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Dynamic analysis of flexible body under large rotation becomes increasingly important in many engineering applications. This work takes rotating flexible beam as numerical example under assumptions of straight beam, small deformation and fixed axis rotation. Results of six finite element methods are compared: floating frame of reference formulation (FFRF), generalized component mode synthesis (GCMS), total Lagrangian formulation (TLF), linear Euler–Bernoulli beam (LEBB), nonlinear Euler–Bernoulli beam (NEBB) and absolute nodal coordinate formulation (ANCF). Due to the effect of geometric nonlinearity or centrifugal stiffening, the results of linear methods FFRF, GCMS and LEBB are different to geometrically nonlinear methods TLF, NEBB and ANCF. Three points of view are obtained through numerical result analysis. Firstly, based on the equivalence between FFRF and GCMS, a special type of parametrically excited nonlinear system is equivalent to linear system, so as to analyze the Lyapunov stability of its solution. Secondly, for the ANCF, the system invariant matrix is presented to calculate elastic force, which avoids element integration or assembling in each time step, and then the computational efficiency is improved by at least an order of magnitude when compared to adopting element invariant matrix. Thirdly, for GCMS, TLF and ANCF, the velocity of relative coordinate for deformation is adopted to calculate linear internal damping force, which gets different deflection result in comparison with adopting velocity of absolute coordinate for deformation, under large rotational speed.

This study proposes an interface localizing scheme to enhance the performance of the previous hybrid-level interface-reduction method. The conventional component mode synthesis (CMS) only focuses on interior reduction, while the interface is fully retained for convenient synthesis. Thus, various interface-reduction methods have been suggested to obtain a satisfactory size for the reduced systems. Although previous hybrid-level interface-reduction approaches have addressed major issues associated with conventional interface-reduction methods—in terms of accuracy and efficiency through considering partial substructure synthesis—this method can be applied to limited modeling conditions where interfaces and substructures are independently defined. To overcome this limitation, an interface localizing algorithm is developed to ensure an enhanced performance in the conventional hybrid-level interface-reduction method. The interfaces are discriminated through considering the Boolean operation of substructures, and the interface reduction basis is computed at the localized interface level, which is constructed by a partially coupled system. As a result, a large amount of computational resources are saved, achieving the possibility of efficient design modifications at the semi-substructural level.

Reduced-order models of the bladed disk of the aero-engine compressor were established by adopting Prestressed component mode synthesis (PCMS) method. The frequency veering characteristics of the tuned bladed disk were analyzed. From the aspect of the strain energy, the forced vibration response of the mistuned bladed disk was analyzed, along with calculation of the contribution degree factors, the localization factors and frequency veering distances, finding the influences of the frequency veering distance, the contribution degree factors and the localization. The results show that frequency veering has significant influence on vibration localization of the mistuned bladed disk; in the region of frequency veering, the degree of vibration localization of the mistuned bladed disk is relatively high; along with the changes of the frequency veering distance, the contribution degree of the strain energy of the blades of localization of the mistuned bladed disk shows the certainty of regularity.

The multiring disk resonator gyroscope (DRG) has been a candidate for high performance gyroscopes, however nowadays the finite element method (FEM) is the main method for its analysis due to its complex structure. In this paper we propose a new method to mathematically model the DRG for its vibrating modes and lumped parameters based on the component mode synthesis (CMS) method. Firstly, the natural frequencies and the associated mode shapes of the DRG are mathematically modeled and a comparison with the FEM results is conducted. It shows that the mode shapes of DRG obtained by FEM and mathematical modeling are identical and in the full ranges of geometrical parameters, natural frequency error of the simulation, and calculation results are limited in ±15%. It demonstrates the effectivity and feasibility of the mathematical modeling method. Then, based on the calculated natural frequencies and mode shapes, the lumped mass-spring model of the DRG and effects of geometry parameters on the lumped mass-spring parameters are investigated, which can be used on the design of the DRG. This mathematical modeling method can effectively improve the analyzing efficiency of the DRG and the method can also be used on the analysis of other complex multiring-type resonators.

Analytical method using Rayleigh–Ritz method has not been widely used recently due to intensive use of finite element analysis (FEA). However as long as suitable mode functions together with component mode synthesis (CMS) can be provided, Rayleigh–Ritz method is still useful for the vibration analysis of many local structures in a ship such as tanks and supports for an equipment. In this study, polynomials which combines a simple and a fixed support have been proposed for the satisfaction of boundary conditions at a junction. Higher order polynomials have been generated using those suggested by Bhat. Since higher order polynomials used only satisfy geometrical boundary conditions, two ways are tried. One neglects moment continuity and the other satisfies moment continuity by sum of mode polynomials. Numerical analysis have been performed for typical shapes, which can generate easily more complicated structures. Comparison with FEA result shows good agreements enough to be used for practical purpose. Frequently dynamic behavior of one specific subcomponent is more concerned. In this case suitable way to estimate dynamic and static coupling of subcomponents connected to this specific subcomponent should be provided, which is not easy task. Elimination of generalized coordinates for subcomponents by mode by mode satisfaction of boundary conditions has been proposed. These results are still very useful for initial guidance.

The modeling method and identified method adapted to multi-degree-of-freedom structures with strucrural nonlinearities are established.The component mode synthesis method is used to establish the nonlinear governing equations by extending the connected relationships.Based on the modeling method,the Hilbert transform method is applied to identify the nonlinear stiffness of multi-degree-of-freedom structures.Nonlinear analysis and identification of a typical folding wing configuration with three freeplay hinges are investigated.The nonlinear governing equation is established based on present methods and the computing results of different stiffness are checked by finite element programming.In order to illustrate the influence of the nonlinearities,the frequency response characteristics of the structure are analyzed and Hilbert transform is performed.The Hilbert transform identification method is utilized to identify the nonlinear stiffness of nonlinear hinges in the time domain and several parametric studies are performed.In addition,the comparison of response is made to illustrate the feasibility of the methods.The results show that the extending component mode synthesis method in the present work can be used to establish the governing equation with structural nonlinearities.Based on the modeling method,the Hilbert transform identified method can be extended to multi-degree-of-freedom structures accurately.

Variable speed operation of the train cause easily the wheel-track slipping phenomenon, inducing strong nonlinear dynamic behavior of the suspended monorail train and bridge system (SMTBS), especially under an insufficient wheel-track friction coefficient. To investigate the coupled vibration features of the SMTBS under variable speed conditions, a novel 3D train–bridge interaction model for the monorail system considering nonlinear wheel-track slipping behavior is developed. Firstly, based on the D’Alembert principle, the vibration equations of the vehicle subsystem are derived by adequately considering the nonlinear interactive behavior among the vehicle components. Then, a high-efficiency modeling method for the large-scale bridge subsystem is proposed based on the component mode synthesis (CMS) method. The vehicle and bridge subsystems are coupled with a spatial wheel-track interaction model considering the nonlinear wheel-track sliding behavior. Furtherly, by a comprehensive comparison with the field test data, the effectiveness of the proposed method is verified, as well as the reasonable modal truncation frequencies of the bridge subsystem are determined. On this basis, the dynamics performances of the SMTBS are evaluated under different initial braking speeds and wheel-track interfacial adhesion conditions; besides, the nonlinear wheel-track slipping characteristics and their influences on the vehicle–bridge interaction are also revealed. The analysis results indicate that the proposed model is reliable for investigating the time-varying dynamic features of SMTBS under variable train speeds. Both the axle load transfer phenomenon and longitudinal slip of the driving tire would be easy to appear under the braking condition, which would significantly increase the longitudinal vehicle–bridge dynamic responses. To ensure a good vehicle–bridge dynamics performance, it is suggested that the wheel-track interfacial friction coefficient is larger than 0.35.

The main objective of the present paper is to determine the influence of rub parameters on the stability of a two-spool rotor system undergoing rub-impact. The parameters such as rotor–stator contact stiffness, coefficient of friction and clearance are varied for understanding their effects on the system response and stability. Moreover, the analysis is performed for two modes of rotor operations, namely co-rotation and counter-rotation, and determines their impacts on rotor–stator rubbing. A time variational method is employed to predict the nonlinear response of the system with a perturbation function applied at the steady-state solution points to investigate their stability. Two types of bifurcations, namely limit point and Neimark–Sacker bifurcations, are observed in the response by monitoring the Floquet exponents of the perturbed system. As the coefficient of friction is increased, the early onset of NS bifurcation has happened and the system enters into the quasi-periodic regime early. However, when the contact stiffness and clearance values are increased, the onset of NS bifurcation is delayed. It is also observed that the response characteristics of the co- and counter-rotating systems are entirely different. The separation between forward and backward whirling frequencies is reduced for the counter-rotating system due to the cancellation of gyroscopic moments. In addition, for the same set of parameters, the counter-rotating system enters into the quasi-periodic regime quickly once the disk starts rubbing.

This work presents a model reduction method suited for performing nonlinear dynamic analysis of high-dimensional rotor-foundation systems modeled by the finite element method. The approach consists in combining the component mode synthesis (CMS) method with the approximate invariant manifold method (AIMM), and allows the obtention of forced responses through the integration of a single pair of ordinary differential equations. The proposed approach is tested using two examples: a simple and a complex rotor-foundation system. In both cases, the nonlinearity comes from the fluid-film bearings. The results show that the method can provide a significant reduction in numerical cost while still retaining good accuracy when compared to direct time integrations. By means of the proposed method, the nonlinear dynamic analysis of high-dimensional rotor-foundation system becomes a feasible option.

Due to thermal expansion of the mechanical structure, assembly processes, bearing wear, and long-term vibration during operation, a clearance fit may occur between the bearing outer ring and its pedestal. The clearance fit may result in relative motion between the bearing outer ring and pedestal, thereby altering the support characteristics of the rotor and subsequently impacting the dynamic characteristics of the rotor-bearing system. The stable operation of the system may be at risk in this case. In this paper, the dynamic model of the coupling system of a dual rotor-bearing outer ring-pedestal-casing with clearance fit is established based on the finite element method and lumped parameter method. The dimensionality of the system equation is reduced using the fixed-interface component mode synthesis (CMS) method and solved numerically. The impact of clearance fit on the vibration characteristics of the system is investigated under three operational conditions: imbalance of the inner rotor, imbalance of the outer rotor, and simultaneous imbalance of both two rotors. Furthermore, an analysis is conducted to evaluate the motion state of the system with clearance fit. Lastly, the vibration transmission characteristics between the rotor-bearing outer ring-pedestal-casing are studied. The results indicate that the harmonic components corresponding to the rotational speed frequency of rotors will appear on the spectrum and envelope spectrum of the system with clearance fit. The natural frequency of the system may be excited in the resonance region. Due to the influence of gravity, the dynamic characteristics of the system vary significantly at low and high rotational speeds. Additionally, the vibration transmission characteristics of the system are significantly influenced by both the rotational speeds and clearance fit.