Showing papers on "Modal testing published in 2007"

Vibration damping, control, and design

Abstract: VIBRATION DAMPING Vibration Damping Clarence W. de Silva Introduction Types of Damping Representation of Damping in Vibration Analysis Measurement of Damping Interface Damping DAMPING THEORY Randall D. Peters Preface Introduction Background Hysteresis - More Details Damping Models Measurements of Damping Hysteretic Damping Failure of the Common Theory Air Influence Noise and Damping Transform Methods Hysteretic Damping Internal Friction Mathematical Tricks - Linear Damping Approximations Internal Friction Physics Zener Model Toward a Universal Model of Damping Nonlinearity Concluding Remark EXPERIMENTAL TECHNIQUES IN DAMPING Randall D. Peters Electronic Considerations Data Processing Sensor Choices Damping Examples Driven Oscillators with Damping Oscillator with Multiple Nonlinearities Multiple Modes of Vibration Internal Friction as Source of Mechanical Noise Viscous Damping - Need for Caution Air Influence STRUCTURE AND EQUIPMENT ISOLATION Y.B. Yang, L.Y. Lu, and J.D. Yau Introduction Mechanisms of Base-Isolated Systems Structure-Equipment Systems with Elastomeric Bearings Sliding Isolation Systems Sliding Isolation Systems with Resilient Mechanism Issues Related to Seismic Isolation Design VIBRATION CONTROL Nader Jalili and Ebrahim Esmailzadeh Introduction Vibration-Control Systems Concept Vibration-Control Systems Design and Implementation Practical Considerations and Related Topics HELICOPTER ROTOR TUNING Kourosh Danai Introduction Neural Network-Based Tuning Probability-Based Tuning Adaptive Tuning Case Study Conclusion VIBRATION DESIGN AND CONTROL Clarence W. de Silva Introduction Specification of Vibration Limits Vibration Isolation Balancing of Rotating Machinery Balancing of Reciprocating Machines Whirling of Shafts Design through Modal Testing Passive Control of Vibration Active Control of Vibration Control of Beam Vibrations Appendix 7A: MATLAB Control Systems Toolbox STRUCTURAL DYNAMIC MODIFICATION AND SENSITIVITY ANALYSIS Su Huan Chen Introduction Structural Dynamic Modification of Finite Element Model Perturbation Method of Vibration Modes Design Sensitivity Analysis of Structural Vibration Modes High-Accuracy Modal Superposition for Sensitivity Analysis of Modes Sensitivity of Eigenvectors for Free-Free Structures Matrix Perturbation Theory for Repeated Modes Matrix Perturbation Method for Closely Spaced Eigenvalues Matrix Perturbation Theory for Complex Modes VIBRATION IN ROTATING MACHINERY H. Sam Samarasekera Introduction Vibration Basics Rotordynamic Analysis Vibration Measurement and Techniques Vibration Control and Diagnostics REGENERATIVE CHATTER IN MACHINE TOOLS Robert G. Landers Introduction Chatter in Turning Operations Chatter in Face-Milling Operations Time-Domain Simulation Chatter Detection Chatter Suppression Case Study FLUID-INDUCED VIBRATION Seon M. Han Description of the Ocean Environment Fluid Forces Examples SOUND LEVELS AND DECIBELS S. Akishita Introduction Sound Wave Characteristics Levels and Decibels HEARING AND PSYCHOLOGICAL EFFECTS S. Akishita Introduction Structure and Function of the Ear Frequency and Loudness Response Hearing Loss Psychological Effects of Noise NOISE CONTROL CRITERIA AND REGULATIONS S. Akishita Introduction Basic Ideas behind Noise Policy Legislation Regulation Measures of Noise Evaluation INSTRUMENTATION Kiyoshi Nagakura Sound Intensity Measurement Mirror-Microphone System Microphone Array SOURCE OF NOISE S. Akishita Introduction Radiation of Sound DESIGN OF ABSORPTION Teruo Obata Introduction Fundamentals of Sound Absorption Sound-Absorbing Materials Acoustic Characteristic Computation Compound Wall Attenuation of Lined Ducts Attenuation of Dissipative Mufflers General Considerations Practical Example of Dissipative Muffler DESIGN OF REACTIVE MUFFLERS Teruo Obata Introduction Fundamental Equations Effects of Reactive Mufflers Calculation Procedure Application Range of Model Practical Example DESIGN OF SOUND INSULATION Kiyoshi Okura Theory of Sound Insulation Application of Sound Insulation STATISTICAL ENERGY ANALYSIS Takayuki Koizumi Introduction Power Flow Equations Estimation of SEA Parameters Application in Structures INDEX

Field trials for dynamic characteristics of railway track and its components using impact excitation technique

Abstract: Assessment of condition of railway track is crucial for track design, repair, and effective maintenance operations. In-field dynamic testing in combination with track modelling represents an efficient strategy for identification of the current condition of railway track structure and its components. Field investigations for the dynamic characteristics of a railway track and its components were carried out and are presented in this paper. A non-destructive technique using impact excitation, so-called ‘modal testing’, was utilized in these trials. Integrated approach combining field measurements, experimental modal analysis, and finite element modelling to evaluate the dynamic parameters of the in situ railway track components are appended. A ballasted railway track site in Central Queensland managed by Queensland Rail (QR) was selected to perform the field tests. Six sleeper-fastening-rail assemblies were selected for dynamic testing. The frequency response functions (FRFs) were recorded by using Bruel & Kjaer PULSE vibration analyser in a frequency domain between 0 and 1600 Hz. The data obtained were best fitted using the least-square technique to determine the dynamic stiffness and damping constants of the tested track components. In addition, the experimentally determined resonance frequencies along with the dynamic properties of the track components can provide an important input for determining the maximum speed and axle load for the future track upgrades. This paper also points out on how to judge the dynamic responses (e.g. FRFs) together with the visual inspection of existing conditions from the field experience. Examples of testing results representing the deficient integrity are additionally highlighted. Based on the results, the impact excitation technique is an efficient method susceptible to the structural integrity of railway track structures.

Damage Identification on the Tilff Bridge by Vibration Monitoring Using Optical Fiber Strain Sensors

Abstract: Vibration testing is a well-known practice for damage identification of civil engineering structures. The real modal parameters of a structure can be determined from the data obtained by tests using system identification methods. By comparing these measured modal parameters with the modal parameters of a numerical model of the same structure in undamaged condition, damage detection, localization, and quantification is possible. This paper presents a real-life application of this technique to assess the structural health of the 50-year old bridge of Tilff, a prestressed three-cell box-girder concrete bridge with variable height. A complete ambient vibration survey comprising both vertical accelerations and axial strains has been carried out. The in situ use of optical fiber strain sensors for the direct measurement of modal strains is an original contribution of this work. It is a big step forward in the exploration of modal curvatures for damage identification because the accuracy in calculating the modal curvatures is substantially improved by directly measuring modal strains rather than deriving the modal curvatures from acceleration measurements. From the ambient vibrations, natural frequencies, damping factors, modal displacements and modal curvatures are extracted by the stochastic subspace identification method. These modal parameters are used for damage identification which is performed by the updating of a finite element model of the intact structure. The obtained results are then compared to the inspections performed on the bridge.

Finite element modal analysis of an HDD considering the flexibility of spinning disk–spindle, head–suspension–actuator and supporting structure

Abstract: This paper presents a finite element method to analyze the free vibration of a flexible HDD (hard disk drive) composed of the spinning disk–spindle system with fluid dynamic bearings (FDBs), the head–suspension–actuator with pivot bearings, and the base plate with complicated geometry. Finite element equations of each component of an HDD are consistently derived with the satisfaction of the geometric compatibility in the internal boundary between each component. The spinning disk, hub and FDBs are modeled by annular sector elements, beam elements and stiffness and damping elements, respectively. It develops a 2-D quadrilateral 4-node shell element with rotational degrees of freedom to model the thin suspension efficiently as well as to satisfy the geometric compatibility between the 3-D tetrahedral element and the 2-D shell element. Base plate, arm, E-block and fantail are modeled by tetrahedral elements. Pivot bearing of an actuator and air bearing between spinning disk and head are modeled by stiffness elements. The restarted Arnoldi iteration method is applied to solve the large asymmetric eigenvalue problem to determine the natural frequencies and mode shapes of the finite element model. Experimental modal testing shows that the proposed method well predicts the vibration characteristics of an HDD. This research also shows that even the vibration motion of the spinning disk corresponding to half-speed whirl and the pure disk mode are transferred to a head–suspension–actuator and base plate through the air bearing and the pivot bearing consecutively. The proposed method can be effectively extended to investigate the forced vibration of an HDD and to design a robust HDD against shock.

Scaling Factor Estimation Using an Optimized Mass Change Strategy, Part 1: Theory

Abstract: In natural input modal analysis, only un-scaled mode shapes can be obtained. The mass change method is, in many cases, the simplest way to estimate the scaling factors, which involves repeated modal testing after changing the mass in different points of the structure where the mode shapes are known. The scaling factors are determined using the natural frequencies and mode shapes of both the modified and the unmodified structure. However, the uncertainty on the scaling factor estimation depends on the modal analysis and the mass change strategy (number, magnitude and location of the masses) used to modify the dynamic behavior of the structure. In this paper, a procedure to optimize the mass change strategy is proposed, which uses the modal parameters (natural frequencies and mode shapes) of the original structure as the basic information.

Eliminating the Influence of Harmonic Components in Operational Modal Analysis

Abstract: Operational modal analysis is used for determining the modal parameters of structures for which the input forces cannot be measured. However, the algorithms used assume that the input forces are stochastic in nature. While this is often the case for civil engineering structures, mechanical structures, in contrast, are subject inherently to deterministic forces due to the rotating parts in the machinery. These forces are seen as harmonic components in the responses, and their influence should be eliminated before extracting the modes in their vicinity. This paper describes a new method based on the well-known Enhanced Frequency Domain Decomposition (EFDD) technique for eliminating these harmonic components in the modal parameter extraction process. For assessing the quality of the method, various experiments were carried out where the results were compared with those obtained with pure stochastic excitation of the same structure. Good agreement was found and the method is shown to be an easy and robust tool for enhancing the EFDD technique for mechanical structures.

Identification of electromechanical modal parameters of linear piezoelectric structures

Abstract: Reduced-order modal models of linear piezoelectric structures are useful in vibration control and health monitoring. We study experimental identification of the fundamental parameters of these modal models. We propose two identification techniques for estimating piezoelectric modal couplings and piezoelectric modal capacitances. Both methods are easily implementable and rely on elementary vibration tests. We show the application of these methods to a sample structure hosting multiple transducers.

Multiresponse Parameter Estimation for Finite-Element Model Updating Using Nondestructive Test Data

Abstract: Structural health monitoring using field measurements has developed into a major research area, responding to an increasing demand for evaluating the integrity of civil engineering structures. Model updating through parameter estimation is a key tool in a successful structural health monitoring program. A method for parameter estimation is developed for simultaneous use of static and modal nondestructive test data called the “multiresponse” parameter estimation. An error function normalization technique is also developed to facilitate effective multiresponse parameter estimation. This normalization technique can mitigate some of the numerical issues encountered during the parameter estimation procedure. However, this technique does not degrade the integrity of the parameter estimation procedure. Multiresponse parameter estimation provides an increased level of flexibility and feasibility of model updating for structural health monitoring. This paper presents full integration of static and modal nondestructive test data using both stiffness-based and mass-based error functions for structural health monitoring. A benchmark laboratory grid model of a bridge deck is utilized to illustrate application of both normalization and multiresponse parameter estimation for updating the stiffness and mass parameters using nondestructive test data.

Support Conditions for Experimental Modal Analysis

Abstract: When modal testing a structure for model validation, free boundary conditions are frequently approximated in the lab to compare with free boundary-condition analyses. Free conditions are used because they are normally easy to simulate analytically and easier to approximate experimentally than boundary conditions with fixed conditions. However, the free conditions can only be approximated in the lab, because the structure must be supported in some manner. This article investigates and quantifies the effects of the support conditions on both the measured modal frequencies and damping factors. The investigation has determined that the measured modal damping is significantly more sensitive to the support system (stiffness and damping) than the measured modal frequency. Included in the article are simple formulas that can be used to predict the effect on measured modal parameters given the support stiffness and damping. Modal testing is frequently used to validate the accuracy of structural dynamic models. Modal tests are performed on a structure to measure the modal frequencies, damping factors, and mode shapes. However during the modal test, a structure must be supported in some manner by the surrounding environment. Very frequently, free boundary conditions are the desired support conditions for comparison with computational results. Free conditions can only be approximated in the lab using soft supports, but the stiffness and damping of these added supports will affect the modal parameters of the combined structural system. A required part of pre-test planning is to design the support system to minimally affect the modal parameters. Obviously, one can include a model of the support system as part of the overall system model, and sometimes that is required due to compromises involved in the support system design. But one would like to be able to calculate the effects of the support system on the modal parameters to determine whether the effects are negligible or need to be accounted for. One of the primary objectives of this article is to derive fairly simple formulas and rules of thumb by which one can calculate the effect of the support conditions on the measured modal frequencies and damping factors so that appropriate support design can be performed before the test. The formulas and the effects of poor support conditions are also illustrated with results from two different modal tests. Historically, there has been concern for support stiffness and its effect on measured modal frequencies. Bisplinghoff, Ashley and Halfman 1 discuss the effects of support stiffness and mass on the modal frequencies, based on results of Rayleigh. 2 Wolf 3 discusses the effects of support stiffness with regard to modal testing of automotive bodies. He reports that the rule of thumb to simulate free boundary conditions is to design the support system so that the rigid-body modes, that is, the modes that would be at zero frequency except for the support conditions, are no more than one-tenth the frequency of the lowest elastic mode. But it is seldom possible to achieve this separation for vehicle tests. He states that test engineers frequently use a 1:3 to 1:5 separation ratio between the rigid-body modes and the lowest elastic mode. Wolf shows that such stiff supports can lead to significant errors in the measured modal frequencies. One of the current authors discussed support conditions in an earlier work, 4 and this article expands on that work with additional theoretical results and illustrates the theory with experiments and modeling. In his second edition of Modal Testing, 5 Ewins briefly discusses the issue of location of suspen sions for free boundary conditions in the test planning chapter. More recently, Brillhart and Hunt presented an exposition of many of the practical difficulties involved in designing good fixtures for a modal test, 6 and Avitabile briefly discussed this issue in a “Back to Basics” article. 7 In this article our primary emphasis here was to develop some quantitative measures of the effect of the support conditions on the modal frequencies and the modal damping ratios. Most finiteelement models could include the support stiffnesses and masses in the model, thus taking into account those effects. However, structural dynamic models often do not initially include damping, but use the measured modal damping ratios from a test to create a model, including damping. There is typically no validation of the damping model; it is taken directly from the test with the support conditions included. Consequently, one must be concerned with how the support conditions affect the measured damping. The remainder of this article is divided into four primary sections. In the first section, simple formulas are derived for a two degree-offreedom system. These formulas are simplistic, but can be used to derive rules of thumb and also easily illustrate the severity of the problem. The next section develops approximate formulas for the multi-degree-of-freedom problem that can be used for general structures. The last two sections further illustrate both the problem and the theory with some example modal tests, first from a very lightly damped uniform beam and second with a wind turbine blade that required a modal test for model validation and damping determination.

Modal Testing and Finite-Element Model Updating of a Lively Open-Plan Composite Building Floor

Abstract: This paper presents results of a combined experimental and analytical approach to investigate modal properties of a lively open-plan office floor. It is based on state-of-the-art finite-element (FE) modeling, FRF-based shaker modal testing, FE model correlation, manual model tuning, and sensitivity-based automatic model updating of a detailed FE model of this composite floor structure. The floor studied accommodates a fully furnished office. Such environments can be problematic regarding their vibration serviceability. However, there is a lack of reliable information about their as-built modal properties and the ability of designers to predict them. Therefore this paper has two aims: (1) to assess the ability to both predict and measure as accurately as possible the fundamental and higher modes of floor vibration, and (2) to correlate and update the initially developed FE model of the floor, so that its modes match as accurately as possible their measured counterparts. It was found that even a very detail...

Multipoint laser vibrometer for modal analysis

Abstract: Experimental modal analysis of multifrequency vibration requires a measurement system with appropriate temporal and spatial resolution to recover the mode shapes. To fully understand the vibration it is necessary to be able to measure not only the vibration amplitude but also the vibration phase. We describe a multipoint laser vibrometer that is capable of high spatial and temporal resolution with simultaneous measurement of 256 points along a line at up to 80 kHz. The multipoint vibrometer is demonstrated by recovering modal vibration data from a simple test object subject to transient excitation. A practical application is presented in which the vibrometer is used to measure vibration on a squealing rotating disk brake.

Simplified seismic analysis of asymmetric building systems

Abstract: The paper reviews the uncoupled modal response history analysis (UMRHA) and modal pushover analysis (MPA) procedure in the analysis of asymmetric structures. From the pushover curves in ADRS format, showing the relationships of base shear versus roof translation and base torque versus roof rotation, a bifurcating characteristic of the pushover curves of an asymmetric structure is observed. A two-degree-of-freedom (2DOF) modal stick is constructed using lump mass eccentrically placed at the end of beam which is connected with the column by a rotational spring. By converting the equation of motion of a whole structure into 2DOF modal equations, all of the elastic properties in the 2DOF modal sticks can be determined accurately. A mathematical proof is carried out to demonstrate that the 2DOF modal stick is consistent with the single-degree-of-freedom (SDOF) modal stick at elastic state. The bifurcating characteristic of modal pushover curves and the interaction of modal translation and rotation can be considered rationally by this 2DOF modal stick. In order to verify the effectiveness of this proposed 2DOF modal stick, a two-storey asymmetric building structure was analysed by the UMRHA procedure incorporating this novel 2DOF modal sticks (2DMPA) and conventional SDOF modal sticks (SDMPA), respectively. The analytical results are compared with those obtained by nonlinear response history analysis (RHA). It is illustrated that the accuracy of the rotational response histories obtained by 2DMPA is much better than those obtained by SDMPA. Consequently, the estimations of translational response histories on flexible side (FS) and stiff side (SS) of the building structure are also improved.

The noise structure of gear transmission units and the role of gearbox walls

Abstract: The noise emission of gear units (gearboxes) depends both on the disturbances (gear meshing, bearing operation, etc) and on the insulating capabilities and modal behavior of the housing. Natural vibrations of the housing walls can be prevented or intensified depending on design parameters. The mechanism of exciting and emission of transmission noise is defined by carrying out the process of propagation of excitation energy through the structure of power transmitters and by modal testing of the housing. The results of vibration and noise testing in comparison to the results of modal testing give the possibility of identification of noise structure for the chosen gearbox. Comparison and analysis of the results obtained lead to precise determination of the causes of creation of the total spectrum of gear transmission units.

Modal testing and finite element model calibration of an arch type steel footbridge

Abstract: In recent decades there has been a trend towards improved mechanical characteristics of materials used in footbridge construction. It has enabled engineers to design lighter, slender and more aesthetic structures. As a result of these construction trends, many footbridges have become more susceptible to vibrations when subjected to dynamic loads. In addition to this, some inherit modelling uncertainties related to a lack of information on the as-built structure, such as boundary conditions, material properties, and the effects of non-structural elements make difficult to evaluate modal properties of footbridges, analytically. For these purposes, modal testing of footbridges is used to rectify these problems after construction. This paper describes an arch type steel footbridge, its analytical modelling, modal testing and finite element model calibration. A modern steel footbridge which has arch type structural system and located on the Karadeniz coast road in Trabzon, Turkey is selected as an application. An analytical modal analysis is performed on the developed 3D finite element model of footbridge to provide the analytical frequencies and mode shapes. The field ambient vibration tests on the footbridge deck under natural excitation such as human walking and traffic loads are conducted. The output-only modal parameter identification is carried out by using the peak picking of the average normalized power spectral densities in the frequency domain and stochastic subspace identification in the time domain, and dynamic characteristics such as natural frequencies mode shapes and damping ratios are determined. The finite element model of footbridge is calibrated to minimize the differences between analytically and experimentally estimated modal properties by changing some uncertain modelling parameters such as material properties. At the end of the study, maximum differences in the natural frequencies are reduced from 22% to only %5 and good agreement is found between analytical and experimental dynamic characteristics such as natural frequencies, mode shapes by model calibration.

Vibration-based damage detection in beams using genetic algorithm

Abstract: In this paper, an improved GA-based damage detection algorithm using a set of combined modal features is proposed. Firstly, a new GA-based damage detection algorithm is formulated for beam-type structures. A schematic of the GA-based damage detection algorithm is designed and objective functions using several modal features are selected for the algorithm. Secondly, experimental modal tests are performed on free-free beams. Modal features such as natural frequency, mode shape, and modal strain energy are experimentally measured before and after damage in the test beams. Finally, damage detection exercises are performed on the test beam to evaluate the feasibility of the proposed method. Experimental results show that the damage detection is the most accurate when frequency changes combined with modal strain-energy changes are used as the modal features for the proposed method.

Factored Modal Combination for Evaluation of Earthquake Load Profiles

Abstract: To accurately predict the inelastic earthquake response of a structure by pushover analysis, the prescribed load profiles should be consistent with the actual force profiles which develop maximum design values during the time-history response of the structure. In the present study, a new modal combination method, factored modal combination (FMC), was developed to predict the earthquake load profiles of building structures affected by higher dynamic modes. In the FMC, multiple story load profiles are predicted by combining the modal spectrum responses multiplied by the modal combination factors. Based on the results of parametric studies on moment-resisting frames and walls, the modal combination factors were defined according to the hierarchy of each mode affecting the dynamic responses of structures. The FMC was applied to prototype buildings with and without vertical irregularity. The results showed that the FMC predicted the actual story load profiles which developed during the elastic and inelastic time-history responses of the structures.