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This paper aims to investigate the nonlinear vibration characteristics and stability of a dual-disk rotor-bearing system under multi-frequency excitations. A 4-degree-of-freedom dynamic model is established using the assumed mode method, considering the bearing's cubic nonlinearity. The system is solved using the multiple scale method combined with arc-length continuation. The stability of the system's solutions is determined by solving the eigenvalues of the Jacobian matrix of the averaged equations. The nonlinear vibration characteristics and stability of the dual-disk rotor system under simultaneous resonance conditions are obtained. The results show that changes in system parameters can lead to Saddle-Node and Hopf bifurcations, as well as the occurrence of multi-valued solutions and symmetry-breaking phenomena. Additionally, simultaneous resonance leads to interaction between the two modes, where the relative positions of the resonance peaks of these modes influence the system's dynamic behavior. Variations in system parameters can alter the relative positions of resonance peaks, leading to more complex effects on nonlinear responses. This research provides significant insights into the dynamic behavior of the dual-disk rotor-bearing system under multi-frequency excitations, which is meaningful for designing and optimizing rotor systems. [ABSTRACT FROM AUTHOR]

Analyzing the nonlinear characteristics of dual-rotor systems under thermo-mechanical (TM) coupling situations is critical, as operational conditions should be accurately determined, to avoid potential thermally-induced failures. This paper proposes the coupled TM model of a dual-rotor system, which considers multiple nonlinearities and heat generation of four bearings that couple the mechanical and thermal fields. Heat dissipation controlled by lubricant flow rates is introduced into the model to simulate different TM coupling degrees. Nonlinear phenomena and stability evolution are analyzed by the modified incremental harmonic balance method (IHB) at primary resonance regions. An increase in TM coupling degrees can lead to more bifurcation points, resonance regions with lower frequencies, larger vibration responses, and unstable regions. It can also transform resonance hysteresis phenomena into more complex nonlinear phenomena and some saddle-node bifurcation points into Neimark–Sacker bifurcation points. The reason for these transformations is that the effective radial clearance (RC) of bearings changes with rotation speed and thermal expansion. Temperature nonlinearities are induced by the radial bearing loads and the lubricant viscosity, which are investigated by various generalized nonlinear thermal forces. These findings can help further understand nonlinear coupled TM problems of complex dual-rotor systems. [ABSTRACT FROM AUTHOR]

Quasi-zero-stiffness (QZS) vibration isolator is widely used in low-frequency vibration isolation due to its high-static-low-dynamic-stiffness (HSLDS) characteristics. The complex nonlinear force of the QZS vibration isolator increases the difficulty of solving it while realizing the HSLDS characteristics. The typical analysis method is to use Taylor expansion to simplify the nonlinear force and make it approximate to polynomial form, which leads to inaccurate analysis results in the case of large excitation and small damping. Therefore, the modified incremental harmonic balance (IHB) method is used to directly analyze the dynamic characteristics of the QZS vibration isolator without simplification in this paper. The classical three-spring QZS vibration isolation model is used as the calculation example. The results are different from the previous approximate equation analysis results in three aspects: (1) There is no unbounded response of the system under displacement excitation; (2) Even harmonics and constant terms also exist in the response of the system and can lead to multiple solution intervals; (3) In the case of small damping and large excitation, both displacement excitation and force excitation have subharmonic resonance, reducing the vibration isolation performance of the system. In addition, the accuracy of the solution obtained by the IHB method is verified by the Runge–Kutta method. The accurate analysis method in this paper provides favorable theoretical support for the design and optimization of vibration isolators. [ABSTRACT FROM AUTHOR]

This paper focuses on the combination resonances of a dual-rotor system with inter-shaft bearing. The motion equations of the dual-rotor system are formulated by the Lagrange equation, in which the unbalanced excitations of the two rotors and the clearance of the inter-shaft bearing are taken into consideration. The HB-AFT method (harmonic balance-alternating frequency/time domain method) is employed to obtain all the periodic solutions including the unstable solutions of the system. The combination resonance characteristics of the system are analyzed in detail by using the frequency response curves and separated frequency responses of the dual-rotor system. Besides the two primary resonance peaks, three more combination resonance regions in the frequency response curves of the system are found, in which the jump and bi-stable phenomena are observed. The primary resonance is mainly dominated by the excitation frequency ω 1 and ω 2 , the combination resonance of the system is mainly dominated by the combined frequency component of 2 ω 2 - ω 1 , 4 ω 2 - 3 ω 1 , 3 ω 2 - 2 ω 1 and is almost independent of other frequency components. Furthermore, the effect of inter-shaft bearing clearance on the combination resonance regions is obtained, it is indicated that increasing the inter-shaft bearing clearance will not only affect the response amplitudes of the combination resonance and change the "softening and hardening characteristic" of the frequency response curves, but also show a certain "stiffness weakening effect" on the rotor system. The study in this paper is of great significance to select the parameters of the dual-rotor system reasonably so as to avoid harmful combination resonance. [ABSTRACT FROM AUTHOR]

In this paper, a three degrees of freedom archetypal model with arbitrary designable features and its inverse construction method based upon the target restoring force functions are proposed. The construction conditions of the zero-stiffness and quasi-zero-stiffness systems with 3-DOF have been studied in detail, by introducing the definitions of the zero-stiffness and the quasi-zero-stiffness system, based upon the archetypal model. The static characteristic and the low-frequency vibration isolation performance of the zero-stiffness and quasi-zero-stiffness systems with 3-DOF in multiple direction have been analyzed, by comparing with the linear system with the same support stiffness. The conclusion shows that there are finite solutions for the construction of 3-DOF zero-stiffness characteristic, and infinite solutions for the construction of 3-DOF quasi-zero-stiffness characteristic, based on 3-DOF archetypal model and its dimensionless parameters. The feasibility of constructing the zero-stiffness system with 3-DOF will lead to a new inspiration for the design of the passive zero-stiffness support structures; and the low-frequency vibration isolation performance of the 3-DOF quasi-zero-stiffness system in multiple direction is significantly improved compared with the linear system, which expresses a great potential in the multi-DOF design of the low-frequency, ultra-low-frequency vibration isolation. [ABSTRACT FROM AUTHOR]

This paper focuses on the nonlinear response characteristics of a dual-rotor system with a breathing transverse crack in the hollow shaft of the high-pressure rotor (rotor 1). A finite element model of the system is set up, and the motion equations of the system are formulated, in which the unbalance excitations of the rotor 1 and rotor 2 (low-pressure rotor) and the time-varying stiffness of the cracked shaft are considered. By using the harmonic balance method, the motion equations are analytically solved to obtain the dynamic responses of the two rotors. Accordingly, the effects of the crack depth and location on the vibration amplitudes are discussed in detail. The results indicate that when a transverse crack appears, it may bring super-harmonic responses to the rotor system, and the resonance peaks at the second, third and even fourth subcritical whirling speeds of the two rotors can be observed. The deeper the crack is, the larger the resonances amplitudes are, especially when the crack is located in the middle of the shaft or around the disks. In addition, the super-harmonic responses of rotor 1 where the crack located, can also be observed in rotor 2, which means that the crack signals can be detected in the entire system. Moreover, the numerical computations are carried out by using the Newmark- $$\beta $$ method, which shows great agreement with the previous analytical results. The results obtained in this paper will contribute to the modeling and the fault diagnosis of dual-rotor systems with hollow-shaft crack. [ABSTRACT FROM AUTHOR]

In this paper, a modified nonlinear proper orthogonal decomposition (POD) method based on transient time series on account of approximate inertial manifold method is proposed to reduce the order of the multiple degrees of freedom (DOFs) of a rotor system. A model of 23 DOFs rotor system comprising a pair of liquid-film bearing with pedestal looseness at one end is established by using the Newton's second law. The multi-DOFs system is reduced to a two-DOFs model by using the modified POD method, which preserves the original dynamics behaviors. The comparison between the modified and the traditional POD method shows that the modified POD method is more effective especially in finding the bifurcation point and detecting the bifurcation diagrams and the mean square error of amplitudes curves. Finally, a relative error analysis is also carried out to evaluate the accuracy of the proposed order reduction method, indicating that the relative error is below 5 % excluding the interval between original bifurcation point and the shift of the reduced system. [ABSTRACT FROM AUTHOR]

This paper focuses on the nonlinear response caused by aircraft turning flight in a rotor-ball bearing system with internal clearances and Hertzian contact forces. The equations of motion are formulated by using Lagrange equation, where the aircraft turning flight is modeled as a maneuver load. Numerical analyses are carried out to detect the response of the system under maneuver load. The sub-harmonic resonance and irregular motions subjected to the maneuver load are obtained and presented by bifurcation diagrams, amplitude spectrum diagrams, Poincare maps and phase portraits. Two typical patterns that the maneuver load inducing response are found: one is the alternating of period 2 motion and period 1 motion for $$\omega =1{,}350\,\hbox {rad/s}$$ ; the other is the alternating of quasi-periodic motion and period 2 motion for $$\omega =1{,}470\,\hbox {rad/s}$$ . Moreover, mass eccentricity shows a significant effect on the sub-harmonic resonance of the rotor-ball bearing system under turning flight, which is different from that without considering maneuvering flight condition (Bai and Zhang in Int J Nonlinear Mech 50:1-10, ). The results obtained in this paper will contribute an understanding of the nonlinear dynamic behaviors of aircraft rotor systems in maneuvering flight. [ABSTRACT FROM AUTHOR]

In this paper, the Hopf bifurcations and limit cycle oscillations (LCOs) of an airfoil with cubic nonlinearity in supersonic\hypersonic flow are investigated. The harmonic balance method and multivariable Floquet theory are applied to analyze the LCOs of the airfoil. Four distinct cases of the LCOs response are detected in this system: (I) supercritical Hopf bifurcation, (II) a single subcritical Hopf bifurcation, (III) two subcritical Hopf bifurcations, and (IV) no Hopf bifurcation. Furthermore, the parameter variations domains separating the supercritical and subcritical Hopf bifurcations are presented using singularity theory. [ABSTRACT FROM AUTHOR]