# MODAL v4 - Abstracts

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

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Allen, J. J. A component synthesis method using Lanczos vectors. 4 (2):33-38; Apr 1989.

ABSTRACT - A component synthesis technique has been developed, which uses a combination of constraint modes and fixed-interface Lanczos vectors. The sequence of Lanczos vectors is obtained via a recursion equation similar to inverse iteration and mass orthonormalized to the previously derived vectors. The static solution of a problem of interest or a set of random vectors can be used as the initial Lanczos vector in the sequence. The fixed interface Lanczos method produces a statically complete model for a given load, if the static solution is the first vector in the sequence. The subsequent Lanczos vectors, X(sub)i, in the sequence can be interpreted as being generated using the dynamic error K(super)-1 MX(sub)i-1 of the previous vector, including constraint modes for the boundary degrees of freedom retains physical degrees of freedom of the boundary, which allows the component to be incorporated into the system by direct matrix assembly. The convergence characteristics of the fixed-interface Lanczos method is studied using static and transient analysis. Various criteria are examined for evaluating the convergence. The results of the fixed-interface Lanczos method will be compared to the component-mode synthesis method developed by Hurly.

Bernasconi, O.; Ewins, D.J. Modal strain/stress fields. 4(2):68076; Apr 1989.

ABSTRACT - The concept of a strain/stress field associated with a mode of a vibrating structure is studied. The notion of massnormalized modal strain field is clearly defined and the general expression of the strain frequency-response function is derived. The correspondence between computed and measured massnormalized modal strain fields is demonstrated on a simple model structure. Strategies for determining modal and dynamic strains and stresses in areas of concentration are proposed, including a simple modal substructuring method involving the finite-element method. This paper gives a theoretical basis for obtaining normalized modal strains, which are intrinsic modal parameters as are the displacement mode shapes, and which can be used for further computation of accurate time-dependent strain/stress fields.

Billings, S.A.; Tsang, K.M.; Tomlinson, G.R. Application of the NARMAX method to nonlinear frequency-response estimation. 4(3):97-102; Jul 1989.

ABSTRACT - The NARMAX method of identifying the frequency-domain characteristics of nonlinear systems is illustrated by computing the first,second and third order generalized frequency-response functions of a heat exchanger.

Cooper, J.E. Comparison of some time-domain-system identification techniques using approximate data correlations. 4(2):51-57; Apr 1989.

ABSTRACT - Most time-domain methods used for modal analysis perform a curve fit to impulse-response data and use the least-squares method as an integral part of their formulations. It is well know that when the data are corrupted, least squares leads to biased parameter estimates, with the damping values being especially sensitive. A number of noniterative techniques that attempt to eliminate the bias–instrumental matrix with delayed observations, double least squares, correlation fit and total least squares–are compared with least squares in terms of the approximate data autocorrelations used in the curve fit. The theoretical comparison is complemented by statistical comparisons upon simply simulated systems. As well as the ability of the methods to reduce the bias on damping estimates, ease of implementation and computational requirements are also investigated.

Cudney, H.H.; Inman, D.J. Determining damping mechanisms in a composite beam by experimental modal analysis. 4(4):138-143; Oct 1989.

ABSTRACT - A method of estimating the distributed damping parameters of a beam based on measured modal parameters (frequency and damping ratios) is derived. Three different mathematical models were used to model the damping mechanism of a quasi-isotropic pultruded cantilevered beam. These three models were (1)viscous (air) damping, (2)strain-rate damping, and (3) both viscous and strain-rate damping. Values were obtained for each of the damping models as well as the modulus of elasticity of the beam. It is found that the two-parameter damping model provides the best fit to measure modal data. However, the two-parameter damping model can only reproduce the measured damping ratios to within 85 percent.

Ebersbach, P.; Irretier, H. On the application of modal-parameter estimation using frequency-domain algorithms. 4(4):109-116; Oct 1989.

ABSTRACT - The aim of this paper is to give a review and comparison of two applied MDOF methods for identification of modal parameters from measured frequency-response date in the form of experimental results. The first method is a nonlinear iterative algorithm based on linearizing the frequency-response function by the first terms of a Taylor series (1,2). Starting with initial values for the modal parameters, the error between the measured values and the calculated frequency will be minimized iteratively. The second method is a modification of a noniterative algorithm, known as a linearized rational polynomial algorithm (3,4). The modification of this algorithm is a new definition of the error function (5), whereby the iteration procedure becomes iterative. In contrast to the first method, this algorithm has a better behavior in the iteration. After the calculation of the poles, the residual terms of the frequency-response function can be calculated directly from the numerator of the polynomial, whereas normally in this method a following linear least-squares algorithm is used.

Both estimation methods work with residual terms to compensate for the influence of modes outside the measured frequency range. They are implemented at a HP deskcomputer at the Institute of Mechanics, University of Kassel, and are applied successfully for estimation of modal parameters from measured data. Experimental results are given from the testing of a turbine blade (impact excitation) and of a circular plate (magnetic exciter with random excitation).

Ewins, D.J.; Vakakis, A.F. An alternative method of SDOF modal analysis. 4(4):1440149; Oct 1989.

ABSTRACT - An analytical method of Modal Analysis is presented. The method takes advantage of the frequency distribution of the receptance points in the complex plane and results in the so-called plots. From these plots the modal parameters are extracted with improved accuracy and the effects of nearby modes can be quantified. The limitations of the method are discussed and the analysis is applied to both theoretical and experimental data.

Fullekrug, U. Structural-dynamics identification in the time domain:estimation of modal parameters based on forced vibrations. 4(2):58-67;Apr 1989.

ABSTRACT - The objective this paper is to present a method for structural-dynamics identification. The proposed method operates in the time domain and utilizes discrete time histories of both the excitation forces and the dynamic responses. Equations are derived for eigenfrequencies, modal damping, eigenvectors and components of the left-hand eigenvectors at the excitation points. The method is applied to a simulated vibrating structure with eleven degrees of freedom.

Hoff, C.; Natke, H.G. Correction of a finite-element model by input-output measurements with application to a radar tower. 4(l):1-7; Jan 1989.

ABSTRACT - The mathematical model of a radar tower is improved by input-output measurements. Two experiments are performed: a free vibration after unloading within the low-frequency range and a forced vibration from impulsive loading with the high-frequency range. The tower itself is modeled with finite elements. The fundament consists of a circular ground plate with piles. These support conditions are the most uncertain quantities of the computational model. The identification method is applied to improve the displacement and torsional spring rate of the foundation in a lumped-parameter model. A least-squares fit with modal residuals and input-output residuals is used to correct the computational model. The results show that the applied identification methods are able to provide improved estimates of the foundation characteristics.

Janter, T.; Heylen, W.; Sas, P. A comparison between model-optimization procedures based on the model-optimization parameter set. 4(3):93-96, Jul 1989.

ABSTRACT - This paper intends to make a profound comparison between model-optimization procedures based on the selection of the model-optimization parameters. Emphasis is placed on the difference in approach depending on whether we use individual mass and stiffness matrix elements, structural submatrices, or more physically interpretable design parameters such as the finite-element input parameters. Advantages and disadvantages of these approaches, as well as the consequences of the choice of the parameters are discussed. Especially aspects of interpretability, application fields, compatibility, controllability of the model and numerical considerations are treated.

Jones, J.D.; Fuller, C.R. Reduction of interior sound fields in flexible cylinders by active vibration control. 4(2):45-50; Apr 1989.

ABSTRACT - An analytical model of a thin, flexible shell is evaluated to study the mechanisms of interior sound reduction by the active control of the shall vibrational response. A single exterior acoustic monopole is used as the primary noise source while the secondary controller is represented as a single point force applied directly to the shell wall. The complex amplitude of the acoustic monopole is specified a prior;however, the complex amplitude of the point controller is initially unknown. The control-force amplitude is evaluated such that the line-weighted mean square pressure is minimized along the shell wall in the excitation plane. The active control model is evaluated for harmonic excitation. Results indicate spatially averaged noise reductions in excess of 20 dB over the source plane for acoustic resonant conditions within the cavity. Modal response of the shell and the coupled interior pressure field indicate substantial control spillover in the shell due to control-force excitation; however, control spillover is predominantly constrained to the shell and thus does not contaminate the contained acoustic field.

Kujath, M.R. Detection of sudden changes of modal parameters in machinery. 4(4):131-137; Oct 1989.

ABSTRACT - The paper deals with operating machines’ dynamic behavior which is monitored by measurement of the forced response at various points on the machine structure. The topic of the paper is focused on abrupt changes of system modal parameters which may indicate a system failure. A method of processing signals for obtaining the information about the presence and the extent of the changes is introduced. The input forces remain unknown during the analysis, and the vibrations alone are used to provide details about the system. The calculation procedures include finding a usable relation between a limited modal data and the system transfer function matrix. The problem of the number of the parameters involved is discussed. Results of a digital simulation support the theoretical analysis.

Lee, J.L.; Lee, S.Y.; Lee, H. Vibration and chatter analysis of an NC lathe.

ABSTRACT - In order to investigate the influence of structural dynamics on the chatter of machine tools, the dynamic characteristics of a newly fabricated NC lathe are analyzed by using the finite-element method. The bed, the base body and the spindle-bearing system of the lathe are analyzed separately and then the total dynamic characteristics are obtained by a component-mode-synthesis method. Also chatter experiments were performed with tapered MTIRA (Machine Tool Industrial Research Association,England) workpieces. With this experimental setup, both the direct cutting test and the excitation test can be performed. The component-mode synthesis along with the direct cutting/excitation test is proposed as the powerful tool for design modification to improve dynamic performance of machine tools.

Lee, S.Y.;Kao,J.J. Flexural waves in beams with periodic, but piecewise constant, impedance. 4(4):124-130; Oct 1989.

ABSTRACT - A systematic method is developed for studying the problem of flexural wave propagation in a beam with periodic, but piecewise constant, impedance. Since several interesting relations between the particularly chosen fundamental solutions of the corresponding eigenvalue equation are found. It is shown that the dispersion equation can be simplified and factorized into product form and the dynamic nature of the system is mainly dominated by a simple function.

Leung, A.Y.T. Dynamic stiffness and nonconservative modal analysis. 4(3):77-82; July 1989.

ABSTRACT - The dynamic stiffness method and the substructure method predict more number of natural modes than the number of master coordinates retained. For nonconservative systems, the dynamic stiffness matrix may be defective. A general algorithm for response analysis is presented. Discrete finite-element system are discussed first and the unwanted coordinates are eliminated. As the number of elements increases, the formulation approaches that of the continuum modeling. Since harmonic and time responses are Fourier pair, initial discussion is concentrated on harmonic analysis and the results are applied to time response by replacing = lw by d/df. New features include the orthonormal condition, the spectral decomposition of dynamic flexibility, the mixed frequency dynamic derivative and the expansion theorem.

Moustafa, K.A.F. On-line extraction of offshore tower vibration parameters from response measurements. 4(3):83-88; July 1989.

ABSTRACT - A linear mathematical model representing the dynamics of offshore towers is considered. An on-line identification scheme is proposed to estimate the modal parameters by using noisy response measurements obtained during tower normal operation. A technique is presented to extract the damping and stiffness matrices required for incipient failure detection from the identified modal parameters. An illustrative numerical example is presented.

O’Callahan, J.C.; Chou, C.M. Localization of model errors in optimized mass and stiffness matrices using modal-test data. 4(1):8-14; Jan 1989.

ABSTRACT - The mass and stiffness matrices of an analytical model can be optimized using a generalized inverse technique on the measured modal data. A spatial representation of the structural-element properly changes resulting from the model errors is generally preferred for engineering applications. This paper proposes a procedure to localize the model errors using a least-squares approach. The error matrices obtained from a system optimization process are projected to the modal space and then are equated to the summation of a series of element modal matrices. The unknown error coefficients associated with the element matrices are formulated into a set of overspecified algebraic equations and are solved using a least-squares method. After having been weighted using the element modal-participation factors, these error coefficients can be directly utilized to quantify the spatial contributions of the mass and stiffness errors in the model.

Numerical examples of a flawed cantilever beam model are used to demonstrate the proposed error-localization procedure.

Sestieri, A.; D’Ambrogio, W. Why be model:how to avoid the use of modes in the modification of vibrating systems. 4(1):25-30; Jan 1989.

ABSTRACT - Modes and modal parameters are the magic and fundamental means through which every linear problem of vibration is usually developed. No doubt that this is the reason for the existence of a large number of codes performing curve-fitting procedures apt to determine modal parameters from experimental transfer functions. The field of structural modification does not take exception to this rule. However modal identification often leads to significant errors. Therefore, in order to avoid the derived pitfalls, a procedure which performs optimal structural modification without the use of modal parameters has been developed. Theoretical and experimental tests show the capability of the method.

Song, T.X.; Zhang, P.Q.; Feng, W.Q., Huang, T.C. Experimental strain modal analysis by space-time regression method in the time domain. 4(1):15-18;Jan 1989.

ABSTRACT - Strain modal analysis has been of particular interest recently. This paper shows the possibility and advantage of using dynamic strain signals as input date for strain modal analysis in the time domain, a method developed by space and time regression. Applications to diagnosis and failure detection and prevention are the motivations.

Stanway, R.; Mottershead, J.E. Experimental techniques for modeling nonlinear stiffness and damping characteristics. 4(3):89-91;Jul 1989.

ABSTRACT - This paper describes the application of sequential filtering to the estimation of parameters in nonlinear models of components in mechanical vibrating structures. The modeling strategy is outlined and the choice of method is justified. Experimental results are included to demonstrate one application of the technique: the identification of a combined viscous plus quadratic damping model associated with an electrorheological vibration damper.

Starkey, J.M.; Merrill, G.L. On the ill-conditioned nature of indirect force-measurement techniques. 4(3):103-108; Jul 1989.

ABSTRACT - Indirect measurement of excitation forces is necessary when they are distributed or inaccessible. The forces can then be inferred from measurements of response if an accurate dynamic model is available; but the computation tends to be ill conditioned. This paper presents results that indicate that the condition of the accelerance matrix is a good indicator of errors in the force predictions. Numerical simulations and experimental results support this claim.

Tzou, H.S. Nonlinear structural dynamics of space manipulators with elastic joints. 4(4):117-123; Oct 1989.

ABSTRACT - Joint dynamic characteristics in flexible space manipulators affect the manipulators’ high-demanding operational performance and accuracy. In this paper, the structural dynamics of a flexible robotic manipulator with elastic joints is studied using nonlinear theoretical and finite-element methods. Dynamic equations of a discretized multi-degree of freedom system with initial joint gaps are derived. Dynamic contacts in an elastic joint are simulated by a nonlinear joint model represented by a set of nonlinear springs and dampers. A pseudo-force approximation method is used in nonlinear finite-element analyses. Nonlinear dynamic contacts resulting from internal joint gap between two links in the manipulator systems are studied. Effect of joint gap size and surface rigidity are evaluated in this paper.

Zhang, Q.; Wang, W.; Allemang, R.J.; Brown, D.L. Prediction of mass modification for desired natural frequencies. 4(2):39-44; Apr 1989.

ABSTRACT - In this paper a method is presented to predict the critical amount(s) and the best location(s) of the mass modification to the structure for certain dynamic requirements. The analysis is made through perturbation theory with the use of measured modal data (natural frequency, damping factor and mode shape). Also, a best-approximation-subspace technique is introduced to find the best combination of mass modifications from several possible measurement points. The method is illustrated by both analytical and experimental data to show how the method handles real normal modes and complex modes.