Showing papers on "Modal testing published in 1998"

Identification of a Dynamic System Using Ambient Vibration Measurements

Abstract: This paper demonstrates how ambient vibration measurements at a limited number of locations can be effectively utilized to estimate parameters of a finite element model of a large-scale structural system involving a large number of elements. System identification using ambient vibration measurements presents a challenge requiring the use of special identification techniques, which can deal with very small magnitudes of ambient vibration contaminated by noise without the knowledge of input forces. In the present study, the modal parameters such as natural frequencies, damping ratios, and mode shapes of the structural system were estimated by means of appropriate system identification techniques including the random decrement method. Moreover, estimation of parameters such as the stiffness matrix of the finite element model from the system response measured by a limited number of sensors is another challenge. In this study, the system stiffness matrix was estimated by using the quadratic optimization involving the computed and measured modal strain energy of the system, with the aid of a sensitivity relationship between each element stiffness and the modal parameters established by the second-order inverse modal perturbation theory. The finite element models thus identified represent the actual structural system very well, as their calculated dynamic characteristics satisfactorily matched the observed ones from the ambient vibration test performed on a large-scale structural system subjected primarily to ambient wind excitations. It is noted that newly developed optical fiber accelerometers were used for this ambient vibration test. The dynamic models identified by this study will be used for design of an active mass damper system to be installed on this structure for suppressing its wind vibration.

Correction of Mass-loading Effects of Transducers and Suspension Effects in Modal Testing

Abstract: The mass cancellation technique for transducers at the driving point has been solved for a long time However, there are few publications about quantification of the mass-loading effects caused by a measuring transducer on FRFs at the non-driving points This article revisits the problem of mass cancellation in modal testing and proposes a general solution based upon a direct substructuring technique, Structural Modification Using experimental frequency Response Functions (SMURF) It is shown that for the non-driving points, the FRFs can be corrected if the measurement is repeated with an accelerometer of different mass It is also shown that the driving point FRF of the response point can be obtained by the same measurement A similar procedure is used to correct the suspension effects on the test structure For the case that the structure is suspended with one spring, it is proved that for all of the points of the structure, the FRFs can be corrected if the measurement is repeated with two other springs with different stiffness To demonstrate the validity of the method for correction of mass-loading effects a system of 12 degree of freedom of masses, springs and dampers was considered The method is exact but in practical situations may be vulnerable to noise Noise has been considered in the measured FRFs and a way to prevent error in the calculation has been investigated

Drive circuit modal filter for a vibrating tube flowmeter

Abstract: A drive system (50, 104) for a vibrating tube-based measurement instrument (5) employing a spatial filter (500) to produce a drive signal having modal content only at a desired vibration mode. Multiple feedback sensors (105, 105') located at different locations along a vibrating tube (103A, 103B) produce multiple feedback sensors. Each feedback signal has applied to it a weighting or gain factor. All of the weighted feedback signals are then summed to produce a drive signal, or a signal proportional to a drive signal, having improved modal content as compared to any of the feedback signals by themselves. The weighting factors are selected by any of several means. One method is to build the eigenvector matrix for the vibrating flow tube by extracting the eigenvectors from a finite element model of the vibrating structure. The inverse or pseudo-inverse of the eigenvector matrix is calculated to obtain the modal filter vector. The appropriate set of weighting coefficients are selected from the modal filter vector.

Vibration and sound radiation controls of beams using layered modal sensors and actuators

Abstract: A new smart structural configuration for beams with symmetrically embedded modal sensors and actuators is proposed. Pairs of symmetrically installed modal sensors and actuators having the same shape of electrode profile are individually connected by a control unit. They are used to control each corresponding vibration mode of the beam independently. Dynamic response of the structure is investigated by the modal analysis method. Numerical simulations for vibration and sound radiation controls presented for illustrations are limited to simply supported beams. Results indicate that modal sensors and actuators, properly selected on the basis of the location and frequency of external forces, can effectively suppress the beam vibration and reduce radiated sound pressure in the far-field.

Method of identifying critical elements in fatigue analysis with von mises stress bounding and filtering modal displacement history using dynamic windowing

Abstract: A method of dynamic durability analysis and fatigue area identification using modal techniques for a structure includes the steps of simulating a finite element model of the structure to determine modal stresses and modal displacements for an element of the structure and performing a modal transient analysis using the modal displacements. The method also includes the steps of determining a stress bound for the element from the modal stresses and modal transient analysis, determining if a stress bound for the element is greater than a predetermined value and identifying the element as a critical element if the stress bound for the element is greater than the predetermined value. The method further includes the steps of determining a stress time history for the critical element and using the stress time history to perform a fatigue analysis to identify an area of fatigue within the structure.

Updating of the Analytical Models of Two Footbridges Based on Modal Testing of Full-Scale Structures

Abstract: This paper describes the analytical FE modelling, modal testing and FE model updating of two full-scale pedestrian footbridges These procedures are well developed in the fields of mechanical and aerospace engineering, and have just started to be applied successfully to large civil engineering structures The aim of this paper is to describe some of the possible problems that may arise when conducting such experimental exercises, and also to give advice on how these problems may be overcome In addition, the paper describes the authors’ experiences in initially constructing the FE models and conducting the updating itself Finally, the practical meaning of the changes to the assumed model parameters, resulting from the updating, is discussed It has been concluded that a period of manual updating should be conducted prior to implementing the automatic updating, as poor starting values may result in the automatic updating software producing unrealistic results

Support Conditions, Their Effect on Measured Modal Parameters

Abstract: During a modal test, a structure must be supported in some manner to the surrounding environment. If a model of the structure is to be reconciled with modal test data, then the support conditions must either be included in the model or assumed to have negligible effects. Frequently, a precise determination of the actual support conditions is not performed. Consequently, there is uncertainty in the conditions and how they affect both the measured modal frequencies and modal dampings. This study examines the effects of support conditions on the measured modal parameters, and discusses the proper design of support conditions for modal testing.

Material characterization for orthotropic shells using modal analysis and Rayleigh-Ritz models

Abstract: Using the method of Bayesian estimation, the elastic constants of specially orthotropic cylindrical composite shells with balanced symmetric lamination were characterized based on their natural frequencies obtained from free-free configuration modal testing Estimation of the various elastic constants of each cylinder involved an iterative tuning of a mathematical model describing its modal response Formulation of the model was accomplished with the Rayleigh-Ritz method in conjunction with characteristic beam functions For a prescribed circumferential wave pattern of the vibration modes, a five-term series was sufficient to describe the deflection shapes By carrying out sensitivity analysis, the natural frequencies of the cylindrical shells were found to have a high dependence on the circumferential and in-plane shear moduli rendering an accurate characterization for these moduli On the contrary, the Poisson's ratios of the specimens cannot be accurately determined

Implementation of coupled mode optimal structural vibration control using approximated eigenfunctions

Abstract: With the approximately normalized eigenfunctions and matching modal equations obtained in a differential form, we have implemented the structural vibration control successfully. In applying the steady-state quadratic coupled mode optimal control algorithm for the control structure, i.e. the all-clamped square plate, the non-orthogonalized extra terms are evaluated. By the suitable formulation of a control system, we could simulate the modal responses of the first six modes showing the validity of proposed modal equations and all the control procedures are considered to be reliable as a structural vibration control scheme. Modal responses for single and double actuators are observed and by changing the other control factors such as impulse position and weighting matrices we could compare the control performance. Moreover, these simulation results provide ideas on how to select the optimal number and positions of the actuators.

Mode identification of a rotating disk

Abstract: A modal testing method permitting identification of the natural frequencies, the number of nodal diameters and wave motions in a rotating disk is presented in this paper. This method is applicable at arbitrary rotation speed without requiring a priori information about the vibration modes of the stationary disk. The influence of disk rotation speed on the prediction of mode shapes with this method is shown, and experimental predictions of modal parameters are presented for both axisymmetric and asymmetric disks.

Estimating turbogenerator foundation parameters

Abstract: Turbogenerators in power stations are often placed on foundation structures that are flexible over the running range of the machine and can therefore contribute to its dynamics. Established methods of obtaining structural models for these foundations, such as the finite element method or modal testing, have proved unsuccessful because of complexity or cost. Another method of foundation system identification, using the unbalance excitation applied by the rotor itself during maintenance run-downs, has previously been proposed but has not yet been experimentally verified. In this paper the necessary theory is developed and certain issues critical to the success of the estimation are examined. The method is tested in both simulation and experiment using a two-bearing rotor rig and good fits between model and measurement are obtained. The predictive capacity of the estimated models when the system is excited with a different unbalance is not as good, and it is surmised that this may be due among other ...

Balanced Shaker and Sensor Placement for Modal Testing of Large Flexible Structures

Abstract: A systematic analytical approach regarding the location of shakers and sensors for the dynamic testing and modal identification of the Z1 truss substructure of the International Space Station(ISS) is discussed in this paper. It is assumed that every degree of freedom of the finite element model is a possible place for sensor location, but shakers can only be placed at selected locations (not all locations are technically suitable for the shaker placement). From this starting point, a subset of four shaker locations and a subset of about 400 sensor locations were selected for the analytical modal identification test of all the ISS modes below 50 Hz of frequency. The locations were selected based on the shaker and sensor performance in the identification test that is comparable to the performance of the full sets. The performance is defined in terms of the Hankel singular values (HSV) that characterize the joint controllability and observability properties of each shaker and sensor for each natural vibration mode of the structure. The additive property of the structural Hankel singular values was used to locate the shakers and sensors. The placement results show good dynamic performance of the structure with the subset of shaker and sensor locations as compared to the structure with the full set of shakers and with sensors located at all degrees of freedom. The main objective of the paper is to present the sound theoretical background and show its practical advantages.

A modal parameter extraction algorithm using best-fit reciprocal vectors

Abstract: The dot product of a reciprocal modal vector with a vector of frequency response functions (FRFs) can produce a generalized coordinate FRF that has single-degree-of-freedom response. A modal extraction algorithm is developed based on this concept. A generalized coordinate FRF is assumed with a corresponding frequency and damping. The least squares fit reciprocal modal vector is determined for a set of experimental FRFs. The correlation coefficient is used to determine the quality of fit. This is done for several discrete frequency and damping values that cover the parameter space of interest. Over this parameter space, local maxima of the correlation coefficient can be used to identify roots of the system. An example is given utilizing experimental data.

Modal testing using impact excitation and a scanning LDV

Abstract: If a laser doppler vibrometer is used in a continuously- scanning mode, its output spectrum contains side-bands from which the response mode shape, as defined along the scan line, may be obtained. With impact excitation, the response is the summation of a set of exponentially-decaying sinusoids which, in the frequency domain, has peaks at the natural frequencies and at 'sideband' pseudo-natural frequencies, spaced at multiples of the scan frequency. Techniques are described for deriving natural mode shapes from these, using standard modal analysis procedures. Some limitations as to the types of mode which can be analyzed are described. The process is simple and speedy, even when compared with a normal point-by-point impact test survey. Information may also be derived, using a circular scan, on the direction of vibration, and angular vibration, at individual points.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Instrumented sledge hammer impact excitation: worked examples

Abstract: The paper firstly outlines typical differences between the philosophy of conducting modal testing in civil engineering compared to the application of the same technology in mechanical, automotive and aerospace engineering. These differences have a strong influence on the selection of a fast modal testing technique suitable for civil engineering applications. The instrumented hammer testing technique, where the impactor is a manually operated sledge hammer proved to be very popular because of its low cost, simplicity and speed of execution. However, specifics of modal testing of civil engineering structures such as the use of portable equipment in open space environments, low natural frequencies, closely spaced modes of vibration and relatively high damping require special consideration. This paper discusses some of these considerations which are not adequately addressed in the available literature. The problems presented are related to the use of a portable spectrum analyser, which typically has a limited number of digital data analysis options, when performing modal testing of long span concrete floors and footbridges using an instrumented sledge hammer.

Advanced Mode Shape Identification Method for Automotive Application via Modal Kinetic Energy Plots Assisted by Numerous Printed Outputs

Abstract: Design optimization procedures of full-vehicle simulation models - such a procedure as shown in this paper - require a very fast and reliable mode shape identification. Just because these simulation models necessarily contain a lot of large concentrated masses and mass moments of inertia, e.g., engine, gear, differential, car wheels, steering wheel, mufflers, airbags, and reduced masses from superelement processing, to name just a few, the kinetic energy method is especially destined to accomplish this task. In the present paper, a graphical Modal Kinetic Energy evaluation technique is described in detail. Moreover, the modal kinetic energy plots are a means to investigate the structure's eigenbevior in the lowfrequency range, e.g., to see where dynamic vibration absorbers have to be attached and where bushings, and instrumentation for modal testing have to be placed. In summary, the presented graphs make even the most complicated subjects clear and provide the dynamicist with information he can use to achieve a better design quickly. The prints of significant values indicate the degree of coupling between energies in rotational and translational direction per mode and the energy portions of the physical residual chassis structure and the energy portions of appended body and subframe superelements. Representative applications for mode shape identification in automotive engineering, V70, are presented extensively in order to demonstrate the strength of the method. Surely, there are many other applications in the engineering structural analysis field where the advanced mode shape identification method will play key roles.

Missing mass effect in coupled analysis. i: complex modal properties

Abstract: New formulations are developed to account for the effect of uncalculated high frequency rigid modes in the seismic analysis of coupled primary–secondary systems by modal synthesis approach. The effect of uncalculated rigid modes is included in terms of residual modal vectors for both the uncoupled primary and the multiply supported secondary systems. The reduced eigenvalue problem, obtained by transforming the original equation of motion in which the displacements at the secondary system degrees of freedom (DOF) are expressed relative to the base of the primary system, gives incorrect results when all the modes of the secondary system are not included and the effect of high frequency modes is included through residual modal vectors. An alternate formulation is presented in which the original equation of motion is transformed such that the displacements at the secondary system DOF are expressed relative to the primary system connecting DOF. The reduced eigenvalue problem is solved using the transformed equ...

Real modes of vibration and hybrid modal analysis

Abstract: Based on continuous Hilbert space basis functions and mean square convergence properties of spatial generalised Fourier series a new technique for hybrid modal analysis (HMA) is proposed The technique utilises a mix of experimental, measured vibration responses and good numerical approximations of well defined, three-dimensional, real, normal modes The modes are assumed to be solutions to an elastic, eigenvalue problem corresponding to the true geometry of the analysed body or structure Starting from a known geometry and a suitable set of modes, it is shown that the measured data may be supplemented with spatial information about the whole vibrational displacement field which is correctly represented by the chosen set of complete (Hilbert space), modal basis vector fields The spatial information is extracted from the measured vibration responses by curve fitting a truncated modal response model to the data As a result of the curve fit a number of generalised Fourier coefficient spectra are obtained which together with the corresponding modes may be used to predict or simulate responses which were not measured or used in the curve fit Given also the true mass density field of the body, the time average of the kinetic energy of the whole body may be approximated using only a restricted set of measured vibration responses The method is completely general and applicable in all cases where the vibrational displacements are small enough compared to the characteristic dimensions of the analysed body The effect of modal truncation and means to approximate corresponding dynamic displacement residuals are discussed for linear, anisotropic solid bodies and structures with general damping Modal coupling due to damping and unknown elastic properties are also discussed The method has been tested, with very good results, on experimental data measured with a laser doppler vibrometer on a plexiglas plate excited with a shaker in the frequency range 25–500 Hz

Estimation of uncertain material parameters using modal test data

Abstract: Analytical models of wind turbine blades have many uncertainties, particularly with composite construction where material properties and cross-sectional dimension may not be known or precisely controllable. In this paper the authors demonstrate how modal testing can be used to estimate important material parameters and to update and improve a finite-element (FE) model of a prototype wind turbine blade. An example of prototype blade is used here to demonstrate how model parameters can be identified. The starting point is an FE model of the blade, using best estimates for the material constants. Frequencies of the lowest fourteen modes are used as the basis for comparisons between model predictions and test data. Natural frequencies and mode shapes calculated with the FE model are used in an optimal test design code to select instrumentation (accelerometer) and excitation locations that capture all the desired mode shapes. The FE model is also used to calculate sensitivities of the modal frequencies to each of the uncertain material parameters. These parameters are estimated, or updated, using a weighted least-squares technique to minimize the difference between test frequencies and predicted results. Updated material properties are determined for axial, transverse, and shear moduli in two separate regions of the blade cross section: in the central box, and in the leading and trailing panels. Static FE analyses are then conducted with the updated material parameters to determine changes in effective beam stiffness and buckling loads.

A method to analyse the interaction between rotor-foundation systems

Abstract: This paper presents a methodology for the analysis of the foundation behaviour and its influence on the whole system (rotor-bearings-foundation), using a mathematical approach to determine its modal parameters such as modal mass, damping factor and natural frequency[1]. The analysis of the complete system is done applying the discretization of the foundation and rotor by finite element method. The analysis of the analytical transfer function of the model was obtained for a unit harmonic force exciting one node. The evaluation of the foundation modal parameters is done by the analysis of the structure frequency response function, obtained by Fourier Transform. The modes associated to the natural frequencies which significantly participate of the system response are chosen using the frequency spectrum. Afterwards, the mass, damping factor and stiffness of the considered modes are obtained, finally, the analysis of the complete system frequency response function is done and the analytical results are showed.

A Correlation Function for Spatial Locations of Scaled Mode Shapes (COMEF)

Abstract: Historically, several indices have been proposed as correlation indices between two sets of modal data Modal Assurance Criterion (MAC) and Modal Scale Factor (MSF) have been used as techniques to relate two mode shapes from the same set or different sets They are also used to update finite element model vectors with respect to experimentally derived modal data Coordinate Modal Assurance (COMAC) was proposed to identify those parts of the structure which are contributing to low degrees of correlation It is also possible to use COMAC between two sets of mode shapes, either from an experimental set of finite element models A new correlation index, the Coordinate Modal Error Function (COMEF) is proposed to correlate two sets of scaled mode shapes Scaling has been employed to minimize the contribution of degrees of freedom, which have low amplitude The locations for low correlation are detected where two sets do not agree It can be used for model updating and damage detection purposes This technique is presented in two examples

Estimating Modal Parameters from Different Solution Sets

Abstract: A method for the estimation of modal parameters (frequency, damping and modal vectors) is presented which utilizes many estimates derived from different model orders, data subsets and parameter estimation methods. Clustering of the modal frequencies in the s-plane is utilized in order to identify valid modal frequencies regardless of the origin of the modal frequency estimate. Singular value decomposition (SVD) of the modal vector sets and/or state vector sets is utilized when the spatial dimension of the modal vector estimates is consistent. Results are shown for test data cases. The clustering method extends the concepts of stability and consistency to what is referred to as a modal frequency density in the s-plane. An important feature of these methods is that the exact model order of the system need not be known in advance. Modal parameter estimates are made using variations in model order, or number of estimated modal frequencies, over a range which encompasses and/or exceeds the system under test. The number of pole clusters provides an indication of the number of system poles. The size and location of the cluster provides an estimate of the mean and variance of the indicated pole. The number of significant singular values also provides an estimate of the number of realistic modal frequencies in the cluster of pole estimates in the s-plane.

Ambient modal testing of the vestvej bridge using random decrement

Abstract: This paper presents an ambient vibration study of the Vestvej bridge. The bridge is a typical Danish two-span concrete bridge which crosses a highway. The purpose of the study is to perform a pre-investigation of the dynamic behaviour to obtain information for the design of a demonstration project concerning application of vibration based inspection of bridges. The data analysis process of ambient vibration testing of bridges has traditionally been based on auto and cross spectral densities estimated using an FFT algorithm. In the preanalysis state the spectral densities are all averaged to obtain the averaged spectral densities (ASD). From the ASD the eigenfrequencies of the structure can be identified. This information can be used in the main analysis, where all modal parameters are extracted from the spectral densities. Due to long cabling and low response levels (small ambient loads) the response measurements might have a low signal to noise ratio. Thus, it might be difficult clearly to identify physical modes from the spectral densities. The Random Decrement (RD) technique is another method to perform the data analysis process in the time domain only. It is basically a very simple and easily implemented technique. In this paper it is demonstrated how the RD technique can be used in the preanalysis state in combination with the FFT algorithm, and how the technique can be used in a full analysis.

Modal testing and analysis of a car under operational conditions

Abstract: Classically, the modal parameters of a car are derived from FRF measurements in well-controlled laboratory conditions using hammer of shaker excitation. However, the modal vibro-acoustic behavior of a car on the road may differ significantly from the one during the laboratory test due to e.g. pre-stress and non-linear behavior of the suspension system. Hence, the need arises to identify a modal model of a car in driving condition. In this case, only response data are measurable while the actual loading condition is unknown. In the last decade, the problem of output-only operational modal analysis has typically been approached by applying a peak-picking technique to the auto-and crosspowers of the responses, resulting in approximate estimates for the resonance frequency and operational deflection shapes. These shapes were then compared to or even decomposed into the laboratory modal results. In this paper, it is investigated how more advanced techniques such as the Polyreference LSCE fed by correlation functions and the stochastic subspace method can be used for the extraction of the modes of a car on the road. The basic principles of the two methods are briefly reviewed and practical advantages and drawbacks are discussed. Subsequently, the two methods are applied to structural response data of the rear suspension system of a family car. The obtained modal parameters are correlated with the values derived from the laboratory FRF data, allowing to assess the modes which are dominant in driving condition.