# MODAL v2 - Abstracts

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

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Abu-Farsakh, G.; Nhader, N. A new triangular finite element for the analysis of free vibration of plates. 2(3):136-143; Jul 1987.

ABSTRACT - A finite-element analysis was carried out using three versions of the TNTE element (ten-node triangular element). The free-vibration problem of a rectangular plate with different boundary conditions was studied. The lowest four frequencies were obtained and compared with the available results. It is shown that reasonably acceptable results can be obtained using the proper version of the element, even with coarse mesh divisions. In some cases, higher mode frequencies were obtained. They are compared with the corresponding experimental and/or analytical values.

Ahme, I.; Tomlinson, G.R. Reducing the effects of residual modes in measured frequency-response data. 2(3):113-120; Jul 1987.

ABSTRACT - A procedure is described for ameliorating the effects of mass and stiffness residuals in measured frequency-response data. The procedure is applied to both simulated and experimental data. It is shown that the modified data set resembles a finite set of modes which can be analyzed without resort to the inclusion of residuals normally used to represent the low- and high-frequency modes.

Akgun, M.; Ju, F.D. Diagnosis of fracture damage in frame structures (a PI-circuit analogy). 2(4):155-162; Oct 1987.

ABSTRACT - The paper applies an aspect of modal analysis to the problem of damage diagnosis in complex frame structures. The criterion is based quantitatively on the changes in modal frequencies as a result of structural softening from fracture damages. The analysis requires accurate structural modelings for the pre- and post-damage structures. A II-circuit analogy is developed for the simulation of the complex frame structure and for the subsequent simplification and formalization of diagnostic analysis. The analogous simulation is based on the algebraic equivalence of the equations for a straight beam with a given shape function and the Kirchhoff’s law for a II-circuit. The end moments and rotations (slopes) are thus algebraically equivalent to the port currents and voltages. The moment equilibrium at a structural node is satisfied by Kirchhoff’s current law at the corresponding electrical node. The rotation (slope) continuation at the node is automatically defined by the modal potential. Moreover, the slope discontinuity at the cracked section becomes the potential difference across an electrical impedance, which is identified as a resistance, equivalent to the negative reciprocal of the ‘fracture-hinge’ spring constant. The natural frequencies of the structure are therefore those of the network of II-circuits. Based on the II-circuit network, the paper establishes a formalism procedure to construct the matrices in the frequency equation without requiring the users of the frequency equation to draw the analog network. The method is therefore readily adaptable to computer programming. Use of the method and the fracture-damage diagnosis is illustrated with a two-story single-span frame structure.

Akgun, M.; Ju, F.D. Diagnosis of multiple cracks on a beam structure. 2(4):149-154; Oct 1987.

ABSTRACT - The paper explores the modal-frequency theory in diagnosis of multiple cracks in a beam structure. The damage functions based on the change in modal frequencies are formulated for a beam with k number of cracks, using the analogy of electrical T-circuits. The modal analysis using electrical analogy is fully developed, for which the individual beam segments are represented by T-circuits while the cracks by resistors. The paper addresses further the uncertainties in the application of the modal-frequency theory for fracture diagnosis, especially for multiple cracks. The paper found that there exists a spacing limit of multiple cracks, below which the modal change is indistinguishable from that of a single crack. Uncertainty could also arise from the tolerance limit in measurement of frequency variations. Then, if it could be ascertained that there exists only a single major crack, the effect of minor cracks on the frequency variations will be of small order. Finally, the paper considers the case that, when inadequate measurements are available, valuable information can be extracted if a crack occurs at a peak-response location of a modal shape.

Brandon, J.A. Eliminating indirect analysis - the potential for receptance sensitivities. 2(2):73-75; Apr 1987.

ABSTRACT - The approach currently dominant in sensitivity analysis for structural dynamics is the use of modal-design sensitivities. These modal properties are often synthesized using receptance data (or other force-response characteristics). It is not unusual that, having evaluated modal-design sensitivities, the analyst will then transform these back into response characteristics. The paper considers transformations which produce receptance sensitivities directly from the experimental study eliminating the need for the modal analysis stages of reanalysis. Thus in design problems where only specific force-response properties are of interest, the indirect route appears unnecessary.

Chua, K.H.; Rahman, M.; Mansur, M.A. Performance evaluation of machine-tool structures using modal analysis. 2(1):43-49; Jan 1987.

ABSTRACT - The use of experimental-modal-analysis technique in the evaluation of machine-tool dynamic performance is discussed and illustrated in this paper. Two machine-tool structures made of different materials, ferrocement and conventional cast iron, are studied. The dynamic performance of these two structures is evaluated and compared. Both structures were designed to give the same static stiffness (1). However, while carrying out modal analysis of these structures, it has been found that the first resonance peak is observed for the cast-iron bed at 125 Hz in the first torsional mode which goes undetected in normal impact test, whereas the first resonance peak for ferrocement is observed at 280 Hz in the first vertical bending mode. The results obtained through modal-analysis tests have further been verified through finite-element analysis. Moreover, the damping ratio of ferrocement, has been found to be significantly higher than cast iron. From the study, it is clear that ferrocement is a very good replacement for cast iron for machine-tool structures because of its good dynamic properties.

Craig, R.R., Jr. A review of time-domain and frequency domain component-mode synthesis methods. 2(2):59-72; Apr 1987.

ABSTRACT - Component-mode synthesis (CMS) is a form of substructure coupling analysis frequently employed in structural dynamics. The dynamic behavior of each substructure is formulated as a superposition of modal contributions. The system model is formed by enforcing equilibrium and compatibility along component interfaces. Both time-domain and frequency-domain approaches are reviewed in this paper, since both may be employed to develop system models using experimental data. Time-domain methods of CMS may be divided into those for undamped structures and those which apply to damped structures. Methods may be further subdivided on the basis of the types of component modes employed in the synthesis procedure, such as free-interface component normal modes, constraint modes, inertia-relief attachment modes, etc. These component modes are described; and their availability from component testing is discussed. The use of state space descriptions for systems with general viscous damping is briefly discussed, along with the use of frequency-domain models for determining response.

Cunniff, P.F.; O’Hara, G.J. Modal characteristics of structures from transient-response data. 2(4):180-191; Oct 1987.

ABSTRACT - This paper examines the problem of extracting useful information from measured-transient-response motion of structural systems that have been shock excited. The structural systems are composed of two parts: the equipment/foundation combination which in turn is attached to a supporting vehicle structure at a single point. Use of the Fourier transformation and manipulation of the transient-response data permit the fixed-base natural frequencies, normal-mode shapes, and modal effective masses to be calculated for the equipment/foundation combination. The normal-mode damping factors for multi-degrees of freedom equipment/foundation combinations can also be approximated for the case of lightly damped structural systems with proportional damping. Finally, transfer functions can be found which allow the analyst to predict responses of the structural systems to other possible shock excitations.

Hermanski, M.; Ostholt, H. Linking finite elements with experimental modal analysis. 2(3):144-147; Jul 1987.

ABSTRACT - A method for linking finite elements (FEM) with experimental modal analysis is presented. Lagrange polynomials and cubic spline functions are used to approximate the rotational degrees of freedom (RDOF) at the linking points in the modal data base.

Ibrahim, A.; Ismail, F.; Martin, H.R. Modeling of the dynamics of a continuous beam including non-linear fatigue crack. 2(2):76-82; Apr 1987.

ABSTRACT - Vibration testing is a fast means of detecting crack development in structures. In previous work by other authors, an open-crack model was assumed and analytical expressions for the change in the resonant frequencies were derived. In this work, numerical simulation is employed to investigate the dynamic behavior of a cantilever beam including nonlinear fatigue crack. This crack is assumed to open and close depending on the vibration direction. A bondgraph model of the cantilever beam is developed in this work. It is verified using the finite-element method. This model is then used in the numerical simulation to obtain frequency-response functions of the cracked beam. Results obtained in this work show that the frequency drop due to a nonlinear fatigue crack is always smaller than that computed assuming an open-crack model. Also, the shape of the frequency-response function can help identify the presence and nature of the crack.

Inman, D.J.; Jiang, B.L. On damping ratios for multiple degree of freedom linear systems. 2(1):38-42; Jan 1987.

ABSTRACT - A commonly used parameter in both experimental and analytical modal analysis is the damping ratio or percent of critical damping. For a single degree of freedom system this concept is clearly defined and knowledge of a system’s spring constant, damping rate and mass allows the calculation of the damping ratio. This concept is extended here and defined for multiple degree of freedom systems. The damping-ratio matrix and a modal-damping-ratio matrix are defined in terms of the mass matrix, damping matrix and stiffness matrix for a multiple degree of freedom system of arbitrary dimension. The definition used for the damping-ratio matrix relies on the definition of critical damping for lumped parameter systems provided previously. The definitions presented here offer a partial physical interpretation of measured modal-damping ratios for nonproportionally damped systems.

Jones, D.I.G.; Muszynska, A. Mechanical-structure improvement by dynamic stiffness methods. 2(2):833-91; Apr 1987.

ABSTRACT - The relationship between the receptance and dynamic-stiffness models of the dynamic response of structures is described. The transformation from receptance to dynamic-stiffness models allows one to determine modifications needed to change the response behavior in a desired manner. Potential applications are described for space structures., turbomachinery blading and extremely large, one of a kind, structures. A simple example is given to illustrate the approach.

Juang, J.N. Mathematical correlation of modal-parameter-identification methods via system-realization theory. 2(1):1-18; Jan 1987.

ABSTRACT - A unified approach is introduced using system-realization theory to derive and correlate modal-parameter-identification methods for flexible structures. Several different time-domain and frequency-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal-parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research towards the unification of the many possible approaches for modal-parameter identification.

Kammer, D.C. Test-analysis-model development using an exact modal reduction. 2(4):174-179; Oct 1987.

ABSTRACT - A new method for test-analysis-model (TAM) development for use in test/analysis correlation and system identification utilizes the finite-element-model (FEM) mode shapes to reduce the associated analytical mass and stiffness matrices. The reduced representation exactly predicts all the FEM mode shapes and frequencies used in the reduction process. This method, termed modal reduction, offers a valuable alternative to the Guyan reduction method in cases where a static reduction requires a prohibitively large number of master degrees of freedom to generate an accurate TAM. It also eliminates all error associated with the TAM reduction from test/analysis correlation and system identification. A numerical example is used to illustrate the accuracy of the method.

Lembregts, F.; Snoeys, R.; Leuridan, J. Application and evaluation of multiple-input modal-parameter estimation. 2(1):19-31; Jan 1987.

ABSTRACT - This paper compares the frequency-domain direct-parameter-identification method (FDPI) to the time-domain least-squares complex exponential algorithm (polyreference) to estimate the modal parameters (natural frequencies, damping values, mode shapes and modal-participation factors) from a most general multiple-input frequency-response-function measurement set. Some practical tools for the parameter-estimation process in general are referenced and/or presented. They deal with order estimation, accuracy of the extracted parameters and rejection of computational modes. Two experimental tests have been carried out to show the use and applicability of these tools as well as the excellent agreement between the two identification methods.

McConnell, K.G.; Abdelhamid, M.K. On the dynamic calibration of measurement systems for use in modal analysis. 2(3):121-127; Jul 1987.

ABSTRACT - Proper calibration of measurement systems for use in modal analysis should include sensitivity, as well as magnitude and phase distortion in the frequency domain. Force, acceleration, and strain are the most frequently measured quantities in modal analysis. Different methods of calibration such as mass, free-free bar, long rod, and an electronic method are discussed. Two simple methods for time-delay compensation are presented.

Natke, H.G. Input and damping identification within the frequency domain. 2(2):92-98; Apr 1987.

ABSTRACT - Input-identification procedures are described using output quantities of the system with a nonsturctured and a structured model of the system including incomplete modal quantities. With regard to the latter, static correction due to the truncated modes is applied. The simultaneous identification of damping matrices is discussed in addition to the input identification. Examples demonstrate the procedures.

Pappa, R.S.; Juang, J. N. Studies of modal-identification performance using hybrid data. 2(2):99-108; Apr 1987.

ABSTRACT - Modal-identification accuracy can be affected significantly in practice by high modal density and nonlinearities. It may be difficult to determine the true number of modes; many of the identified mode shapes may be questionable. Results can vary considerably using different analysis techniques. This paper introduces a new method for studying modal-identification performance under such circumstances. A difficult set of test data from an erectable truss structure was modified numerically by adding two artificial modes with known parameters. These ‘hybrid data’ were then analyzed with the polyreference technique and the eigensystem realization algorithm (ERA). Identification performance is studied by comparing the identified modal parameters for the artificial modes with their known values.

Patton, M.E.; Trethewey, M.W. A survey and assessment of nonintrusive-modal-testing techniques for ultralightweight structures. 2(4):163-173; Oct 1987.

ABSTRACT - Lightweight delicate mechanical structures do not lend themselves to typical modal-analysis procedures. Either the application of an artificial excitation or a response transducer may alter the system sufficiently to preclude accurate modal-parameter extraction. The current work surveys experimental methods to identify suitable excitation and transducer techniques for the nonintrusive modal analysis of lightweight structures. A total of eight response transducers and six excitation techniques are presented. The operating fundamentals of each identified technique are briefly reviewed to illustrate their capabilities and limitations for nonintrusive testing. The operational specifications of the various systems are compared to assess the current state of technology. The assessment indicates that many transducer techniques are well suited for nonintrusive vibration measurement,whereas nonintrusive excitation techniques are not as easily adapted or developed for modal-analysis applications. The assessment indicates that the technology exists to perform effective nonintrusive modal analysis on lightweight structures, but that careful consideration must be given to the entire test-system compatibility.

Robertson, B.P.; Pilkey, W.D. Limiting performance for the control of large vibrating structures by a modal approach. 2(1):32-37; Jan 1987.

ABSTRACT - The absolute optimal response of a system for a given performance index is referred to as the limiting performance. In this study, the limiting performance characteristics of large structures, perhaps formed of substructures, subjected to transient disturbances, are investigated using modal responses. Equations of motion are developed for both systems with imbedded control forces and systems with generic-control-force connections between substructures. A linear programming formulation of the limiting performance problem is obtained by discretizing in time a modal formulation of response variables. The limiting performance of a three-degree-of-freedom system is solved as an example.

Wang, B.P. Structural dynamic optimization using reanalysis techniques. 2(1):50-58; Jan 1987.

ABSTRACT - The problem of designing a structure with multiple natural-frequency constraints is investigated in this paper. Several gradient-based methods are considered. The salient feature of the current approaches are the use of assumed-mode reanalysis method for the repeated solutions of eigenproblems during the iterative design process. These approaches can be implemented readily with any general-purpose finite-element-analysis program. Two such implementations were attempted. Numerical experience with some real design problems indicates that the combined assumed-mode reanalysis and numerical optimization techniques can be a powerful tool in synthesizing structures with multiple frequency constraints.

Wang, M.L.; Paez, T.L.; Ju, F. System identification of nonlinear damaged structure. 2(3):128-125; Jul 1987.

ABSTRACT - In structural engineering, it is necessary to design each structured system to survive the inputs anticipated over its design life. Although a structure may experience a variety of stresses, one important type is strong motion which causes systems to execute nonlinear responses. This, in turn, may subsequently induce cumulative structural damage. Therefore the capability of modeling nonlinear responses and using these to assess the damage level in a structure is essential for structural design. This paper discusses the development of this type of approximate linear model that can simulate an inelastic system response and can measure damage accumulation in a structure. The paper also discusses using the frequency-domain technique for identifying model parameters, calculating techniques for energy dissipation during strong motion and finally compares model prediction with results from actual structures. The results show that structural damage can be predicted even in the presence of measurement noise.

Wicks, A.L.; Mitchell, L.D. Methods for the estimation of frequency-response functions in the presence of uncorrelated noise, a review. 2(3):109-112; Jul 1987.

ABSTRACT - The estimation of frequency-response function (FRF) from measured sources is fundamental to many areas of engineering experimentation. The quality of these estimates is dependent on identifying the bias errors from the random errors, thus permitting statistically meaningful estimates of the FRF. In recent years a variety of techniques has been developed to form this estimation from data contaminated by noise. This paper reviews the techniques available, identifying the limitations of each in terms of the assumptions governing the estimation model. In addition, the coherence function is discussed relative to each estimation procedure and its usefulness in identifying the random-error content.