A particle damper consists of a bed of granular materials moving in cavities within a multi degree-of-freedom (MDOF) structure. This paper deals with the damping effects on forced vibrations of a MDOF structure provided with the vertical particle dampers. In the analysis, the particle bed is assumed to be a single mass, and the collisions between the granules and the cavities are completely inelastic, i.e., all energy dissipation mechanisms are wrapped into zero coefficient of restitution. To predict the particle damping effect, equations of motion are developed in terms of equivalent single degree-of-freedom (SDOF) system and damper mass with use made of modal approach. In this report, the periodic vibration model comprising sustained contact on or separation of the damper mass from vibrating structure is developed. A digital model is also formulated to simulate the damped motion of the physical system, taking account of all vibration modes. Numerical and experimental studies are made of the damping performance of plural dampers located at selected positions throughout a 3MDOF system. The experimental results confirm numerical prediction that collision between granules and structures is completely inelastic as the contributing mechanism of damping in the vertical vibration. It is found that particle dampers with properly selected mass ratios and clearances effectively suppress the resonance peaks over a wide frequency range.

Masanobu Inoue

Isao Yokomichi

Koju Hiraki

Particle Damping with Granular Materials for Multi Degree of Freedom System

This paper investigates synchronization of two self-synchronous vibrating machines on an isolation rigid frame. Using the modified average method of small parameters, we deduce the non-dimensional coupling differential equations of the disturbance parameters for the angular velocities of the four unbalanced rotors. Then the stability problem of synchronization for the four unbalanced rotors is converted into the stability problems of two generalized systems. One is the generalized system of the angular velocity disturbance parameters for the four unbalanced rotors, and the other is the generalized system of three phase disturbance parameters. The condition of implementing synchronization is that the torque of frequency capture between each pair of the unbalanced rotors on a vibrating machine is greater than the absolute values of the output electromagnetic torque difference between each pair of motors, and that the torque of frequency capture between the two vibrating machines is greater than the absolute value of the output electromagnetic torque difference between the two pairs of motors on the two vibrating machines. The stability condition of synchronization of the two vibrating machines is that the inertia coupling matrix is definite positive, and that all the eigenvalues for the generalized system of three phase disturbance parameters have negative real parts. Computer simulations are carried out to verify the results of the theoretical investigation.

Chunyu Zhao

Qinghua Zhao

Zhaomin Gong

Bangchun Wen

Synchronization of Two Self-Synchronous Vibrating Machines on an Isolation Frame

The dynamic behavior of rotor containing crack is a subject of particular interest and has been extensively investigated by researchers. The effects of crack on the natural frequencies and modal shapes and motion orbits of rotor systems have already been well explored by researchers. In the present study, the infl uence of crack on the transmission matrices of the rotor systems is investigated by using the FEM (finite element method) analysis and the HBM (harmonic balance method) technique. It is for the first time revealed that there are differences between the transmission matrices for the fundamental frequency components and the transmission matrices for the super-harmonic components, and the differences are mainly determined by the crack location. The results are validated by numerical experiments where the system responses of a rotor system are obtained using Runge-Kutta method. The results are of significance for the development of effective crack detection methods in practice.

Z.K. Peng

Z.Q. Lang

G. Meng

F.L. Chu

The Effects of Crack on the Transmission Matrix of Rotor Systems

Residual stress is very important to the straightened quality of rail, this paper adopts explicit dynamics FEM to study on residual stress. We established compound roller model and calculated the residual value of heavy rail through 9 roller horizontal straightening and 8 roller vertical straightening. The reductions of straightening rollers are taken as the main effective factor to the residual stress in the straightening process. We adopt orthogonal calculation method to obtain the main effective factor to residual stress. On the base of assurance of the straightness, we obtained the optimal regulation in which the residual stress is the smallest, so the paper makes the important theoretical and actual sense to formulate the rational straightening regulation and improve the straightening quality of rail.

Hua Song

Peilong Wang

Lihua Fu

Ming Chen

Zhongqiang Wang

Huiyuan Sun

Straightening Regulation Optimization on the Residual Stress Induced by the Compound Roll Straightening in the Heavy Rail

The validity of the application of energy flow analysis for beam structures under random excitations is investigated in this paper. The approximate solutions of energy density and intensity in a beam subject to random loadings are obtained by solving the governing equation of random energy flow analysis using Fourier transform technique. The formulations of the exact energy density distribution and intensity in the beam are derived using the classical modal analysis method. For a simply supported beam subject to distributed or concentrated random excitations, the validity of random energy flow analysis is investigated through comparisons between solutions obtained from the approximate and exact methods for energy response as well as intensity. The results indicate that, the mode count of the analysis frequency band, which means the number of modes involved in the band, is the key factor affecting the prediction accuracy of random energy flow analysis, and that if the mode count of the band is sufficiently large, random energy flow analysis can provide rather accurate estimates for both energy density and intensity in a wide frequency range.

Jin You

Hong-Guang Li

Guang Meng

Validity Investigation of Random Energy Flow Analysis for Beam Structures

With the analytic method and numerical method respectively, the asymptotic solutions and finite element model of rotor system with single slowly varying mass is obtained to investigate the time frequency features of such rotor system; furthermore, with given model of slowly varying mass, the rotor system with dual slowly varying mass is studied. For the first order approximate solution is used, there exists difference between the results with analytic method and numerical method. On the base of common characteristics of rotor system with dual slowly varying mass, the general rules and formula describing the frequency distribution of rotor system with multiple slowly varying mass are proposed.

Tao Yu

Qingkai Han

Time Frequency Features of Rotor Systems with Slowly Varying Mass

On the basis of the Bouc-Wen hysteretic model, the effective numerical method for the response of nonlinear multi-degree-of-freedom (MDOF) stochastic hysteretic systems is presented using second moment method. Using this method, the mean values, variances and covariances are computed. The Monte Carlo simulation is applied to validate the method. The results obtained by the two methods are contrasted, and the solutions of the method in this paper agreed very well with the Monte Carlo simulation. It has solved the random response of nonlinear stochastic vibration systems which is caused by the stochastic hysteretic loop itself.

Yimin Zhang

Stochastic Responses of Multi-Degree-of-Freedom Uncertain Hysteretic Systems

Nonlinear models of transverse vibration of axially moving viscoelastic beams subjected external transverse loads via steady-state periodical response are numerically investigated. An integro-partial-differential equation and a partial-differential equation of transverse motion can be derived respectively from a model of the coupled planar vibration for an axially moving beam. The finite difference scheme is developed to calculate steady-state response for the model of coupled planar and the two models of transverse motion under the simple support boundary. Numerical results indicate that the amplitude of the steady-state response for the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters and the integro-partial-differential equation gives results more closely to the coupled planar vibration.

Hu Ding

Li-Qun Chen

Nonlinear Models for Transverse Forced Vibration of Axially Moving Viscoelastic Beams

The present work carries out a comprehensive investigation into the border distortion deficiency for the conventional scalogram and the reassigned scalogram. The reasons for this deficiency are analyzed, and a simple way is suggested to determine the border distortion ranges. New methods are proposed to reduce the border distortions in both the scalograms. The practical meanings of the border distortion improvement method are demonstrated by applying both the scalograms with and without border distortion improvements to estimate the modal parameters for a 2-DOF linear system. The estimation results indicate that, in the presence of noise, which is inevitable in practice, for the mode with weak amplitude, the reassigned scalogram can perform better than the conventional scalogram in estimating the modal parameters. In addition, for the mode with short effective duration, its frequency components at the border distortion ranges are of great importance for the modal parameter estimation purpose, and the border distortion improvement method can greatly increase the estimation accuracy.

F. L. Chu

Improved Wavelet Reassigned Scalograms and Application for Modal Parameter Estimation

In this paper, the dynamical performance of polishing robot working in unstructured environment is investigated. Structure mechanism and operating principle of a polishing robot are introduced firstly, and its dynamical model is established. Then, a S-shaped acceleration-deceleration path planning method and a human-simulated intelligent control (HSIC) strategy are proposed. The S-shaped acceleration-deceleration path planning method is to switch the magnitude and direction of the abrupt velocities between motion sections in order to improve the work efficiency, the smoothness of movement and the processing accuracy. The HSIC control strategy is built based on the unstructured environment information measured by ultrasonic sensors, in which the appropriate programs prepared in advance are determined according to the size and sign of both the control error and its change rate. Simulation results show that the intelligent control strategy combining with optimum path planning method are effective to reduce the structure vibration, to improve the stability and the control accuracy of the polishing robot system.

Zhong Luo

Shuxian Yang

Yilan Sun

Hongyi Liu

Optimized Control for Dynamical Performance of the Polishing Robot in Unstructured Environment

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Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience.&nbsp;

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Chief Editor&nbsp;Dr Tai Thai&nbsp;is based at the University of Melbourne and his current research focuses on high strength materials for sustainable construction of buildings, bridges and other infrastructure.

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