# MODAL v1 - Abstracts

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

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Allemang, R.J.; Brown, D.L. Multiple-input experimental modal analysis - a survey. 1)1:37-44; Jan 1986.

ABSTRACT - The technology of experimental modal analysis is expanding rapidly as the impact of multiple inputs, or references, is being realized. This paper traces the development of experimental-modal-analysis techniques while noting this current trend toward multiple-input utilization in the estimation of system parameters. Over the past 40 years, at least four general categories of experimental-modal-analysis methods can be identified as follows: (1) Forced-Normal-Mode Excitation, (2) Frequency-Response Function, (3) Damped-Complex Exponential Response, and (4) Mathematical Input-Output Modal. Experimental-modal-analysis methods in each of these categories can incorporated multiple-input concepts in one way or another. Historically, the modal characteristics of mechanical systems have been estimated by techniques that fall into either the first or second category. The forced-normal-mode-excitation method has always included the multiple-input concept while the frequency-response-function method, until recently, only involved the repeated application of single inputs. This paper reviews both of these methods with emphasis on the current trends in the refinements of these methods involving multiple-input concepts. The experimental-modal-analysis methods that fall into the last two categories are composite approaches that utilize elaborate parameter-estimation algorithms based upon structural models and include multiple-input concepts. The current developments in these areas are reviewed as well.

Doyle, J.F. Application of the fast-Fourier transform (FFT) to wave-propagation problems. 1(4):18-25; Oct 1986.

ABSTRACT - The time variation of the wave signals is replaced by a summation over its frequency components. This is done efficiently by use of the FFT algorithm but in doing so a number of problems arise. The procedures and problems are elucidated by considering the impact of a beam and the resulting wave propagations.

Engles, R.C. A solution to the Craig/Bampton eigenvalue problem for multicomponent structures. 1(2):19-24; Apr 1986.

ABSTRACT - A cost-effective technique is presented to solve the system eigenvalue problem associated with the Craig/Brampton component-mode synthesis method. Subspace iteration is employed in order to take advantage of the special form of this eigenvalue problem.

Gaught, T.M.; Dobson, B.J. The transient analysis of a structure using a modal model. 1(1):11-16; Jan 1986.

ABSTRACT - Experimental modal analysis is used to characterize the dynamic behavior of a structure in terms of natural frequencies, mode shapes and damping. Using the parameters extracted from this analysis a mathematical model is generated to predict the transient behavior of the structure subjected to an impact. A time-marching algorithm is employed to predict the acceleration response which is compared to experimental data. It is shown that a comparison between the measured and predicted responses can be used to identify errors in the mode-shape parameters extracted from the experimental modal analysis.

Haisty, B.S.; Springer, W.T. A simplified method for extracting rotational degree-of-freedom information from modal-test data. 1(3):35-39; Jul 1986.

ABSTRACT - A method is presented which uses third-order spline curves to approximate the deflected shape of a vibrating structure. These curves can then be used to determine the rotational degree-of-freedom (RDOF) contributions to the deflection curve, thereby allowing structural-dynamics-modification (SDM) techniques requiring this information to be correctly applied to the modal data.

Haynes, F.D. Vibration analysis of the Yamachiche lightpier. 1(2):9-18; Apr 1986.

ABSTRACT - The Yamachiche lightpier, located in Lac St. Pierre, Quebec, was instrumented with geophones, accelerometers and an inclinometer. In order to determine is dynamic characteristics, 15 breakable bolts with failure strengths from 10,000 to 101,000 lb were used to apply a step unloading force on the pier. The damping and stiffness were obtained from the data in the time domain. The natural frequencies and mode shapes were obtained from the data transformed into the frequency domain. A modal-analysis computer program was used to verify the natural frequencies and mode shapes. A mathematical modal was developed which includes translation, rotation and shear-beam deformation of the pier.

He, J.; Ewins, D.J. Analytical stiffness matrix correction using measured vibration modes. 1(3):9-14; Jul 1986.

ABSTRACT - Correction of analytical stiffness and mass matrices of a vibration structure by correlating the experimental and analytical models has recently attracted considerable attention. This paper proposes a method to localize the region of errors existing in the analytical stiffness matrix and introduces an iteration concept into the model-correction process. The methods are justified by numerically simulated results showing that this location technique, together with the iteration process, brings about a dramatic improvement in the correction of an analytical stiffness matrix. Also, it becomes possible to estimate directly the errors existing in analytical stiffness matrix by using measured modes available, once the region of errors is pinpointed. The same methodology can be applied to mass-matrix correction problem.

Huang, T.C.; Zhang, P.Q.; Feng, W.Q. Multiple single-input space-time regression method in modal analysis. 1(4):1-7; Oct 1986.

ABSTRACT - The concept of the multiple single-input space-time regression method (MS-STRM) in modal analysis is explained. Its feasibility, advantages, and ability to deal with systems with repeated roots, high modal density, or high damping are proved through the identification of both computer-simulated systems and actual experimental systems.

Ibrahim, S.R. Incipient failure detection from random-decrement time functions. 1(2):1-8; Apr 1986.

ABSTRACT - Changes in the physical properties of structures, such as cross sectional areas, inertias, and damping properties, can cause measurable changes in the modal properties of these structures. Periodic identification of the natural frequencies, damping factors, and mode shapes institutes a credible means of nondestructive evaluation for structural-integrity monitoring and incipient failure detection. It is desirable that such periodic testing be performed without disrupting the operation of the structure under test. Offshore platforms, bridges and piping systems are among the structures that may benefit from such procedures. This paper deals with a class of structures whose operating responses are due to some stationary random input(s) plus some possible harmonic excitation. These inputs need not be known or measurable. A time-domain modal identification technique developed for a limited number of measurements possible one, with high identification accuracy and repeatability is suggested as the modal-identification method for this purpose. Converting the operational responses to a form usable for identification will be performed using the multi-measurement-multimode random-decrement technique. The theoretical basis and possible limitations of rht random-decrement technique are summarized. The computational requirements for the two combined techniques are simple and stable and could possible be implemented on minicomputers.

Leuridan, J. The use of principal inputs in multiple-input multiple-output data analysis. 1(3):1-8; Jul 1986.

ABSTRACT - In many areas of vibration and acoustical analysis, one needs to establish multiple-input multiple-output relations. A typical example for structural testing is the estimation of frequency response functions (FRFs) with simultaneous multiple-input excitation. A typical example in acoustical analysis is the noise-ranking problem, where the contributions of different potential noise inputs (or sources) to a given output are to be established. Solutions for these multiple-input multiple-output problems have been worked out for the case that the inputs are not correlated. Most solution techniques can handle the case of some correlation between the inputs, but fail if the inputs become very highly correlated. The aim of this paper is to discuss techniques for verifying correlation between multiple inputs, and between multiple inputs and one output. Classical techniques based on ordinary, partial and multiple coherence function calculations are reviewed. A new technique that is based on the calculation of a set of principal inputs is introduced and is compared with classical techniques. An example of its application is worked out to demonstrate the new techniqueâ€™s feasibility and interesting features.

Matzen, V.C.; Murphy, C.E. On obtaining mass participation factors using equivalent structures. 1(1):17-23; Jan 1986.

ABSTRACT - Mass participation factors appear in the forcing function of modal descriptions of the behavior of structures subjected to support excitation. Exact calculation of these factors for a given structural discretization is theoretically possible, but it requires either the full mass matrix or the full matrix of eigenvectors. For many applications, both of these approaches are impractical, and the only recourse is to use some type of approximate method. Approximate analytical methods are based on the use of reduction schemes, which eliminate unwanted DOFs. After the system has been reduced, the participation factors are obtained using the same procedures as those used on the original system. Experimental methods require either modal parameters (modal masses and eigenvectors) or the structural response in the time domain to obtain the participation factors. In this paper, two analytical and three experimental methods for finding mass participation factors are described and compared using simulated experimental data.

Mitchell, L.D. Signal processing and fast-Fourier-transform (FFT)analyzer

- a survey. 1(1):24-36; Jan 1986.

ABSTRACT - This paper will act as a tutorial for the use of fast-Fourier-transform (FFT) techniques in the analysis of experimental dynamic data for the purpose of the identification of the physical characteristics of the measured system. Consideration will be given to transducer and system calibration, signal conditioning, the relationship of sample rate to frequency range, anti-aliasing filter processes, time-domain windows and their data-leakage effects, channel-to-channel crosstalk, various algorithms for computing frequency-response function, and the coherence function. This paper should make the readers aware of what FFT signal processing will do for them and what it will do to their data. Recent information concerning the ability of the modalanalysis community to make proper measurements indicates that the expert and the novice alike need to review the basics of FFT signal processing.

Muszynska, A. Modal testing of rotor/bearing systems. 1(3):15-34; Jul 1986.

ABSTRACT - Several aspects of modal testing of rotating machines are discussed. Advantages of the nonsynchronous perturbation technique used for identification of rotor/bearing system parameters are outlined. Several application examples of perturbation testing for rotating systems are given. The obtained results are discussed. The perturbation testing of rotor/bearing systems has revealed the existence of new modes generated by solid/fluid interaction. These modes were unknown in classical modal analysis.

Rogers, J.D.; McConnell, K.G. Damping in aluminum-filled epoxy using two different flexural-testing techniques. 1(4):8-17; Oct 1986.

ABSTRACT - Two flexural-test methods were used to measure the loss factor of a commercially available aluminum particle-filled epoxy. The results were compared to results from the same tests performed on an aluminum alloy. Amplitude and frequency effects on the loss factor were considered for each material.

Shen, C.L.; Tsuei, Y.G.; Allemang, R.J.; Brown, D.L. Analytical and experimental study of inextensional modes of a circular cylinder. 1(4):26-32; Oct 1986.

ABSTRACT - Modal analysis of a plastic cylinder, a steel cylinder and a steel ring has been conducted. With these materials and geometries, the lowest measurable modes under investigation are from inextensional modes which are primarily due to flexural bending. They can be classified into three groups: (a) cylinder surface remains prismatic, (b) cylinder surface becomes nonprismatic, and (c) vibration of a ring due to bending in axial direction with twist. The analytical expressions for frequencies and modes are obtained and verified by experiments. As expected, repeated eigenvalue occurs. For special geometry, multiplicity of four might appear.

Snyder, V.W. Structural modification and modal analyses - a survey. 1(1):45-52; Jan 1986.

ABSTRACT - This paper discusses the mechanism for the determination of dynamic characteristics of linear systems which has been modified. The mechanism can be used to marry both analytical and experimental techniques. Typically, when structural modifications are made it requires building a new model and testing it; or running additional costly computer runs. Complex structures may be difficult to mathematically or physically model; the method presented here permits a very logical substructuring to be performed. The modification technique uses the solution already available to find the solution to the modified or combined structure in a fast and efficient manner. The technique is effective on systems with complex eigenvalues and eigenvectors. Many samples are given for clarity of the technique and to show the versatility of the method.

Stevens, K.K.; Loeps, J.B. Modal testing of circular plates with partial viscoelastic damping treatments. 1(1):1-10; Jan 1986.

ABSTRACT - Application of modal-testing techniques to determine the modal parameters and mode shapes of an edge-fixed circular plate with a free-layer viscoelastic damping treatment extending over a portion of the surface is described. The test specimen and test procedures are discussed, and experimentally determined values of the system natural frequencies and loss factors for varying degrees of damping treatment are presented. These results show that partial damping treatments can be as effective as complete treatments, while providing significant savings in material costs and added weight. For a plate with complete damping treatment, the values of the natural frequencies are found to compare favorably with those predicted by a laminated plate theory. It is also found that addition of the damping treatment had little effect upon the flexural mode shapes of the plate.

Williams, R.; Vold, H. Multiphase-step-sine method for experimental modal analysis. 1(2):25-34; Apr 1986.

ABSTRACT - This paper presents an approach to large-scale modal tests that combine the multishaker methodologies of sinusoidal and random excitation. The first phase of this method consists of verifying a single exciter location with either stepped sine or random excitation. Then, using closed-loop force control, a series of multishaker stepped-sine surveys are performed, alternating polarity patterns between the surveys (multiphase step sine). The responses in each such survey may be considered frequency-response functions with respect to a generalized force, since force amplitudes and polarities are controlled to be constant within each survey. Mode-indicator functions may hence be calculated and modal parameters can be extracted from these individual surveys, just as for standard single-point excitation methods. From the multiple surveys with alternating polarity patterns, a standard multiple-column FRF matrix may also be extracted, using HI or Hv estimators. One will now normally calculate the multivariate mode-indicator functions and the corresponding force patterns to identify resonances and their multiplicity. From this data set, one may either proceed to extract a modal model using phase-separation methods or, if the situation warrants, go back to perform a tuned-sine dwell test, with initial appropriated force patterns from the multivariate modeindicator functions. An attractive feature of this approach is that the decision to employ particular modal-parameter extraction techniques can be postponed to later stages of the project. Modal parameters may also be obtained from classical phase-resonance techniques, guided by the insight acquired from the frequency-response function calculations.