Showing papers on "Modal testing published in 1992"

Flexibility by multireference impact testing for bridge diagnostics

Abstract: Modal testing by impact is a practical tool for structural identification, integrity monitoring, and diagnostics of bridges. Typically, nonlinearities in bridge response as well as sensitivity to ambient conditions are observed during modal tests. Therefore, impact tests should be planned and executed so that the effects of nonlinearities are incorporated in estimating modal parameters of a test structure. Furthermore, indexes more reliable than the modal parameters are needed to diagnose local and/or obscure damage. These and other shortcomings in current modal test‐based diagnostic studies are reviewed. A multireference impact testing of a bridge, in which frequency‐response functions (FRF) are measured and a large number of modal parameters are reliably identified, is presented. The mode shape coefficients obtained through processing measured FRF are directly transformed into flexibility of the test bridge without assuming mass. Analytical studies of a calibrated analytical model are presented to demon...

Nondestructive evaluation of damage in composite structures using modal parameters

Abstract: The problem of using measured modal parameters to detect and locate damage in structures made of fiberreinforced composites is investigated. Recent work in this area using modal sensitivity equations is used in conjunction with internal-state variable constitutive theory to derive a set of damage-detection equations which are used to predict, from changes in measured modal parameters, the current value of the internal-state variables in each finite element. The value of the internal-state variable determines the extent of damage at a given location. Numerical examples involving damaged composite beams are used to demonstrate the capability of the theory to predict the exact location and the severity of damage. To provide experimental evidence to support the theory, mechanical and modal tests are performed on a [0,903]s laminated composite beam in the undamaged state and in three additional states of progressive damage. At each stage of damage, edge replications are taken to determine the crack density along the length of the beam. The predicted values of the internal-state variables, obtained from the modalsensitivity equations using measured modal information, are compared with the values of the internal-state variables obtained from crack-density measurements along the length of the beam. Good agreement between the predicted and the measured values is found.

Multiobjective shape and material optimization of composite structures including damping

Abstract: A multiobjective optimal design methodology is developed for lightweight, low-cost composite structures of improved dynamic performance. The design objectives may include minimization of damped resonance amplitudes (or maximization of modal damping), weight, and material cost. The design vector includes micromechanics, laminate, and structural shape parameters. Constraints are imposed on static displacements, static and dynamic ply stresses, dynamic amplitudes, and natural frequencies. The effects of composite damping tailoring on the dynamics of the composite structure are incorporated. Applications on a cantilever composite beam and plate illustrate that only the proposed multiobjective formulation, as opposed to single objective functions, may simultaneously improve the objectives. The significance of composite damping in the design of advanced composite structures is also demonstrated, and the results indicate that the minimum-weight design or design methods based on undamped dynamics may fail to improve the dynamic performance near resonances. Nomenclature A = area [C],[c] = global and modal damping matrices, respectively E = normal modulus F(z) = objective functions / = frequency fd = damped frequency G = shear modulus G(z) = inequality constraints h = thickness [/£],[/:] = global and modal stiffness matrices, respectively k = volume ratio [M],[m] = global and modal mass matrices, respectively p^p = global and modal excitation force, respectively q — modal vector 5 = strength t = time U = dynamic amplitude u = displacement vector

Underlying modal data issues for detecting damage in truss structures

Abstract: Independent of the modal identification techniques employed for damage detection, use of measured modal data limits the expectations for damage location. These limitations are examined using the distribution of modal strain energy and the sensitivity of the frequency and mode shapes to structural stiffness changes. For given measured modal information of specific accuracy, this examination reveals the following: (1) damage detection is feasible for members that contribute significantly to the strain energy of the measured modes, (2) the modes which are most effective in detecting damage to certain critical members can be identified, and (3) a relationship can be drawn between the accuracy of the measured modes and frequencies and damage detection feasibility.

Prediction and measurement of modal damping factors for viscoelasticspace structures

Abstract: The procedure outlined in this paper extends the finite element method to viscoelastic space structures; predictions of mode shapes, frequencies, and damping factors can be made based on a new modeling approach that uses specific measured material data. Briefly, the procedure is as follows: 1) the modulus function of the material is measured from free-decay tests of a uniform cantilever beam of the subject material, and 2) these material data are then inserted into the new damped-structure modeling technique. These two steps are illustrated and validated using a strawman space structure fabricated entirely from a single epoxy material. Predicted damping characteristics based on material data and the new modeling technique are compared with modal data obtained for the test structure. Using commercially available software, the modal test data are processed to obtain mode shapes, frequencies, and damping factors. A comparison between predicted eigenvalues and experimentally determined modal frequencies and damping factors indicates that the proposed new technique is a valuable tool in structural analysis.

Modal Analysis of Multistage Gear Systems Coupled With Gearbox Vibrations

Abstract: This paper presents an analytical procedure to simulate vibrations in gear transmission systems. This procedure couples the dynamics of the rotor-bearing gear system with the vibration in the gearbox structure. The modal synthesis method is used in solving the overall dynamics of the system, and a variable time-stepping integration scheme is used in evaluating the global transient vibration of the system. Locally each gear stage is modelled as a multimass rotor-bearing system using a discrete model. The modal characteristics are calculated using the matrix-transfer technique. The gearbox structure is represented by a finite element model, and modal parameters are solved by using NASTRAN. The rotor-gear stages are coupled through nonlinear compliance in the gear mesh while the gearbox structure is coupled through the bearing supports of the rotor system. Transient and steady state vibrations of the coupled system are examined in both time and frequency domains. A typical three-geared system is used as an example for demonstration of the developed procedure.

Elastic Wood Properties from Dynamic Tests and Computer Modeling

Abstract: Elastic moduli for a specimen of Norway spruce (Picea abies) have been evaluated by dynamic tests and corresponding computer calculations. Modal testing of a wooden beam of structural size resulted in modal properties for 13 different modes of vibration. Corresponding modes of vibration were calculated using a finite element model based on Timoshenko beam elements with constant homogeneous properties. Similarity between experimental and theoretical values for eigenfrequencies for the fundamental axial mode of vibration required a value for Young's modulus E=11,444MPa. Corresponding matching of the fundamental frequency for torsional vibration yielded G=1,074MPa. The calculated eigenfrequencies for higher modes of vibration correspond very well to the experimental values. It should be noted specifically that the eigenfrequencies for edge‐wise bending modes correspond well, although the value for the shear modulus was based on a torsional mode matching.

Application of an enhanced Coordinate Modal Assurance Criterion

Abstract: This paper presents an extension of the Coordinate Modal Assurance Criterion (COMAC) for spatial comparison of mode shapes. As is the case for the original COMAC, this enhanced COMAC helps identify degrees of freedom differences between test and analysis modes, but also overcomes some of the limitations of the original COMAC. The original COMAC cannot identify errors caused by scaling or polarity mistakes in the test data. Such mistakes are easily made during modal tests and not always easily detected since they do not affect the subjective quality of a frequency response function.

Ground vibration tests of a high fidelity truss for verification of on orbit damage location techniques

Abstract: This paper describes a series of modal tests that were performed on a cantilevered truss structure. The goal of the tests was to assemble a large database of high quality modal test data for use in verification of proposed methods for on orbit model verification and damage detection in flexible truss structures. A description of the hardware is provided along with details of the experimental setup and procedures for 16 damage cases. Results from selected cases are presented and discussed. Differences between ground vibration testing and on orbit modal testing are also described.

Variation in the modal parameters of space structures

Abstract: An analytic and experimental study of gravity and suspension influences on space structural test articles is presented. A modular test article including deployable, erectable, and rotary modules was assembled in three one- and two-dimensional structures. The two deployable modules utilized cable diagonal bracing rather than rigid cross members; within a bay of one of the deployable modules, the cable preload was adjustable. A friction lock was used on the alpha joint to either allow or prohibit rotary motion. Suspension systems with plunge fundamentals of 1, 2, and 5 Hz were used for ground testing to evaluate the influences of suspension stiffness. Assembly and reassembly testing was performed, as was testing on two separate shipsets at two test sites. Trends and statistical variances in modal parameters are presented as a function of force amplitude, joint preload, reassembly, shipset and suspension. Linear finite element modeling of each structure provided analytical results for 0-g unsuspended and 1-g suspended models, which are correlated with the analytical model.

Modal Testing and Suboptimal Vibration Control of Flexible Rotor Bearing System by Using a Magnetic Bearing

Abstract: A suboptimal output feedback controller is designed based on a reduced order model and applied to a flexible rotor bearing system in order to control the unstable or lightly damped vibrations occurring during operation. The reduced order model is a truncated modal equation of the distributed parameter system obtained through the singular perturbation. The instability problem arising from the spillover effects caused by the uncontrolled high frequency modes is prevented through the constrained optimization by incorporating the spillover term into the performance index

Development of an on-line parameter estimation system using the discrete modal filter

Abstract: Ongoing development of an automated system for monitoring the frequency and damping of time varying structural systems is discussed. A spatial filtering technique called the discrete modal filter is used to uncouple multiple response measurements into modal coordinate responses. Since the modal coordinate responses are the responses of single-degree-of-freedom systems, the frequency and damping may be accurately estimated with short data records. An on-line monitoring system is discussed which may be useful in a variety of applications. The focus in this paper is on the application to aircraft flight flutter testing.

Sensor placement for on-orbit modal testing

Abstract: A systematic procedure of placing sensors for the on-orbit modal identification of large flexible space structures is addressed. The concepts of system and component modal costs are introduced as a means of selecting target modes for modal testing. Assuming that a time-domain modal identification algorithm is employed to identify the modes from measured time response data, the sensors are placed to enhance the recovery of the target modes. As an application example of the procedure, an accelerometer placement study for the Space Station Freedom On-Orbit Modal Identification Experiment is presented.

Analysis of natural frequencies and modal loss factors of simply supported beams with adhesively bonded double‐strap joints

Abstract: This paper presents a dynamic model for the transverse vibration analysis of an adhesively bonded composite double‐strap joint. The differential equations of motion of the joint system are derived using the energy method and Hamilton’s principle. It is assumed that the energy dissipated by the joint system is contributed by both the shear and longitudinal deformation of the adhesive layers. The combination of natural boundary conditions, forced boundary conditions, and continuity conditions yields the frequency equations to predict the system resonance frequencies and modal loss factors. The effects of structural parameters and material properties of the adhesive layer on the system modal loss factors and resonance frequencies are also studied.

Damage detection in a tripod tower platform (ttp) using modal analysis

Abstract: When structural damage occurs, the dynamic characteristics of the structure change correspondingly. Consequently, Frequency Response Functions (FRFs) of the structure could be used to detect the damages in a Tripod Tower Platform (TTP) structure. A 1/50th scale elastic model made of acrylic plastic is used to represent the real TTP structure. Strain gauges are used, along with accelerometers and displacement transducers, for modal testing. Since strains and stresses are the prime response parameters of interest in structural behaviour, and strain gauges are widely used to monitor them, FRFs using strains, displacements and accelerations, are obtained at different damage levels of the structure. Effects of damage on FRFs are investigated considering frequency shifts, damping, and amplitude changes. Strain FRFs are also compared with the acceleration and displacement FRFs, and the differences discussed. The experimental values are compared with the numerical computations carried out using the finite element modules available in the computer program SDRC-IDEAS. The sensitivities of the various sensors to detect changes are also determined and compared.

Nonlinear modal analysis of frames by the incremental harmonic-balance method

Abstract: A modal incremental harmonic-balance method for the steady-state vibration of geometrically nonhnear frames by finite-element analysis is introduced. The nonlinearity is in the coupling of the axial and flexural deformations through the induced axial force along the element. Free and forced vibrations for damped or undamped systems are studied. It is shown that the method allows accurate response curves to be constructed with minimum effort

An Experimental Study of the Local Parameters of a Damaged Cantilever

Abstract: The introduction of a crack in a structure will cause a local change in stiffness and damping capacity. The local change in stiffness, normally a decrease, will lead to a change of the natural frequencies of the structure and a discontinuity in the mode shapes. This report contains a presentation of results from experimental tests with six hollow section steel cantilevers containing a fatigue crack introduced from a narrow laser cut slot. The modal parameters have been identified for different size and location of a crack. The modal parameters have been estimated by mean of frequency domain and time domain system identification techniques. A short description of these system identification methods is given. MODAL PARAMETERS OF A DAMAGED CANTILEVER 3

Comparison of two dissimilar modal Identification Techniques.

Abstract: Recent laboratory results using a refined phase resonance method and the eigensystem realization algorithm on the same test structure are reported. These methods are dissimilar modal identification techniques suitable for future large spacecraft. The theory, application approach, and results obtained for each technique are summarized and compared. Although both methods worked well in this investigation, significant differences occurred in some identified mode shapes. Comparison of independently derived modal parameters provides the means for disclosing such discrepancies in flight projects.

Modal information from acoustic measurements for fatigue crack detection applications

Abstract: When structural damage occurs in structures due to cracking at critically-stressed sections, it reduces the stiffness and increases the damping at the local section. This change is reflected globally in the structure through changes in its dynamic behaviour, viz., natural frequencies, modal damping, modal shapes and system transfer functions. Acoustic energy is radiated into the surrounding medium from the structural vibration. This acoustic energy carried considerable information about the state of the structure which, when analysed, could give details about the defects in the structure. A steel vibrating cantilever beam is currently being used as simple mechanical system upon which quantitative acoustic measurement procedures can be developed for non contact fatigue crack detection in more complicated steel structures. In this paper we focus on the ability to obtain modal information on the state of the cantilever from non-contact acoustic measurements. This paper summarises the results of modal analysis of a cantilever beam based on measurements with an accelerometer and a force transducer, measurements with a pair of pressure microphones. The results from each method are illustrated for a machined smooth cantilever specimen. Finite element analysis predictions are also included. The long term objective is to combine finite element analysis, modal analysis and acoustic measurement techniques into the global monitoring capability for fatigue crack detection in steel structures. This paper shows the typical confidence level that has been achieved in extracting modal shape and damping information from acoustic measurements versus more conventional mechanical acceleration measurements.

A modal test of a space-truss for structural parameter identification

Abstract: The Jet Propulsion Laboratory is developing a large space-truss to support a micro-precision interferometer. A finite element model will be used to design and place passive and active elements in the truss to suppress vibration. To improve the model`s predictive capability, it is desirable to identify uncertain structural parameters in the model by utilizing experimental modal data. Testing of both the components and the system was performed to obtain the data necessary to identify the structural parameters. Extracting a modal model, absent of bias errors, from measured data requires great care in test design and implementation. Testing procedures that are discussed include: verification of non-constraining shaker attachment, quantification of the non-linear structural response, and the design and effects of suspension systems used to simulate a free structure. In addition to these procedures, the accuracy of the measured frequency response functions are evaluated by comparing functions measured with random excitation, using various frequency resolutions, and with step sine excitation.

Determining the accuracy of modal parameter estimation methods

Abstract: The most common type of modal testing system today uses an FFT analyzer to measure a set of Frequency Response Functions (FRFs) from a structure, and then uses a parameter estimation (curve fitting) method to determine the structure’s modal properties from the FRF measurements. The curve fitting method typically “fits” an analytical model to the FRF data, (or its equivalent Impulse Response data) and estimates of the unknown modal parameters of the model are determined by this process. These parameter estimates are then assumed to be the correct modal parameters of the structure. In this paper, a number of “standard test cases” of synthesized FRFs are presented for testing modal parameter estimation methods. Twelve different FRFs are presented, that are synthesized using the parameters for three modes. Frequency spacings between the modes and modal damping values are varied to make up the different cases, which range from light modal coupling (or modal density) to very heavy coupling. Random noise is also added to the synthesized FRFs to simulate noisy measurements, giving a total of twent y-four different test cases. The advantage of this approach to curve fitter testing is, of course, that the right answers (the modal parameters used to synthesize the FRFs) are known, and can therefore be used as the basis for determining the accuracy of the fitter. Two different curve fitting methods, an SDOF (single mode-at-a-time) and an MDOF (multiple modes-at-a-time) rational fraction polynomial fitter, were tried on the test case FRFs, and the results are presented. In publishing these “standard test cases” the authors hope to encourage the adoption of a suite of published test cases by the modal testing community which could then be used to qualify the accuracy of commercially available modal testing software.

Sensitivity of Space Station alpha joint robust controller to structural modal parameter variations

Abstract: This paper describes the photovoltaic array sun tracking control system of Space Station Freedom. A synthesis procedure for determining optimized values of the design variables of the control system is developed by use of a constrained optimization technique. The synthesis is performed to provide a given level of stability margin, achieve the most responsive tracking performance, and meet other design requirements. Performance of the baseline design, which is synthesized using predicted structural characteristics, is discussed, and the sensitivity of the stability margin is examined for variations of the frequencies, mode shapes, and damping ratios of dominant structural modes. The design provides enough robustness to tolerate a sizeable error in the predicted modal parameters. The paper concludes with an investigation on the sensitivity of performance indicators as the modal parameters of the dominant modes vary, which would be useful in improving the control system performance if accurate modal data are provided through an on-orbit modal identification experiment.

On the Use of Simulated "Experimental" Data for Evaluation of Modal Analysis Methods

Abstract: The purpose of this paper is to investigate the effect of measurement errors. such as the mass loading effects or transducers. shaker/structure interaction, sign3l conditioning errors. signal processing .errors. etc. - on measurements of frequency response functions(FRFs) and on the modal parameters extracted from the FRFs. A computer program has been developed which can be used to simulate various measurement errors. The "experimental"' FRFs calculated using this simulation program can be used to test realistically the performance of different modal parameter identification programs and. thus. of the various applications to winch these modal data are put. including model updating.

Modal Identification Algorithm with Unmeasured Input

Abstract: This paper investigates the possibility of generating a time‐domain modal identification algorithm that does not need measurements of the input signals. Such a technique is useful when complete input data acquisition cannot be performed. The approach is based on the Yule‐Walker equations, extended to the case where the input signal is not white noise. The algorithm is written recursively both to minimize data acquisition and to be flexible enough when time‐varying modal parameters are tracked. Natural frequencies and damping ratios are extracted with an error magnitude inferior to impulse response techniques but superior to methods using the input time history. From a computational aspect, the algorithm only introduces scalar inversions, which presents an important gain of time and stability. Examples and comparisons with other techniques are presented. The case where a change in the modal parameter values occur is also highlighted. A normalized error, taking into account the quality and the swiftness of ...

Comparison of candidate methods to distinguish noise modes from system modes in structural identification

Abstract: In modal identification, nonphysical noise or computation modes always appear to help match the input-output data. This paper studies the ability of four criteria to distinguish which modes in a model are noise modes: (1) modal amplitude coherency, (2) the relative contribution of each mode to the pulse response indicated by the mode singular value, (3) the variances of the mode frequencies and damping factors produced by a chosen measurement noise level, and (4) identification of the backward-time in order to let the shift from positive to negative damping of the true system modes distinguish these modes from noise modes. Both simulated and experimental data are used to study the four criteria.

A modal hybridization method for vibroacoustic studies at medium frequencies

Abstract: A general size reduction procedure of large modal models is set up by means of Ritz–Galerkin projection techniques based on a reduced set of hybrid modes defined in each frequency band by an appropriate linear combination of the eigenmode shapes of the modal reference model. This method applies in the case of ‘‘broadband excitation’’ such as transient or random forces and leads in this case to good estimates of the vibration energy and of response maxima. It appears that the present approach differs from the well‐known SEA mainly by accounting for the specificity of the external (or coupling) loads−an appropriate space averaging of the MHM leading to equipartition of energy and therefore to the SEA results. In a first part, this method is introduced in the modal analysis of the response of a structure to external forces (resp. to a prescribed motion) imposed on its interaction surface. It is shown that the hybrid modes cumulate the modal excitabilities (resp. the effective modal masses) of the ‘‘component modes.’’ The second part is devoted to the coupled vibroacoustic problem viewed through the coupling of two sets of acoustic and structure oscillators. It is shown that the resonant coupling problem can be reduced−in each frequency band−to the coupling of N acoustic hybrid modes with N structure hybrid modes corresponding to the N predominant singular values of the (rectangular) coupling matrices (additional structure hybrid modes must be considered for accounting for the external loading). The explicit solution of this problem is given in the case of a frequency band in which a cluster of modes of one subsystem is coupled with a single mode or a pair of modes of the other subsystem.