both Heaviside function and exact contact time calculations produce similar convergent results. In addition, the obtained numerical simulation results show that the stator-rotor rub-impact is found to excite the Po-BW and affects their recurrence and intensity. Accordingly, the current study provides a more insight to the impact of rotor-stator rubbing on Po-BW excitation. Therefore, the rotor-stator rub-impact is found to be one of the main factors that lead to excite the Po-BW during the rotor transient operation.