Q.S. Lu

Bio: Q.S. Lu is an academic researcher from Beihang University. The author has contributed to research in topics: Saddle-node bifurcation & Resonance. The author has an hindex of 2, co-authored 4 publications receiving 45 citations. Previous affiliations of Q.S. Lu include Brunel University London.

Dynamic stability and bifurcation of an alternating load and magnetic field excited magnetoelastic beam

Abstract: A mechanical model of a magnetoelastic buckled beam subjected to an external axial periodic force in a periodic transversal magnetic field is investigated. Taking account of the effect of induced currents, the model is described by a two-frequency parametric vibration system with self-excitation. The method of multiple scales and qualitative analysis are used to study the dynamic behaviours and stabilities of steady state responses, limit cycle responses and[formula]-responses of the principal parametric resonance. These theoretical results are verified by numerical solutions using the fourth order Runge-Kutta algorithm.

The existence of periodic motions in rub-impact rotor systems

Abstract: The existence of rub-impact periodic motions in an eccentric rotor system is considered. A criterion for the periodicity condition of n-periodic impacts is derived and other conditions for real rub-impacts are also discussed. A method consisting of analytical and numerical techniques is presented to solve the existence problem of rub-impact periodic motions. Some special results are obtained by theoretical analyses for rub-impact rotor systems, including the existence of grazing circle motions and that of single-impact periodic motions.

Secondary bifurcations of two non-linearly coupled oscillators

Abstract: The studies of periodically perturbed primary bifurcations of two non-linearly coupled oscillators have been presented in a companion paper [1]. In this paper a further investigation is reported of periodically perturbed secondary bifurcations of the same system, which has more complicated phenomena in non-resonant, subharmonic or principal parametric resonant, and main resonant cases. A modified Krylov-Bogoliubov-Mitrolposky (KBM) averaging method, the concept of normal form, singularity and unfolding theory, the theory of Z 2 -symmetry bifurcations, and path formation technique are employed to analyze the bifurcation problems. By applying the proposed technique, in the main resonant case, the problem of co-dimension 5 bifurcation, which has no symmetry property, is investigated. Various secondary bifurcation diagrams in different components of bifurcation hypersurface in parameter space are shown. A comparison of periodically perturbed secondary bifurcations with periodically perturbed primary bifurcations is presented.

Subharmonic. superharmonic and quasiperiodic oscillations induced by vortices

Abstract: Structural oscillations of non-inner resonance and inner resonance induced by vortex shedding are studied using the method of multiple scales under different conditions. It is shown that the vortex-excited system exhibits complicated dynamic behaviours such as frequency-locked, subharmonic, superharmonic and quasiperiodic oscillations.

Nonlinear phenomena, bifurcations, and routes to chaos in an asymmetrically supported rotor-stator contact system

Abstract: The efficiency of rotating machines can be improved via precisely manufactured bearings with reduced clearances; consequently, the proclivity for rotor–stator contact is increased. A common model used to investigate rotor–stator contact in previous studies is the two degree-of-freedom (DOF) rotor with symmetric support stiffness, where the contact assumes a linear elastic normal restoring force proportional to the rotor–stator interference and a tangential dry Coulomb friction force. Switching between the contacting and non-contacting states creates strong nonlinearity in the equations of motion, and the dynamic response displays a rich profile of behaviors including periodic, quasiperiodic, and chaotic responses via period-doubling, sudden transitions, quasiperiodicity, and intermittency. For the first time, this work emphasizes an asymmetric support stiffness matrix with cross-coupling between the x and y direction stiffnesses. The influence of support asymmetry on the nonlinear rotor response is shown using rotor orbits, frequency spectra, Poincare sections, and bifurcation diagrams. It is found that the cross-coupling stiffness coefficient kxy has negligible effect on the dynamic response until its magnitude is on the same order as the direct stiffness coefficients. Direct stiffness coefficient asymmetry is shown to affect the rotor׳s response, where even small asymmetries can qualitatively change the response. Additionally, the importance of including gravity is investigated, and a method is provided for determining the threshold shaft speed above which gravity can be ignored. The dominant route to chaos is period-doubling for the parameters considered here, though other routes to chaos are seen such as a direct transition from periodic to chaotic motion. Finally, observations pertaining to rotor modeling, design, and fault diagnostics are discussed.

Nonlinear vibration phenomenon of an aircraft rub-impact rotor system due to hovering flight

Abstract: This paper focuses on the nonlinear vibration phenomenon caused by aircraft hovering flight in a rub-impact rotor system supported by two general supports with cubic stiffness. The effect of aircraft hovering flight on the rotor system is considered as a maneuver load to formulate the equations of motion, which might result in periodic response instability to the rotor system even the eccentricity is small. The dynamic responses of the system under maneuver load are presented by bifurcation diagrams and the corresponding Lyapunov exponent spectrums. Numerical analyses are carried out to detect the periodic, sub-harmonic and quasi-periodic motions of the system, which are presented by orbit diagrams, phase trajectories, Poincare maps and amplitude power spectrums. The results obtained in this paper will contribute an understanding of the nonlinear dynamic behaviors of aircraft rotor systems in maneuvering flight.

Bifurcation and stability analysis of a nonlinear rotor system subjected to constant excitation and rub-impact

Abstract: This paper focuses on the mechanism of a complex bifurcation behavior caused by flight maneuvers in an aircraft rub-impact rotor system with Duffing type nonlinearity. The maneuver load during flight maneuvers may induce a rub-impact phenomenon, accompanied by complex nonlinear behaviors such as periodic, sub-harmonic and quasi-periodic motions, but the bifurcation mechanism is not so clear. In this study, the harmonic balance method combined with an alternating frequency/time domain procedure (HB-AFT method) is formulated and used to derive the approximate periodic solutions of the system. In conjunction with the arc-length continuation, the solution branches for both periodic 1-T motion (synchronous oscillation) and periodic 2-T motion (sub-harmonic oscillation) are traced. Then with the aid of the Floquet theory, the stabilities of the obtained periodic solutions are examined. The changes in the number or the stability of the solutions lead to the identification of the bifurcation points, which can be classified qualitatively into three types, i.e. Neimark-Sacker bifurcation point (NSBP), quasi-periodic Hopf bifurcation point (QPHBP) and saddle-node bifurcation point (SNBP). In addition, the constant excitation significantly affects the instability as well as the bifurcation of the rotor system. In the case of a smaller constant excitation, the rotation region with respect to the quasi-periodic motions may disappear, accompanied with a PBP (pitchfork bifurcation point) instead of the two NSBPs and one QPHBP. The bifurcation analysis in this paper provides deep insight into the mechanism of the complex nonlinear phenomenon induced by the constant excitation. The results obtained will also contribute to a better understanding of the nonlinear dynamic behaviors of aircraft rotor systems during flight maneuvers.

Fixed-point rubbing characteristic analysis of a dual-rotor system based on the Lankarani-Nikravesh model

Abstract: A dual-rotor system dynamics model is established for simulating the aero-engine vibration with unbalance-partial rubbing coupled faults. The main characteristics of the dual-rotor model are as follows: (1) the compressor disc and turbine disc are considered in both low pressure rotor and high pressure rotor; (2) two eccentricities exist in the LP and HP turbine discs, respectively; (3) two convex points exist in the casing and then fixed-point rubbing may occur in the LP and HP turbine discs, respectively; (4) coatings are painted on the surfaces of all the discs and casing. Taking into account the soften characteristics of coatings, the Lankarani-Nikravesh model is used to describe the impact forces between two convex points and two turbine discs. Then, the case of two fixed-point rubbings is simulated by the Runge-Kutta method. At different rotational speeds, the responses of the dual-rotor system are analyzed by spectrum cascades and waveforms. Meanwhile, the effects of rotational speed ratio, initial clearance and curvature radius of convex point on the dynamic characteristics and impact force are discussed. Finally, the experiment performed on a dual-rotor test rig proves the validity of the dynamics model.

Nonlinear dynamic analysis of a rub-impact rotor supported by oil film bearings

Abstract: A general model of a rub-impact rotor system is set up and supported by oil film journal bearings. The Jacobian matrix of the system response is used to calculate the Floquet multipliers, and the stability of periodic response is determined via the Floquet theory. The nonlinear dynamic characteristics of the system are investigated when the rotating speed and damping ratio is used as control parameter. The analysis methods are inclusive of bifurcation diagrams, Poincare maps, phase plane portraits, power spectrums, and vibration responses of the rotor center and bearing center. The analysis reveals a complex dynamic behavior comprising periodic, multi-periodic, chaotic, and quasi-periodic response. The modeling results thus obtained by using the proposed method will contribute to understanding and controlling of the nonlinear dynamic behaviors of the rotor-bearing system.