Vibration reduction technology using modal energy propagation analysis method

The vibration analysis of beams with cracks is an important problem in the structural dynamics community. In this study, a general model for the vibration analysis of a cracked beam with general boundary conditions was developed and investigated, emphasizing its vibration and power flow characteristics. The beam crack was introduced via torsional and translational coupling springs, which separated the beam structure into two segments, and the corresponding vibration characteristics were investigated via an energy-based formulation in conjunction with the Lagrangian procedure. A boundary-smoothed Fourier series was employed to construct the beam displacement field to avoid boundary differential discontinuities. Various crack statuses, including their depths or positions can be easily considered by adjusting the stiffness coefficient of the artificial springs. Several examples were presented to validate the effectiveness and accuracy of the proposed model. The modal characteristics and forced response of a cracked beam were predicted and analyzed, respectively, with a detailed depiction of the power flow around the crack. The results indicate that the presence of a crack has an important effect on the modal characteristics of an elastically restrained beam, as well as on the power flow distribution across the beam structure. This study can provide an effective tool for the dynamic analysis and power flow mechanism of beam structures with various cracks and complex boundary conditions.

A steady state analysis is applied to study the voltage collapse problem. The modal analysis method is used to investigate the stability of the power system. Q-V curves are used to confirm the obtained results by modal analysis method and to predict the stability margin or distance to voltage collapse based on reactive power load demand. The load characteristics are considered in this research. Different voltage dependent loads are proposed in order to be used instead of the constant load model. The effect of induction machine load is considered in this study. The load is connected to several selected buses.;The analysis is performed for three well-known system; Western System Coordinating Council (WSCC) 3-Machines 9-Bus system, IEEE 14 Bus system and IEEE 30 Bus system. The modal analysis technique is performed for all systems using the constant load model, the voltage dependent load models and induction machine load model. Then, the most critical mode is identified for each system. After that, the weakest buses, which contribute the most to the critical mode, are identified using the participation factor. The Q-V curves are generated at specific buses in order to check the results obtained by the modal analysis technique and to estimate the stability margin or distance to voltage collapse at those buses.

Modal analysis techniques are widely used to characterize vibrations in structures, vehicles, machinery, etc. Modal parameters obtained through modal analysis are useful for structural health monitoring and condition monitoring. The common goal is to ensure the integrity of a mechanical system through monitoring of different operational conditions. Operational conditions described by spatial measurements can for instance be used to observe the vibration characteristics of the system and its parts. Therefore, the main originality of this work is to experimentally investigate if the presence of a turbulent gas flow in seal geometries can facilitate operational modal analysis for a coupled rotor–foundation system. A consistent and automatic way of obtaining the vibration characteristics is necessary to be included in the monitoring schemes. Therefore, this work also proposes a method to automatically obtain modal parameters for a bed plate of a rotor–foundation system when the rotor is affected by active magnetic bearings and gas seals. The automatic modal parameter algorithm is built on the stabilization diagram of modal parameters obtained from the stochastic subspace identification. Intermediate results from the automatic modal parameter algorithm show that some of the distance measures i.e., dωn,d, dζ, dMACX, dλ, dMACXωn,d, dMACXζ, and dMACXλ, for modal parameters in a stabilization diagram are better suited than others when distinguishing between possible physical modes and certainly spurious poles. The frequency band of interest for the system is found to influence the number of possible physical modes identified by the automatic algorithm. Measurements from 13 roving accelerometers are combined with the automatic modal parameter algorithm to obtain the vibration characteristics of the rotor and bed plate. For different operational conditions in the seal geometry, seven modes are consistently identified as physical modes by the automatic modal parameter algorithm. The algorithm uses (i) a combination of a white noise disturbance pattern intentionally introduced into the system through the active magnetic bearings and (ii) the operational disturbance coming from the seals, non-intentionally introduced by the turbulent gas flow. The seven physical modes are also identified when (iii) the rotor–foundation system is only disturbed from the turbulent gas flow in the seals. The seven physical modes identified by the algorithm under conditions (i), (ii), and (iii) compare well to the vibration characteristics found in experiments via experimental modal analysis and impact hammer testing as well as via a mathematical model of the rotor–foundation system.

Due to the non-periodic operation of the cylindrical linear induction motor, the vibration characteristics cannot be studied by the conventional steady-state method. In this paper, the finite element modal analysis method is used to describe the natural vibration characteristics of linear motor with different connection conditions, and the contribution factors of modal on the overall vibration are quantitatively analyzed. Besides, the modal change law of linear motor is analyzed, and the transient dynamics method is used to investigate the transient forced vibration characteristics of the linear motor during the movement of the mover. The research shows that the elastic connection can greatly reduce the natural vibration frequency of the linear motor; when the excitation force is applied, the mover bracket is the most easy to vibrate; the motion of the mover has little effect on the linear motor mode, and the difference is reflected in the different mode of stator because of the different relative position of mover and stator.

Modal synthesis method is a method which can reduce structural degrees of freedom, it is applicable for analysis and calculations of Machining centers and other large-scale structure. In this paper, the dynamical performance of Five-axis boring and milling processing center was studied with component mode synthesis technology . Compared with full model FEM, component mode synthesis technology could meet the accuracy requirements and have higher computational efficiency. Modal characteristics of processing center in different positions was studied, the result showed that each frequency of processing center in different position was different while the vibration mode remained unchanged.

\n \nA modal synthesis method to solve the elastoacoustic vibration problem\nis analyzed. A two-dimensional coupled fluid-solid system is considered;\nthe solid is described by displacement variables, whereas displacement \npotential is used for the fluid. A particular modal synthesis leading to \na symmetric eigenvalue problem is introduced. Finite element discretizations \nwith Lagrangian elements are considered for solving the uncoupled problems.\nConvergence for eigenvalues and eigenfunctions is proved, \nerror estimates are given, and numerical experiments exhibiting the good \nperformance of the method are reported.\n\n

This paper presents a rigorous field theoretical analysis of slow wave mode propagation in coplanar waveguide (CPW) metal-insulator-semiconductor (MIS) transmission lines with a laterally confined doping profile. Two types of transmission line structures are investigated-bulk silicon and semiconductor-on-insulator (SOI). In both cases a Gaussian profile of the doping depth is assumed. It was found that an optimum lateral width of the doping region exists for which both structures exhibit a much better slow wave factor at lower losses than traditional thin-film MIS transmission lines. The abrupt transition between MIS, CPW, and CPW on a normal insulating substrate was investigated as well. It was found that the reflection coefficient increases significantly with frequency and when the lateral width of the doping region is extended over the whole cross section of the CPW. The investigation was carried out using the frequency-domain transmission line modeling (TLM) (FDTLM) method.

MODELLING AND CONTROL OF A TWO-AXIS ROBOT WITH FLEXIBLE LINKS

<div class="htmlview paragraph">This paper adopts a method of tire modeling which uses tire experimental modal parameters which are obtained by means of radial and tangential excitation. The action force from ground to tire are treated as inputs for model. Calculations of static properties are dealt with transfer functions at 0 frequency. An iterative algorithm is used to work out the vertical properties, contact length and vertical and frictional force distribution in longitudinal direction. The vertical vibration characteristics under 300Hz of a pre-loaded tire are given, and that of the system composed of wheel, suspension and car body are analyzed by using modal synthesis method. The study shows the feasibility and advantages of this method.</div>

The paper presents how to identify natural frequencies and mode shapes of structures by Operational Modal Analysis (OMA) technique, in which the Frequency Domain Decomposition (FDD) method is used. This method is an experimental method only base on the data of measuring the dynamic response of the structures under the excitation due to ambient forces and operational loads to determine the vibration characteristics. Measure vibration (acceleration) and determine spectral density matrix, using the singular values decomposition method of spectral density matrix to determine the natural frequencies and mode shapes of structures. The calculation results show that the natural frequencies, the mode shapes form determined by the OMA technique is consistent with the calculation results according to the theory and show the reliability of the method.KeywordsNatural frequencyMode shapeIdentifyEMAOMAFDD

An optimum multimode interference coupler as an all-optical switch based on nonlinear modal propagation analysis

For large and complex structures with repetitive characteristics, a multi-stage substructure dynamic analysis method based on modal synthesis is proposed to effectively improve the efficiency of simulation calculation. First, the repetitive components are taken as the primary substructure, and the components that produce local modes in the primary substructure are taken as the secondary substructure. The modal synthesis method is used to truncate all modal characteristics of the secondary substructure, and the constrained modal parameters and main modal parameters of the primary substructure are obtained. Then, according to the spatial coordinates, the primary substructure stiffness matrix and mass matrix are repeatedly assembled to obtain the condensation model of the whole structure. The condensation model is used for dynamic simulation to obtain the acceleration load of the substructure installation interface. Finally, the internal dynamic response of the substructure at all levels is obtained by using the super-element method. The simulation analysis of space-borne phased array synthetic aperture radar antenna shows that the multi-stage substructure dynamic simulation analysis results are highly consistent with the traditional analysis results, and the calculation efficiency is increased by more than four times. The substructure dynamic analysis method is reasonable and reliable.

This study describes the rotordynamics analysis of the Space Shuttle Main Engine (SSME) high-pressure oxidizer turbopump. Modal synthesis methods were used to account for the complex coupling of the pump and engine structure. Cross-coupling elements effecting rotor stability were included in the analysis. Results of the analysis indicated that smaller bearing clearances and a smooth turbine interstage seal would result in longer bearing life and improved stability. Subsequent testing with these design features has shown the same results.

The large flexible solar array for the satellite will deploy when it reaches the scheduled orbit by the space rocket, which is key for the normal running of the satellite. However, undesirable and unpredicted frequency vibration may be resulted from the flexibility of elements of the solar array. In this paper, the dynamic model of the solar panel was firstly developed based on the modal synthesis method. Moreover, the stretchable mechanism in the solar array was introduced by applying Euler-Bounerlli beam theory. Also, guide ropes, hinges and electric cables were considered in the proposed model. It was found the proposed model could achieve a higher accuracy of simulation compared to the traditional method with the coordinate method. Especially, the dependence of the guide rope tension on the deployment dynamic behavior of the solar array was explored by this model. Results showed that vibrations of the solar array could be reduced by improving the guide rope tension, which could be used in design and operation of the solar array.

The free vibrations of a complex system with a natural frequency identical to that of one of its subsystems is discussed. Such eigenvibrations need special consideration in many modal synthesis methods as the characteristic matrix (equation) does not exist. Particular emphasis has been placed on the case where a resonating subsystem is subjected to forces from other subsystems, which has not received sufficient attention in the literature on substructure synthesis methods. Examples of such eigenvibrations for two simple systems are given. A general equation for system eigenfunctions corresponding to eigenfrequencies of the isolated subsystems is presented and discussed.