# MODAL v5 - Abstracts

NOTE: The journal articles are listed alphabetically by first author.

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Arif, G. M. and Pettersson, O., Lund University

5(3):141-154; Jul. 1990.

APPLICATION OF FINITE ELEMENT METHOD TO THE STABILITY OF AN ECCENTRICALLY LOADED COLUMN BY SLAVE LOADS INCLUDING DAMPING

ABSTRACT - The finite element method is used to analyze the stability of a cantilever column resting on elastic foundation and subjected to an eccentric slave load at its free end. The analysis has been conducted according to Bernoulli-Euler and Timoshenko beam theories. Effects of the mass offset, coupling effects and damping has been taken into account.

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Biswas, M., Pandey A. K., and Samman, M. M., Duke University

5(1):33-42; Jan. 1990.

DIAGNOSTIC EXPERIMENTAL SPECTRAL/MODAL ANALYSIS OF A HIGHWAY BRIDGE

ABSTRACT - Experimental modal analysis is considered a viable method of non-intrusive inspection for detecting incipient failure in bridges. For evaluation of such techniques, a probable failure mode of a large fatigue crack was simulated by unfastening a set of high- strength bolts of a splice connection of a steel girder of a typical highway bridge and experimental modal testing was performed for the intact case as well as the cracked case. Details of experiments and typical test results are presented. Test and analysis data includes time domain records, frequency spectra, frequency response functions, modal parameters and modal assurance criteria. As a result of simulated crack development, detectable sensitivity of response data are observed. An Appendix includes information about equipment and instruments used.

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Brandon, J., University of Wales College of Cardiff

5(4):205-212; Oct. 1990.

CHARACTERISTIC BEHAVIOR OF RANDOM AND SYSTEMATIC ERRORS IN INVERSE PLANE FREQUENCY IDENTIFICATION ALGORITHMS

ABSTRACT - This paper describes three types of error, each of which has a different, and distinctive, effect on the results of inverse plane circle fitting algorithms. By examining the characteristics of the error patterns, strategies for eliminating their effects are devised. This paper demonstrates how these errors may be identified by consideration of data plots and indicates how their identification may be incorporated in software.

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Cobb, R. E., Contract Engineer and Mitchell, L. D., Virginia Polytechnic Institute and State University

5(3):185-194; Jul. 1990.

ESTIMATES OF VARIANCE AND CONFIDENCE BANDS FOR THE THREE-CHANNEL FREQUENCY RESPONSE FUNCTION ESTIMATOR

ABSTRACT - Closed-form and numerical methods of calculating three- channel FRF magnitude variance are discussed. The closed-form solution is shown to be numerically ill-conditioned, while the numerical method is shown to give good estimates of FRF magnitude variance in both simulations and experimental results. Variance estimates allow ?confidence bands? to be placed on the experimentally measured FRF magnitude. This quantifies the amount of variation that can be expected in the FRF measurement at any given spectral line and should be useful in assigning weighting factors for curve-fitting algorithms. This magnitude bias is shown and discussed.

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Craig R. R., Jr., University of Texas, Kurdila, A. J., Texas A & M University, and Kim, H. M., McDonnell Douglas Astronautics Co.

5(3):169-183; Jul. 1990

STATE-SPACE FORMULATION OF MULTI-SHAKER MODAL ANALYSIS

ABSTRACT - As modal testing techniques have improved in recent years, the demands placed on the accuracy of modal test results has increased. This paper describes a multi-input, multi-output modal parameter estimation algorithm suitable for the identification of reduced-order models of structures. The method described is a frequency-domain method based on excitation and response spectra. The principal features of the algorithm are: (1) its applicability to general linear, time-invariant systems, (2) the direct use of multiple input and multiple response data, (3) the identification of reduced- order models with minimum user interaction through the use of two automatic model-reduction techniques and the (4) identification of a consistent set of modal parameters through the use of numerically stable least-squares techniques.

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Doyle, J. F., and Farris, T. N., Purdue University

5(2):99-107; Apr. 1990

A SPECTRALLY FORMULATED FINITE ELEMENT FOR FLEXURAL WAVE PROPAGATION IN BEAMS

ABSTRACT - A spectral formulation of the dynamics of beams suitable for a finite element implementation is presented. The analysis gives the exact frequency dependent stiffness matrix for the beam. The frequency domain response is converted to the time domain response using the Fast Fourier Transform algorithm. The formulation is verified by comparison with conventional finite element results.

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Doyle, J. F., and Farris, T. N., Purdue University

5(4):223-237; Oct. 1990.

A SPECTRALLY FORMULATED ELEMENT FOR WAVE PROPAGATION IN 3-D FRAME STRUCTURES

ABSTRACT - A spectral formulation of the dynamics of frame structures suitable for a computer matrix method implementation is presented. The analysis is based on a spectral frame element that is assembled to give the exact frequency dependent stiffness matrix for the complete structure. The frequency domain response is converted to the time domain response using the fast Fourier transform algorithm. The formulation is verified by comparison with conventional finite element techniques. It is found that the spectral method can be less costly from a computational standpoint than the conventional finite element method. This is especially true for events involving high frequencies such as impact. The most significant strength of the spectral method, however, lies in its ability to go directly to the heart of dynamics problems; namely, the system frequency response function. Some of the implications of this are discussed.

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Ismail, F., University of Waterloo, and Fyfe, K. R., University of Alberta

5(1):25-32; Jan. 1990.

MODELING CYLINDER ACOUSTICS OF FLEXURAL AND SHELL MODES

ABSTRACT - A boundary element model is presented in this work to study the acoustic radiation of a finite cylinder in flexural and shell modes of vibration. For flexural modes, numerical results compare well with experimental measurements reported in the literature. These results have the same trend as the infinite length cylinder solution. Computed results for shell modes are also compared with test measurements performed on a configured cylinder. Modal analysis testing was employed to obtain the shell mode velocity profiles which were input to the acoustic model. Details of the experimental setup and procedure are given. Results from the acoustic model compared well with measurements for the low order shell modes.

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Jones, J. D., Purdue University, and Fuller, J. D., Virginia Polytechnic Institute and State University

5(3):123-140; Jul. 1990.

ACTIVE CONTROL OF STRUCTURALLY-COUPLED SOUND FIELDS IN ELASTIC CYLINDERS BY VIBRATIONAL FORCE INPUTS

ABSTRACT - Active control of structurally-coupled sound fields in elastic cylinders is analytically and experimentally studied. The primary (noise) field in the cylinder model is generated by the coupled dynamic response of the shell under loading by a single exterior acoustic source. Control of the interior sound field is achieved by applying vibrational force inputs directly to the shell wall. Action of the point controllers serve to increase the input impedance of select structural modes of the shell which are well- coupled to the interior acoustic cavity, thus substantially reducing sound transmission into the cavity. Spatially-averaged noise reductions in excess of 30 dB are demonstrated for acoustic resonant conditions within the cavity. Twin controller configurations are presented which demonstrate the ability to independently control orthogonal modes of the interior acoustic space. Benefits and drawbacks of this new methodology for noise control are discussed and clearly demonstrated.

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Kim, M. J., and Gupta, A., Northern Illinois University

5(3):195-203; Jul. 1990.

FINITE ELEMENT ANALYSIS OF FREE VIBRATIONS OF LAMINATED COMPOSITE PLATES

ABSTRACT - The effects of lamination and extension-bending coupling, shear and twist-curvature couplings on the lowest frequencies and corresponding mode shapes for free vibration of laminated anisotropic composite plates are presented by using a finite element method based on the first order shear deformation theory. The finite element method uses quadratic interpolation functions with 5 degrees of freedom (3 displacements and 2 slopes) to model the composite plates and material properties typical of a highly directional composite material (high modulus graphite/epoxy). The numerical results for the case of all edges simply supported show that the mode shapes are not affected as much as the frequencies by the coupling effects of laminated plates.

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Larsson, P. O., ABB Corporate Research

5(1):1-12; Jan. 1990.

DYNAMIC ANALYSIS OF ASSEMBLED STRUCTURES USING FREQUENCY- RESPONSE FUNCTIONS: IMPROVED FORMULATION OF CONSTRAINTS

ABSTRACT - Methods for the analysis of assembled structures using a set of frequency-response functions, or FRFs, were studied. The FRFs of the components, or substructures, are either measured or calculated. The main objective was to show how the required constraints, corresponding to the coupling of two substructures, can be formulated in cases where only FRFs between translations, and not between rotations, are available. This is of interest since only FRFs between translations can be measured effectively. A new method of formulating the constraints is presented which is useful when the substructures are beam-like in the vicinity of the interface between the coupled structures. It is based on an interpolation of the deformation of the substructures using polynomials. It was found from numerical simulations of ideal beams that the new method brings considerable improvements in certain cases. Therefore, the accuracy of the resulting FRFs and their sensitivity to small errors in the FRFs of the substructures, as well as the choice of the points where the FRFs are measured, were investigated.

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Lee, C. W., and Hong, S. W., Korea Advanced Institute of Science and Technology

5(2):51-65; Apr. 1990.

ASYNCHRONOUS HARMONIC RESPONSE ANALYSIS OF ROTOR/BEARING SYSTEMS

ABSTRACT - This paper develops a generalized modal analysis scheme for forced vibration analysis of rotor bearing systems with rotational speed dependent parameters subject to asynchronous harmonic excitations. The essence of the method is that the rotational speed dependent eigenvalue problem of the original system is transformed into the rotational speed independent eigenvalue problem by introducing a lambda matrix, assuming that the bearing dynamic coefficients are well represented by polynomial functions of rotational speed over the operating speed range of interest. This method deals with closed form solution in response calculations and the influence coefficients, the critical speeds and the corresponding logarithmic decrements for an asynchronous harmonic excitation are readily identified.

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Lu, S. L., National Taiwan Institute of Technology, and Ju, F. D., University of New Mexico

5(4):251-260; Oct. 1990.

THE RANDOM STRUCTURAL RESPONSE OF A SDF SYSTEM WITH STIFFNESS DEGRADATION

ABSTRACT - This paper presents a stochastic model to describe the response of hysteretic, degrading structures subjected to random excitations. The analysis calculates the response using a nonlinear hysteretic structural model, which takes into account both work hardening and stiffness degradation effects. The constitutive hysteretic loop is modeled by linear segments, with degrading elastic stiffness. Since the restoring force of a hysteretic system depends on both the current displacement and the history, it is a loop- dependent variable which is a random process in this study. The mean and variance of displacement and restoring force are computed with the finite difference method with recursive scheme. The present investigation emphasizes the effects of the system degradation and the randomness of stiffness for the random response analysis.

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Moustafa, K. A. F., King Fahd University of Petroleum and Minerals, and Asfar, K. R., Jordan University of Science and Technology

5(4):213-221; Oct. 1990.

IDENTIFICATION OF JOURNAL BEARING MODAL PARAMETERS

ABSTRACT - Identification of the natural frequencies and modal dampings of a flexible rotor-journal bearing system is considered in this paper and a real-time modal sweeping scheme which identifies the unknown parameters on-line is proposed. The identification is carried out by using a single excitation and a single response record. This simplifies considerably the measurement and instrumentation requirements for experimental work.

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Ojalvo, I. U., Ting, T., and Pilon, D., University of Bridgeport

5(1):43-49; Jan. 1990.

PAREDYMâ€“A PARAMETER REFINEMENT COMPUTER CODE FOR STRUCTURAL DYNAMIC MODELS

ABSTRACT - A computationally efficient parameter refinement program, named PAREDYM, for structural dynamic models with up to 100 variables has been developed. The method compares limited modal test data with corresponding analytical results and employs a minimum least squares algorithm, based upon modal parameter sensitivities, to iteratively improve model stiffness and mass parameters. Sensitivity computations are augmented with scaling techniques to facilitate numerical solution by minimizing matrix ill-conditioning. PAREDYM has been applied successfully to a beam model with 83 mass and stiffness parameters, starting with artificially manufactured parameter errors of the order of 10\%. Results to date have yielded rapid convergence to the known exact answer within a few iterations.

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Smallwood, D. O., and Lauffer, J. P., Sandia National Laboratories

5(2):115-122; Apr. 1990.

QUALIFICATION OF FREQUENCY-RESPONSE FUNCTIONS USING THE RIGID-BODY RESPONSE

ABSTRACT - The response of a structure at low frequencies with free boundary conditions is dominated by the rigid-body modes. The displacement shapes obtained form the low frequency values of the frequency-response functions can be compared with ideal rigid-body motion to point out errors in the measurements. Insight is enhanced when the comparisons are made in the coordinate system of the measurements. Without this procedure intuition can rarely determine the proper rigid-body response at each measurement location. Typical errors identified are scaling errors, errors in location or direction, measurements with poor dynamic range and other instrumentation problems. The procedure is particularly useful when the test object is multi-dimensional, has a complicated geometry, has measurements in other than rectangular coordinates, and where more than one rigid-body mode is excited. It is suggested that data qualification using this method would be a useful addition to most modal tests. A least squares approach, to determine the proper rigid-body response, is reviewed and several experimental examples are given.

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Sriram, P., Craig, J. I., and Hanagud, S., Georgia Institute of Technology

5(3):155-167; Jul. 1990.

A SCANNING LASER DOPPLER VIBROMETER FOR MODAL TESTING

ABSTRACT - Accelerometers are widely used to sense structural response in modal testing. The mass loading and local effects due to accelerometers are not always negligible. The laser Doppler velocimeter/vibrometer (LDV) is a noncontact optical sensing tool for accurately measuring point velocities. The noncontact nature of the instrument makes it particularly attractive for use on lightweight structures where measurement interaction must be minimized. Real-time scanning LDV?s have recently been introduced to measure fluid flow velocity profiles rapidly. In this paper, the development of a real- time scanning LDV for structural applications is described. The instrument can be used to simultaneously measure the velocity response at a series of locations on a vibrating structure. Standard modal analysis techniques can then be applied to extract the usual modal data, e.g., natural frequencies, damping and mode shapes. The special case of beam vibration is considered in this paper though the technique can be readily extended to generic planar measurements. The measurement technique has been validated through modal testing of a simple beam structure. Comparisons between theoretical and LDV measured mode shapes and natural frequencies are presented.

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Stubbs, N., Texas A & M University, and Osegueda, R., University of Texas at El Paso

5(2):81-97; Apr. 1990.

GLOBAL DAMAGE DETECTION IN SOLIDS - EXPERIMENTAL VERIFICATION

ABSTRACT - Experimental evidence, obtained from controlled laboratory experiments, is provided to support a recent theory of nondestructive damage detection. In the experiment, known magnitudes of damage are inflicted on cantilevered specimens and the dynamic responses of the undamaged and damaged specimens are measured. Using the experimental frequency response of the specimens and a numerically-generated sensitivity matrix, the theory is used to predict the location and magnitude of damage inflicted in the specimens. All damage locations considered in this series of tests are correctly predicted by the theory. The correct order of magnitude is always predicted by the theory and the error in the magnitude of the predicted damage decreases with increasing damage magnitude.

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Stubbs, N., Texas A & M University, and Osegueda, R., University of Texas at El Paso

5(2):67-79; Apr. 1990.

GLOBAL NON-DESTRUCTIVE DAMAGE EVALUATION IN SOLIDS

ABSTRACT - Variational analysis is applied to the homogeneous equations of motion of an undamaged structure to yield expressions for changes in modal stiffnesses in terms of modal masses, modal damping, eigenfrequencies, eigenvectors, and their respective changes. Expressions relating variations in stiffnesses of structural elements to the variations in modal stiffness are generated from matrix structural analysis. The result is a system of algebraic equations with a known load vector of fractional changes in modal stiffness and unknowns of fractional changes in member stiffnesses. Methods of solution for the resulting system of equations are discussed along with special cases in which the structure may be modeled to yield unique predictions. A numerical example is presented to demonstrate the potential of the formulation.

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Wang, J. H., and Liou, C. M., National Tsing Hua University

5(1):13-24; Jan. 1990.

EXPERIMENTAL SUBSTRUCTURE SYNTHESIS WITH SPECIAL CONSIDERATION OF JOINTS EFFECTS

ABSTRACT - A method was proposed in this work to experimentally synthesize the frequency-response functions (FRF) of a whole structure using the FRF of each substructure and giving special consideration to the effects of joints. To identify the dynamic properties of joints, a simple method based on statistical criteria is introduced to overcome the problem caused by measurement noise. The experimental results show that the FRF of the whole structure can be accurately reproduced by the FRF of substructures even with the effects of joints.

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Weisensel, G. N., IBM Corporation, and Schlack, A. L.,Jr., University of Wisconsin

5(4):239-250; Oct. 1990.

ANNULAR PLATE RESPONSE TO CIRCUMFERENTIALLY MOVING LOADS WITH SUDDEN RADIAL POSITION CHANGES

ABSTRACT - The forced dynamic response of annular plates to circumferentially moving concentrated transverse loads of harmonically varying amplitude with sudden changes in radial position is investigated. Classical plate theory is used with damping included. The boundary conditions are that the inner boundary of the plate is clamped and the outer boundary is free. The loading function describes a concentrated transverse load of harmonically varying amplitude moving around the plate in a concentric circular path at a constant radial position which instantaneously moves to a concentric circular path at a different radial position. The general solution for this loading function is derived in integral form. This integral is then solved to determine the forced response in Fourier-Bessel series form. The sudden change in radial position requires the transient deflection of the plate to be included as well as the steady state deflection due to the moving load at each of the constant radial positions before and after the sudden change. The transient and maximum deflections are studied in detail.

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Zeng, Z., and Huang, T., Tianjin University, and J. F. Hamilton, Purdue University

5(2):109-104; Apr. 1990.

AN EFFECTIVE APPROACH TO DETERMINE NATURAL FREQUENCIES AND MODE SHAPES OF CONSTRAINED BEAMS USING LAGRANGE MULTIPLIERS

ABSTRACT - In this paper, an approach using Lagrange multipliers is presented for determining the eigenfrequencies and eigenfunctions of beams with a variety of elastic and rigid support conditions. The presented approach utilizes component modal synthesis and results in a linear generalized eigenvalue problem which can be solved by standard procedures.

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