Random stability for lateral vibration on footbridge based on IEVIE-PDE method

The pedestrian-induced lateral vibration of footbridges is essentially classified as a nonlinear stochastic vibration.Accordingly,bridge vibration stability falls within the field of nonlinear stochastic vibration stability.At present,the Lyapunov method is mainly used to analyze such stability.However,this method is qualitative,and it cannot quantitatively analyze the vibration stability probability.In this study,a new analytical method based on a comparison of the input energy and the variation of intrinsic energy(IEVIE)is used to analyze the nonlinear stochastic vibration stability of the lateral vibration of the footbridge.The improved Nakamura model is used to describe the lateral nonlinear stochastic vibration of the footbridge.A combination of the IEVIE method and the probability density evolution(PDE)method is then proposed,in which the IEVIE method is utilized to determine vibration stability.The PDE method is used to obtain the reliability of vibration stability.The proposed method is successfully applied to the Millennium Bridge,and its effectiveness is verified by comparing the Monte Carlo and Lyapunov methods.The proposed method can obtain the dynamic probability of the vibration as stable or instable and provide a reference for quantitative analysis of lateral nonlinear stochastic vibration stability of footbridges.

Theoretical and experimental research on characteristics of lateral vibration for a pre-stress bolt supporting system

According to the structure and stress trait of bearing bolts,a lateral-vibrationmechanics model was established for them,and the relation between lateral-vibration frequencyand axial load was analyzed;then,lateral-vibration trait of bearing bolts was studiedthrough laboratory simulation test.The results indicate that vibration frequency of boltsupport system increases as well as axial force,the detection on axial load of bolts can bemade by generating lateral vibration of bearing bolts.Theoretical and experimental researchresults show that frequency method is effective for detecting the axial force of boltsupport system.

Experimental and theoretical investigations of the lateral vibrations of an unbalanced Jeffcott rotor

The current work experimentally explores and then theoretically examines the lateral vibrations of an unbalanced Jeffcott rotor-system working at several unbalance conditions.To this end,three conditions of eccentric masses are considered by using a Bently Nevada RK-4 rotor kit.Measurements of the steady-state as well as the startup data at rigid and flexible rotor states are captured by conducting a setup that mimics the vibration monitoring industrial practices.The linear governing equation of the considered rotor is extracted by adopting the Lagrange method on the basis of rigid rotor assumptions to theoretically predict the lateral vibrations.The dynamic features of the rotor system such as the linearized bearing induced stiffness are exclusively acquired from startup data.It is demonstrated that,with an error of less than 5%,the proposed two-degrees-of-freedom model can predict the flexural vibrations at rigid condition.While at flexible condition,it fails to accurately predict the dynamic response.In contrast to the other works where nonlinear mathematical models with some complexities are proposed to mathematically model the real systems,the present study illustrates the applicability of employing simple models to predict the dynamic response of a real rotor-system with an acceptable accuracy.

ZERO MODE NATURAL FREQUENCY AND NONLINEAR VIBRATION OF COUPLED LATERAL AND TORSION OF A LARGE TURBINE GENERATOR

Zero mode natural frequency (ZMNF) is found during experiments. The ZMNF andvibrations resulted by it are studied. First, calculating method of the ZMNF excited byelectromagnetic in vibrational system of coupled mechanics and electrics are given from the view ofmagnetic energy. Laws that the ZMNF varies with active power and exciting current are obtained andare verified by experiments. Then, coupled lateral and torsional vibration of rotor shaft system isstudied by considering rest eccentricity, rotating eccentricity and swing eccentricity. UsingLargrange-Maxwell equation when three phases are asymmetric derives differential equation of thecoupled vibration. With energy method of nonlinear vibration, amplitude-frequency characteristics ofresonance are studied when rotating speed of rotor equals to ZMNF. The results show that ZMNF willoccur in turbine generators by the action of electromagnetic. Because ZMNF varies withelectromagnetic parameters, resonance can occur when exciting frequency of the rotor speed is fixedwhereas exciting current change. And also find that a generator is in the state of large amplitudein rated exciting current.

On dynamics of elastic rod based on exact Cosserat model

The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.

Modeling unbalanced rotor system with continuous viscoelastic shaft by frequency-dependent shape function

A reduced-order dynamic model for an unbalanced rotor system is developed, taking the coupling between torsional and lateral vibrations into account. It is assumed that a shaft is regarded as a continuous viscoelastic shaft with unbalanced and small deformation properties. The equations of motion for the torsional and lateral vibrations are derived using Lagrange's approach with the frequency-dependent shape function. The rotor torsional vibration is coupled with the lateral vibrations by unbalance elements in a way of excitations. Simulation and experiment results show clearly that the torsional vibration has strong impact on the rotor lateral vibrations, and it causes subharmonic and superharmonic excitations through unbalance elements, which leads to the superharmonic resonances in the lateral vibrations. This model with low-order and high accuracy is suitable for rotor dynamic analysis in real time simulation as well as for active vibration control syntheses.

Flow-pipe-soil coupling mechanisms and predictions for submarine pipeline instability

The stability of a submarine pipeline on the seabed concerns the flow-pipe-soil coupling, with influential factors related to the ocean waves and/or currents, the pipeline and the surrounding soils. A flow-pipe-soil coupling system generally has various instability modes, including the vertical and lateral on-bottom instabilities, the tunnel-erosion of the underlying soil and the subsequent vortex-induced vibrations（VIVs） of free-spanning pipelines. This paper reviews the recent advances of the slip-line field solutions to the bearing capacity, the flow-pipe-soil coupling mechanism and the prediction for the lateral instability, the multi-physical coupling analysis of the tunnel-erosion, and the coupling mechanics between the VIVs and the local scour. It is revealed that the mechanism competition always exists among various instability modes, e.g., the competition between the lateral-instability and the tunnel-erosion. Finally, the prospects and scientific challenges for predicting the instability of a long-distance submarine pipeline are discussed in the context of the deep-water oil and gas exploitations.