Showing papers on "Modal testing published in 2001"

Modal identification of output-only systems using frequency domain decomposition

Abstract: In this paper a new frequency domain technique is introduced for the modal identification of output-only systems, i.e. in the case where the modal parameters must be estimated without knowing the input exciting the system. By its user friendliness the technique is closely related to the classical approach where the modal parameters are estimated by simple peak picking. However, by introducing a decomposition of the spectral density function matrix, the response spectra can be separated into a set of single degree of freedom systems, each corresponding to an individual mode. By using this decomposition technique close modes can be identified with high accuracy even in the case of strong noise contamination of the signals. Also, the technique clearly indicates harmonic components in the response signals.

Damping Estimation by Frequency Domain Decomposition

Abstract: In this paper it is explained how the damping can be estimated using the Frequency Domain Decomposition technique for output-only modal identification, i.e. in the case where the modal parameters is to be estimated without knowing the forces exciting the system. Also it is explained how the natural frequencies can be accurately estimated without being limited by the frequency resolution of the discrete Fourier transform. It is explained how the spectral density matrix is decomposed into a set of single degree of freedom systems, and how the individual SDOF auto spectral density functions are transformed back to time domain to identify damping and frequency. The technique is illustrated on a simple simulation case with 2 closely spaced modes. On this example it is illustrated how the identification is influenced by very closely spacing, by non-orthogonal modes, and by correlated input. The technique is further illustrated on the output-only identification of the Great Belt Bridge. On this example it is shown bow the damping is identified on a weakly exited mode and a closely spaced mode.

Application of a Fast-Stabilizing Frequency Domain Parameter Estimation Method

Abstract: A new noniterative frequency domain parameter estimation technique is proposed. It is based on a weighted total least squares approach, starting from multiple input multiple output frequency response functions. One of thespecific advantages of the technique lies in the very stable identification of the system poles as a function of the specified system order leading to easy-to-interpret stabilization diagrams. This implies a potential for automating the method and to apply it to "difficult" estimation cases. Several real-life case studies are discussed, one related to holographic modal analysis in the medium frequency range, one to the modal testing of a fully trimmed vehicle.

Modal analysis and testing of rotating structures

Abstract: This paper surveys the state of the art of modal testing or experimental modal analysis of rotating structures. When applied to ordinary, nonrotating structures, modal testing is considered to be w...

Vibration Control of Plates Using Discretely Distributed Piezoelectric Quasi-Modal Actuators/Sensors

Abstract: A novel approach is presented for vibration control of smart plates using discretely distributed piezoelectric actuators and sensors. The new method consists of techniques for designing quasi-modal sensors and quasi-modal actuators. The modal coordinates and the modal velocities are obtained approximately from the outputs of the discretely distributed piezoelectric sensor elements, whereas the modal actuators are implemented by applying proper voltages on each actuator element. The observation error of the modal sensor is analyzed, and an upper bound for the observation error is determined. The control spillover of the modal actuator is also estimated, and an upper bound of the control spillover is also found. The criteria are developed for finding the optimal locations and sizes of both piezoelectric sensor and actuator elements. In the optimality criteria the optimal locations and sizes of the sensor elements can be found by minimizing the observation error of the modal sensor, and those of the actuator elements can be obtained by minimizing both the control energy and the control spillover. The results obtained using the present optimal criteria show that they do not depend on the initial condition of vibration of the structures, nor do they depend on the control gains.

Modal damping measurement for damage detection

Abstract: This paper describes the application of arrays of surface-bonded piezoelements to determine modal damping characteristics of a tested structure. This information may be used for structural damage detection or structural dynamics evaluation. Any array element can be used as a sender, to generate a mechanical signal sweeping the frequency range of interest. Thus induced mechanical vibrations can be picked up either by the sender, or by another transducer. Modal characteristics, and in particular damping levels, are obtained using standard modal analysis methods from the resulting frequency transfer function. Since structural or material damage is frequently associated with changes in damping, the method described in this paper can be applied for structural health monitoring. It is expected that the approach presented will be particularly useful for testing light-weight and micro-structures.

Probabilistic Fault Identification Using a Committee of Neural Networks and Vibration Data

Abstract: Bayesian-formulated neural network architecture is implemented using a hybrid Monte Carlo method for probabilistic fault identification in a population of ten nominally identical cylindrical shells using vibration data. Each cylinder is divided into three substructures. Holes of 12 mm in diameter are introduced in each of the substructures. Vibration data are measured by impacting the cylinders at selected positions using a modal hammer and measuring the acceleration responses at a fixed position. Modal energies, defined as the integrals of the real and imaginary components of the frequency response function over 12-Hz frequency bandwidths, are extracted and transformed into the coordinate modal energy assurance criterion. This criterion and the identity of faults are used to train the frequency response function (FRF) neural network. Modal analysis is then employed to identify modal properties. Mode shapes are transformed into the coordinate modal assurance criterion. The natural frequencies and the coordinate modal assurance criterion, as well as the identities of faults, are utilized to train the modal-property neural network. The weighted average of the modal-property network and the FRF network form a committee of two networks. The committee approach is observed to give lower mean square errors and standard deviations (thus, a higher probability of giving the correct solution) than the individual methods. This approach gives accurate identities of damage and their respective confidence intervals while requiring affordable computational resources.

Modal and operating characterization of an Optical telescope

Abstract: As part of the overall assessment of the dynamic characteristics of the Gemini Optical Telescope, an experimental modal test was performed on this structure along with the collection of operating data. For modal testing, multiple reference impact testing was performed to characterize the structure. Time data were acquired and processed to compute multiple referenced frequency response functions. Modal parameters were extracted as part of the overall assessment of this optical telescope. For the operating assessment, many tests were conducted to determine the effects of wind loading. A variety of different structural configurations was evaluated during a series of tests on the telescope. Several days and nights were used to measure its behavior under a variety of different wind loading conditions. Operating data were collected and reduced for all of the tests conducted to identify wind loading conditions that hinder normal operations of the telescope. This article presents some of the significant considerations regarding the data obtained and the determination of modal and operating mode shapes. Some thoughts on the acquisition of the data and its reduction are presented along with the extraction of modal parameters and operating deflection shapes.

A piezoelectric array for sensing vibration modal coordinates

Abstract: The ability to sense vibration modal coordinates in real time brings much advantage in sensing and controlling structural vibration and acoustic radiation. This paper discusses results from an experiment with a modal coordinate sensor. A modal coordinate sensor for a beam is created from an array of rectangular segments of piezoelectric film. The output voltages of the segments are multiplied by appropriate gains so that the weighted combinations of the outputs approximate the modal coordinates of the beam. The gains are components of a matrix which is obtained from the relationship between the slopes of the beam deflection and the output voltages of the film segments. After numerical simulation, the method is experimentally verified for a beam with simple boundary conditions. The beam is covered with segments of piezoelectric film. The electric current outputs from the segments are linearly combined with weights calculated by the theory. It is shown that this linear combination of segment outputs with correct weights results in a sensor that is sensitive to only a selected vibration mode and filters out other modes. A few problems in laboratory implementation of the sensor are addressed. This discretized version of modal sensor shows promising application in structural monitoring and vibration control.

Modal identification of structures from ambient vibration, free vibration, and seismic response data via a subspace approach

Abstract: This work presents a unified procedure for determining the natural frequencies, modal damping ratios and modal shapes of a structure from its ambient vibration, free vibration and earthquake response data. To evaluate the coefficient matrices of a state-space model, the proposed procedure applies a subspace approach cooperating with an instrumental variable concept. The dynamic characteristics of a structure are determined from the coefficient matrices. The feasibility of the procedure is demonstrated through processing an in situ ambient vibration measurement of a five-storey steel frame, an impulse response measurement of a three-span continuous bridge, and simulated earthquake responses of five-storey steel frames from shaking table tests. The excellent agreement of the results obtained herein with those published previously confirms the feasibility of the present procedure. Copyright © 2001 John Wiley & Sons, Ltd.

On the Modal Testing of Microstructures: Its Theoretical Approach and Experimental Setup

Abstract: Small and lightweight structures have very high natural frequencies and small elastic displacement compared to ordinary structures. Due to limited excitation bandwidth and relatively large size of pick up devices, conventional modal testing facilities are not feasible for testing MEMS structures. A modal testing system based on the base excitation principle was developed in this research. In the meantime, the associated mathematical model for frequency response functions was derived as well. Testing structures are mounted on a rigid platform that can move essentially with only one translational degree of freedom. An electric discharge pulse strikes the platform to provide a very wide band excitation. Laser Doppler vibrometers are used to pick up both input and output signals. Since these signals are picked up without contacting structures, the structural dynamic characteristics remain intact without any distortion. With this system, modal parameters of a miniature structure can be extracted, and the receptance functions are synthesized successfully.

Structure Dynamic Analysis of a Horizontal Axis Wind Turbine System Using a Modal Analysis Method

Abstract: This paper considers the structural dynamic analysis of horizontal axis wind turbine (HAWT) rotor blades. Initially a blade from a 300 W machine was used, using both experimental and theoretical modal analyses. In the experiments, a DAS (Dynamic Signal A nalysis and Fault Diagnosis System) was used to extract modal parameters by measuring vibrations at various locations along the blade surface. A finite element analysis (FEA) method was used for the theoretical modal analysis. Comparison of experiment and theory explains the low order vibration conditions. The effects of different constraint conditions of the FE model are discussed. Finally, theoretical modal analysis is used to analyze a 600 kW rotor blade. The results are compared with those calculated using 'Bladed for Windows' of Garrad Hassan and Partners Ltd (UK), and satisfactory agreement between them is obtained.

Dynamics of an Inflatable Structure in Vacuum and Ambient Conditions

Abstract: In the dynamic modal testing of extremely lightweight inflatable structures, the results may vary dramatically according to the presence of either thermal vacuum or ambient atmospheric conditions. Unique aspects of modal testing techniques for an inflatable solar concentrator are identified, including the use of a noncontacting laser vibrometer measurement system. For the thermal vacuum environment, mode shapes and frequency response functions are compared for three different test article inflation pressures at room temperature. Modes that persist through all inflation pressure regimes are identified, as are modes that are unique for each pressure. In atmospheric pressure and room temperature conditions, dynamic measurements were obtained for the expected operational inflation pressure. Experimental mode shapes and frequency response functions for ambient conditions are described and compared to the results from the thermal vacuum tests. There is a surprising lack of correlation in test results between the two test conditions, which may be explained by damping and air mass considerations. Results of this investigation point out the necessity of testing inflatable space structures in vacuum conditions before they can be launched.

A study of the modal strain energy method for viscoelastically damped structures

Abstract: The modal strain energy (MSE) method has been proposed to estimate the modal loss factors or modal damping ratios of structures with viscoelastic dampers. There are certain assumptions made in deriving the MSE method, such as the computation of the modal loss factor directly from the ratios of the imaginary and real parts of the eigenvalues, and the neglect of the influence of the imaginary mode shapes, etc. These assumptions may result in overestimating the modal damping ratios of viscoelastically damped structures when the added damping is high. In this study, the effect of the assumptions made by the MSE method is investigated, and modified formulations of the MSE method are derived. The modified MSE method removes the assumptions made in the original MSE method. Furthermore, earthquake responses of a complex stiffness system and a linear viscous damping system, of which the modal damping ratios are estimated by the MSE method, are compared. Study results indicate that the difference arising f...

Mode isolation: A new algorithm for modal parameter identification

Abstract: Multiple degree of freedom (MDOF) algorithms are the dominant methods for extracting modal parameters from measured data These methods are founded on the notion that because the response of a linear dynamic system is the sum of many modal contributions, the extraction technique must deal with all of the modal parameters in a simultaneous fashion The Mode Isolation Algorithm (MIA) described here is a frequency domain formulation that takes an alternative viewpoint It extracts the modal parameters of each mode in an iterative search, and then refines the estimation of each mode by isolating its effect from the other modal contributions The first iteration estimates modes in a hierarchy of their dominance As each mode is estimated, its contribution is subtracted from the data set, until all that remains is noise The second and subsequent iterations subtract the current estimates for all other modes to identify the properties of the mode under consideration The various operations are described in detail, and then illustrated using data from a four-degree-of-freedom system that was previously used to assess the Eigensystem Realization Algorithm (ERA) and Enhanced ERA Eigenvalues and mode shapes are compared for each algorithm Another example analyzes simulated data for a cantilever beam with three suspended one-degree-of-freedom subsystems, in which the parameters are adjusted to bring two natural frequencies into close proximity The results suggest that MIA is more accurate, and more robust in the treatment of noisy data, than either ERA version, and that it is able to identify modes whose bandwidth is comparable to the difference of adjacent natural frequencies

Design of Modal Transducers by Optimizing Spatial Distribution of Discrete Gain Weights

Abstract: A general method is developed of designing distributed modal transducers, especially for use in the active vibration control of structure. For this purpose, a new two-dimensional modal transducer theory has been developed. This theory is based on the finite element model of the structure, which makes it possible to determine spatial gain distribution of the specific modal transducer without restrictions on the geometry and boundary conditions of the structure. Although the optimal gain distribution can he obtained theoretically, there is no practical means of implementing it. Therefore, two design methods of distributed modal transducer are developed, which optimize available parameters of piezoelectric film to approximate optimal gain distribution best. The first method uses multilayered polyvinylidene fluoride (PVDF) films as a single transducer. The electrode pattern, the lamination angle, and the relative poling direction of each PVDF layer are optimized to obtain the desired transducer. In the second method, the whole electrode area on a single PVDF film is divided into several segments, and the gain weight imposed on each segment by interface circuit is optimized. Sensor/actuator systems for the vibration control of cantilever composite plate are designed using the proposed methods. The performance of the designed transducers is verified experimentally. The real-time vibration control of integrated smart structure has been successfully achieved.

Modal Testing of Mechanical Structures Subject to Operational Excitation Forces

Abstract: Operational Modal Analysis also known as Output Only Modal Analysis has in the recent years been used for extracting modal parameters of civil engineering structures and is now becoming popular for mechanical structures. The advantage of the method is that no artificial excitation need to be applied to the structure or force signals to be measured. All the parameter estimation is based upon the response signals, thereby minimising the work ofpreparation for the test. This test case is a controlled lab set-up enabling different parameter estimation methods techniques to be used and compared to the Operational Modal Analysis. For Operational Modal Analysis two different estimation techniques are used: a non-parametric technique based on Frequency Domain Decomposition (FDD), and a parametric technique working on the raw data in time domain, a data driven Stochastic Subspace Identification (SSI) algorithm. These are compared to other methods such as traditional Modal Analysis.

Development and Application of a Nonlinear Modal Analysis Technique for MDOF Systems

Abstract: This work presents a frequency-domain technique that extends the concept of linear modal super position to nonlinear systems by using the normal nonlinear mode approach so that a generalized parameter identification method can be formulated for MDOF nonlinear systems. The methodology is compatible with existing established vibration analysis techniques such as finite element (FE) modeling and experimental modal analysis. Furthermore, once the nonlinear modal parameters are identified at some reference force level, the nonlinear response can be predicted at any arbitrary excitation level using standard modal sum mation techniques. The numerical study is focused on a 4-DOF system with friction damping nonlinearity, for which both the macro- and microslip representations are considered. Simulated nonlinear frequency re sponse functions, obtained for a given excitation level using a harmonic balance method, were subjected to a nonlinear modal analysis procedure, and the modal parameters were extracted as a fu...

Fault Identification Using Pseudomodal Energies and Modal Properties

Abstract: The pseudomodal energy, dee ned as the integrals of the real and imaginary components of the frequencyresponse functions over various frequency ranges, is proposed for fault identie cation in structures. Equations that formulate pseudomodal energies in the modal domain and their respective sensitivities are derived in receptance and inertance form. When tested on a simulated cantilevered beam, pseudomodal energies are found to be more resistant to noise in the data than the mode shapes and are able to take into account the out-of-frequency-band modes and to be better indicators of faults than the modal properties. Furthermore, they are more sensitive to faults than the natural frequencies and are equally as sensitive to faults as the mode shapes. The pseudomodal energies are computationally faster to calculate than the modal properties. When tested on a population of 20 steel cylinders, the pseudomodal energies are, on average, better indicators of faults than the modal properties. Nomenclature aq = lower frequency bound for the qth pseudomodal energy bq = upper frequency bound for the qth pseudomodal energy [C] = damping matrix fFg = force input vector gp = changes in the pth structural parameter Hkl = frequency-response function due to excitation at k and measurement at l j = p i1 [K] = stiffness matrix [M] = mass matrix