Natural Frequency Of System Research Articles

A Combined Numerical and Modal Analysis on Vertical Vibration Response of Railway Vehicle

In this paper the vertical vibration response of a 9 degrees-of-freedom (DOF) 4-axle freight wagon, modeled as a multi-body system is investigated. The Lagrange's equation is used to obtain the equations of motion, and the corresponding system matrices are then assembled. A combined modal analysis and numerical integration of the convolution integral is adopted, which is achieved by programming a MATLAB script. Modal analysis is used to uncouple the differential equations and thereafter, the convolution integrals are numerically integrated using piecewise constants as interpolating functions. The Complex-Exponential Method (CEM) is then used to extract damping ratio, mode shapes and the system's natural frequencies from test data, this information is then used to compute the numerical solution. The developed models are then validated with measured data.

Model Based Research of Dynamic Performance of Shaft-Bearing System in High-Speed Field

Dynamic performance of the high-speed running shaft-bearing system (SBS) is different from that of idle state system due to the high-speed effects (HSE), including shaft centrifugal force, gyroscopic moment, and nonlinear bearing operational stiffness. In this paper, aiming at improving the operation stability, dynamic performance of SBS operating in high-speed field is investigated based on a finite element (FE) dynamic model. Firstly, the Timoshenko beam elements are applied to develop the SBS FE model with full consideration of HSE. Secondly, idle state frequency response function at the front tip is obtained analytically and experimentally to validate that the FE model can illustrate the system dynamic behaviors in static condition. Finally, by substituting various rotational velocities into the FE model, the HSE on system natural frequencies are studied one by one as well as together. The results show that, when bearing is being extremely light preloaded, SBS frequencies are affected by the HSE of shaft more than bearing, especially where the gyroscopic moment effect of shaft is the most influential factor. Moreover, the nonmonotonic variation of bearing operational stiffness is analyzed. The “stiffen” phenomenon explained in this paper provides a more comprehensive understanding of the nonlinear bearing operational stiffness.

空间臂式补偿机构轴承预紧力与系统刚度关系分析

When the spatial telescope tracks the target on the orbit,move and rotation will occurr between the visual axis of the telescope and target( namely pointing deviation and oscillation) due to all kinds of factors in space. In order to compensate above errors,the arm compensation mechanism is designed to compensate the errors between the visual axis and the target. Because the size and weight of the arm compensation mechanism are restricted severely,and the size of the telescope is huge and its weight is more than 3 000 kg,this configuration results in lower stiffness of the system. In order to satisfy higher machinery stiffness required by the control system,the feasibility is analyzed to improve system stiffness through forcing preload on bearing after the system configuration is confirmed. This paper studies on the relationship among bearing preload,bearing stiffness and system stiffness,and the relationship curve between bearing preload and system natural frequency is obtained. The analysis proves that forcing an appropriate preload to bearing can improve system stiffness on the condition that the system configuration is confirmed,and it is also an effective method to confirm the optimumbearing preload.

Comparison of Robust Input Shapers for Elimination of Residual Vibrations

Input shaping is a feedforward control technique for improving the settling time and positioning accuracy, while minimizing residual vibrations. Shaped command profiles are generated by convolving a sequence of impulses. To design an input shaping controller, estimates of the system natural frequency and damping ratio are required. However, real systems cannot be modeled exactly, making the robustness to modeling errors an important consideration. Many robust input shapers have been developed, but robust shapers typically have longer durations that slow the system response. This creates a compromise between shaper robustness and rise time. This paper analyses the compromise between shaper duration and robustness for several robust input shapers

Influence of inerter on natural frequencies of vibration systems

Abstract This paper investigates the influence of inerter on the natural frequencies of vibration systems. First of all, the natural frequencies of a single-degree-of-freedom (SDOF) system and a two-degree-of-freedom (TDOF) system are derived algebraically and the fact that the inerter can reduce the natural frequencies of these systems is demonstrated. Then, to further investigate the influence of inerter in a general vibration system, a multi-degree-of-freedom system (MDOF) is considered. Sensitivity analysis is performed on the natural frequencies and mode shapes to demonstrate that the natural frequencies of the MDOF system can always be reduced by increasing the inertance of any inerter. The condition for a general MDOF system of which the natural frequencies can be reduced by an inerter is also derived. Finally, the influence of the inerter position on the natural frequencies is investigated and the efficiency of inerter in reducing the largest natural frequencies is verified by simulating a six-degree-of-freedom system, where a reduction of more than 47 percent is obtained by employing only five inerters.

Shear wave velocity measurements and soil–pile system identifications in dynamic centrifuge tests

This paper presents a pre-shaking technique for measuring the \(V_{s}\) profile of sand deposits and determining the natural frequencies of the sand bed and soil-structure system in a centrifuge model at an acceleration of 80 g. The pre-shaking technique is a non-destructive test. It uses a shaker as a wave generation source and a vertical array of accelerometers embedded in the sand bed and the accelerometers attached to the pile head as receivers. The pre-shaking method can be easily used for in-flight subsurface exploration (\(V_{s}\) profile measurements) and in-flight system identification of soil-structure systems (natural frequency measurements). A soil–pile centrifuge model is used to demonstrate the versatility of pre-shaking during a routine centrifuge shaking table test. This paper discusses the testing setup, testing procedures, related SI techniques, and signal processing for the soil–pile system. The natural frequencies measured by the pre-shaking tests are consistent with theory-based results. This technique can be conducted at any time before and after major earthquake events occur in a test.

Characteristics Analysis of the Automobile with Negative Stiffness Suspension

One new negative stiffness suspension is introduced in this paper. The vehicle with negative stiffness suspension has good ride comfort and handling stability. The natural frequency of system could be reduced in vertical direction by applying negative stiffness suspension. The vehicle model with negative stiffness suspension or not is built in ADAMS. The comparison of simulation results show that the vehicle with negative stiffness suspension could reduce the natural frequency of system and vibration transmissibility, and also improve the vehicle ride comfort and vehicle handling stability.

Design of a New Piezoelectric Vibrating Feeder

With two upper and nether piezoelectric vibrators to provide excitation in the same time, vertical double driven piezoelectric feeder (vertical double driven feeder for short in the paper) has smaller piezoelectric ceramics (PZT), and lower driving voltage to prolong the lifetime of the PZT, meanwhile, its carrying capacity gets stronger, compared with vertical single driven piezoelectric feeder (vertical single driven feeder for short in the paper). Vibration analysis was carried out on the feeder system, and the affection factors on the system natural frequency and feeder tray amplitude were received. Based on the modal analysis, the system theoretical resonant frequency was got as 135.95Hz. In the end, the prototype was tested to analyze the relationships among the feeding speed, feeder tray amplitude, driving voltage and driving frequency.

The dynamic characteristics of harvesting energy from mechanical vibration via piezoelectric conversion

As an alternative power solution for low-power devices, harvesting energy from the ambient mechanical vibration has received increasing research interest in recent years. In this paper we study the transient dynamic characteristics of a piezoelectric energy harvesting system including a piezoelectric energy harvester, a bridge rectifier, and a storage capacitor. To accomplish this, this energy harvesting system is modeled, and the charging process of the storage capacitor is investigated by employing the in-phase assumption. The results indicate that the charging voltage across the storage capacitor and the gathered power increase gradually as the charging process proceeds, whereas the charging rate slows down over time as the charging voltage approaches to the peak value of the piezoelectric voltage across the piezoelectric materials. In addition, due to the added electrical damping and the change of the system natural frequency when the charging process is initiated, a sudden drop in the vibration amplitude is observed, which in turn affects the charging rate. However, the vibration amplitude begins to increase as the charging process continues, which is caused by the decrease in the electrical damping (i.e., the decrease in the energy removed from the mechanical vibration). This electromechanical coupling characteristic is also revealed by the variation of the vibration amplitude with the charging voltage.

Effect of coupling between passenger compartment and trunk of a car on coupled system natural frequencies using acoustic frequency response function

Conventional numerical techniques, used to study the acoustics of a car passenger cabin, treat the cabin as an isolated cavity excited by the cavity boundaries. Realistically, other cavity volumes such as the trunk communicate with the cabin through the holes in the parcel shelf of the car. An extended acoustic model of a car is formed by the cavity volumes of the passenger compartment and the trunk as well as air leakages through the holes provided for electrical devices and ventilation on the parcel shelf. In this study, the dynamic influence of air leakages between the passenger and trunk compartments on the first and second coupled system modes was investigated experimentally using acoustic frequency response function. The response to the acoustic excitation was measured for four different configurations of trim and holes of the parcel shelf. The natural frequencies of the first and second coupled system modes increased with increasing holes size with and without the trim of the parcel shelf. The experimental results were in good agreement with the reported results of coupling effects of double cavities connected by a neck. In the low frequency region since the wavelength is longer compared to the holes dimension, these holes act as point sources.

A Circuit-Based Dynamic Characteristic Analysis on the Propelling Flow System in Liquid Rockets

To penetrate into the study of POGO vibration, by taking the LRC equivalent circuit analyzing method, based on two boundary conditions in document [, taking the flow pulse drive into consideration, this paper proposes four boundary conditions specific to the propelling flow system in liquid rockets, and at the same time, complements the mathematic model. Further, by way of network function, under the liquid system flow parameter, this paper infers transfer function expressions, and makes the accurate solution of the natural frequency under every boundary condition. At last, from the statistic point of view, by the method of correlation coefficient, this paper studies the influence that the flow parameter may have on the system natural frequency, and set the major influential liquid flow parameter to the system natural frequency of liquid propelling flow system in liquid rockets.

Research Modal Analysis Method of MW Wind Turbines

In order to explore the modal characteristics of the wind turbine, this paper researches how these natural frequencies of the major structural components within the operation speed range to avoid coupled resonance phenomenon. Aiming at 1500kW variable speed variable pitch double-fed wind turbines which are the mature products in market, the whole wind turbine dynamic modal equations are established by Lagrange method, and then process on-site testing is carried out to obtain measured modal characteristic parameters. The results of both theoretical and measured dates show that deviation between theoretical data and measured data, how the subsystem boundary conditions simplified methods to influence the rotor system natural frequencies, how the subsystem boundary conditions simplified methods to change the cross point of the rotor system natural frequencies with rotor speed 3P, and solution for wind turbine pass the cross point. The results will provide a certain extent guidance for the wind turbine development, design and optimization.

Vibration-based damage identification of reinforced concrete member using optical sensor array data

To detect and locate the structural damage from direct measurements can be done only when the sensors are very closely located to the damage initiating point, which is generally impossible to predict, particularly for the reinforced concrete structures. With the availability of high-resolution distributed sensing, using optical tracker on light targets, the damage location as well as the level of damage can be identified. The objective of this article is to conduct structural system identification of a reinforced concrete frame by using the proposed structural integrity index (identify the element curvature and null-space damage index) and the estimation of finite element strain. Finally, a discussion on the identified time-varying system natural frequency and stiffness/strength degradation of the reinforced concrete structure from global measurement in relation to the calculated structural integrity index using optical sensing array data and element strain on the identification of damage location and damage severity are presented.

Structural damage assessment using output-only measurement: Localization and quantification

In this article, a systematic way of structural damage assessment algorithm, including identification of damage location and damage quantification, is proposed using output-only measurement. First, the null-space-based and subspace-based damage detection methods are used to confirm the damage severity of a structure. Then, the stochastic subspace identification technique is adopted to identify the time-varying system natural frequencies from the global response measurement. Finally, the novelty index, defined as the Euclidean norm of the time–frequency Hilbert amplitude spectrum of measurement between the intact and the damaged structures, is applied to locate the damage. To quantify the damage, the complete system realization is obtained from the identified modal properties through stochastic subspace identification method. From which, the inter-story stiffness reduction ratio can be identified using the normalized stiffness matrix. For case of limited measurement, the multi-setup operational modal analysis is applied to construct the complete system matrix. Verification of the proposed damage assessment algorithm using response data from a series of shaking table test of a six-story steel structure with the cut in column member to simulate the damage is demonstrated.

Transfer Matrix Method for the Determination of the Free Vibration of Two Elastically Coupled Beams

The feasibility of using the transfer matrix method (TMM) to compute the free vibration characteristics of a system composed of continues and discrete elements vibrating in a plane is explored theoretically. In the approach to the problem, a general analytical method based on TMM is developed for the vibrations of two uniform Euler-Bernoulli beams coupled by a spring. The components of the transfer matrix are all functions of the systems natural frequency. The overall transfer equation only involves boundary state vectors, whereas the state vectors at all other connection points do not appear. The state vectors at the boundary are composed of displacements, rotation angles, bending moments and shear forces, which are partly known and partly unknown. Moreover, the overall transfer matrix is independent of the degrees of the freedom. A non-trivial solution of the final overall transfer equation requires the coefficient matrix to be singular. This paper reduces the zero search of its determinate to a minimization problem and demonstrates a simple, robust algorithm being much more efficient than direct enumeration. A numerical result is presented to demonstrate the proposal method.

The Herringbone Gear Box Modal Analysis and Experimental Study

In order to more accurately estimate the intrinsic mode of herringbone gear transmission box, fluid-structure interaction model of gear box and lubricants is established. Gear system natural frequencies and mode shapes is calculate out on the establishment of the fluid-solid coupling dynamics equations. The finite element models of gearbox and lubricating oil are build by ANSYS software, and the results of inherent characteristics are given. The top ten order natural frequency is distributed between 611.8HZand 2487HZ, and the first two order mode shape is respectively shown as the axial swing and horizontal swing. In order to verify the analysis results, the hammering method of single-input multiple-output (SIMO) is used to test gearbox structure modal. The results show that the mode shapes get from ANSYS analysis are consistent with the datas of experimental measurements, and the maximum deviation of natural frequency between experiment and theory is blew 15%. So it can be shown the fluid-structure interaction model in this paper is effective and reasonable.

Dynamics Analysis of Milling Machine Spindle

The paper takes the numerical control milling machine xk8140 as the research object. The machine tools spindle system digital model is established in UG. The spindle systems natural frequency is obtained throng dynamics analysis of milling machine spindle under specific working conditions, as well as the relational of vibration and error in harmony response situation. In view of the result the rational appraisal to the spindle system structure rationality is made. Accordingly, the irrational causes removed, that noise increasing, processing quality reducing obviously and so on attribute to the irrational structure of the spindle system machine tools when the spindle rotational speed achieve 4000rpm or higher.

Suspension point vibration parameters for a given equilibrium of a double mathematical pendulum

The motion of a double mathematical pendulum under the action of the gravity force and a vibration force whose frequency substantially exceeds the system natural frequencies is considered. An oblique vibration stabilizing the pendulum in an arbitrarily given position is sought. The domain of existence of the pendulum equilibrium points and the vibration parameters corresponding to a given equilibrium of the pendulumare obtained analytically. In the domain of existence of equilibrium points, the subdomain of their stability is distinguished.

The modelling, simulation and experimental testing $60#?tjl$62#?>of the dynamic responses of an elevator system

Vertical vibrations affect passenger comfort during an elevator travel. This work presents the results of a study of vertical vibrations caused by torque ripple generated at the elevator drive system. Tests are performed on a 1:1 roping configuration laboratory model; the acceleration response at the suspended masses and at the drive machine, the machine shaft velocity and the three phase current intensities supplied to the machine are measured during several travels. The machine torque is estimated from the current intensities. A non-stationary model of an elevator is then developed to simulate the acceleration response. The model accommodates the drive system dynamics. The machine parameters are computed by means of the Finite Element Method simulation software FLUX. FLUX computes the amplitudes of the torque ripple and the radial forces at the air-gap. As the torque ripple computed by FLUX is smaller than that torque estimated from the machine currents, the latter is added as a perturbation to the controller generated torque. With respect to the car–counterweight–sheave–ropes assembly a five degree-of-freedom lumped-parameter model (LPM) and a novel distributed-parameter one (DPM) are developed. The elevator dynamics represented by the DPM is described by a partial differential equation set that is discretised by expanding the vertical displacements in terms of the linear stationary mode shapes of a system composed of three masses constrained by the suspension rope. The models are implemented in the MATLAB/Simulink computational environment and the system response is determined through numerical simulation. It is shown that the LPM forms a good approximation of the DPM. The frequency content of the computed and measured accelerations demonstrates that the elevator car vibrates at frequencies generated at the machine, especially when they are close to the system natural frequencies.

Free vibration and dynamic response of a fluid-coupled double elliptical plate system using Mathieu functions

A three-dimensional analytic model involving products of angular and radial Mathieu functions is developed for the exact free vibration analysis and transient acousto–structural response of two parallel elliptical plates, coupled with an internal bounded inviscid and compressible fluid medium, and under general external transverse loads of arbitrary temporal and spatial variations. Extensive numerical data are presented in an orderly fashion for the first ten symmetric/anti-symmetric system natural frequencies as a function of fluid layer thickness parameter for selected plate aspect ratios. Also, the occurrences of frequency veering phenomena between various modes of the same symmetry group and the interchange of associated mode shapes in the veering region are noted and discussed. Moreover, selected fluid-coupled structural deformation mode shapes are presented in vivid graphical form and the issue of mode localization is examined. The Laplace transform with respect to the time variable is subsequently invoked and a linear system of coupled algebraic equations is ultimately obtained, which is truncated and then solved by implementing Durbin's Laplace inversion algorithm accompanied with special solution convergence enhancement techniques for eradication of spurious oscillations (Gibbs' phenomenon). Numerical simulations are conducted for the displacement time histories of water-coupled double aluminum plates of selected aspect ratios and fluid depths, subjected to external loads of practical interest (i.e., an impulsive point load, a concentrated pulse load, and a uniformly distributed blast load). Validity of the results is established through computations made by using a commercial finite element package as well as by comparison with the data available in literature.