Showing papers on "Modal testing published in 1987"

Sensitivity of Subsynchronous Resonance Predictions to Turbo-Generator Modal Parameter Values and to Omitting Certain Active Subsynchronous Modes

Abstract: In a subsynchronous resonance stability stuiy the predicted CRITICAL COMPENSATION LEVEL (CCL) depends on the mathematical model and parameter values, particularly on the mechanical damping or decrement factor. Measurements of the mechanical parameters yield values for modal inertia, modal damping etc. so that the mechanical system equations have to be transformed into modal form in order to use the measured data in simulation studies. This paper investigates the sensitivity of the predicted CCL values (for a particular case study) to uncertainties in the different modal parametes and finds that the modal damping or decrement factor is more critical than modal inertia or mode shape. It carries on to show how the modal model can be reduced from 12th to 4th order and still yield acceptable results; this would lead to considerable simplfication and saving of computer time in multi-machine SSR studies.

Method of Estimating Equivalent Mass of Multi-Degree-of-Freedom System

Abstract: To attain the optimum design of vibration controllers to suppress the many resonance peaks of machine structures, it is necessary to know the equivalent mass at the location at which the controller is mounted. This paper shows two ways of estimating equivalent mass, one is a modal analysis method, and the other is called the mass response method which utilizes the change in natural frequency of a structure when an additional mass is attached. The first method is useful for identifying a modal mass having a physical meaning, while the other method is more suitable for application to experimental analysis. The accuracy of these methods are compared by applying them to three kinds of mechanical structure.

Mass, Stiffness, and Damping Matrix Estimates from Structural Measurements

Abstract: Modal testing has traditionally been used to confirm the validity of finite element models of structures. This is normally done by identifying the modal properties of a structure from test data, and then comparing them with the modal properties of the finite element model. In this paper an alternative approach of directly compar ing the mass, stiffness, and damping matrices of the dynamic model is explored. A new algorithm which estimates the mass, stiffness, and damping matrices of a structure from Frequency Response Function (FRF) measurements is also presented. These matrix estimates are compared to the matrices of an analytical model of the same structure, and the differences are noted. Clearly, if the dynamics of the structure are represented by FRF measurements, and some significant part of the measurement data is left out of the estimation process, the matrix estimates will be deficient. The effect upon the accuracy of the matrix estimates is illustrated by examples, for cases when an inadequate frequency range of FRF data is used, and when a reduced number of degrees -of-freedom (DOFs) is used. NOMENCLATURE n = number of DOFs of the model m = number of modes r = number of reference points of the FRF measurements t = time variable s = Laplace variable

Experimental Modal Analysis and Dynamic Component Synthesis. Volume 1. Summary of Technical Work

Abstract: : This report is one of six reports that represent the final technical report on the work. Experimental Modal Analysis and Dynamic Component Synthesis. The reports that are part of the documented work include the following: Vol. I Summary of Technical Work; Vol. II Measurement Techniques for Experimental Modal Analysis; Vol. III Modal Parameter Estimation; Vol. IV System Modeling Techniques; Vol. V Universal File Formats; Vol. VI Software User's Guide; For a complete understanding of the research conducted under this contract, all of the Technical Reports should be referenced. Keywords: Modal testing; Vibration testing; Dynamics.

The effect of modal truncation on modal modification

Abstract: Several investigators have shown that the ability of modal modification routines to accurately predict dynamic structural changes is highly dependent on the completeness of the original modal database of the structure-modal truncation. This paper more closely examines the effects of modal truncation on modal modifications. The results of this study show the modified modal vector to be a weighted linear sum of the original modal vectors. Due to this weighted linear sum process, modal truncation might affect almost any mode in a modification process. Therefore, the quality of a modal modification is not necessarily dependent on the number of modes present in a database, but more importantly on which modes are present.

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 have increased. This paper describes a new 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) applicability to general linear, time-invariant systems, (2) direct use of multiple input and multiple response data, (3) identification of reduced-order models with minimum user interaction through the use of two automatic model-reduction techniques, (4) identification of a consistent set of modal parameters through the use of numerically stable least-squares techniques, and (5) complete user documentation.

Evaluation of spacecraft modal test methods

Abstract: Modal testing methods have undergone great changes in recent years as new testing methods are being created. Although devoted advocates of each method can be found to argue the relative advantages and disadvantages, the general superiority, if any, of one or the other is not yet evident. The present paper evaluates various modal testing methods based on the results of tests performed on a complex, realistic spacecraft structural system. It concludes that the selection of a modal testing method should be determined by the test requirement, constraints, and nature of the test article.

Modal damping of flexural oscillation in suspended cables

Abstract: The modal damping of flexural oscillation of suspended cable models was measured and is reported in this paper. Numerical analyses of free oscillation of the cables were also made to calculate natural frequencies, normal modes and additional dynamic strains. It is found that the additional dynamic strain of each normal mode is the primary cause of modal damping and that the damping of the first in-plane symmetric mode is much larger than that of other modes around the ‘crossover’ point of the first and second natural frequencies. The effects of the span length, the tensile rigidity and the chord inclination are also investigated.

Hilbert transform procedures for detecting and quantifying non-linearity in modal testing

Abstract: A description and a review of the Hilbert transform procedures for detecting and quantifying structural non-linearity in frequency response functions obtained during modal testing is presented in this paper. A method of minimizing the effect of residual modes of vibration, previously a problem with the numerical Hilbert transform, is also described.

Frequency Component and Modal Synthesis Analysis of Large Rotor-Bearing Systems with Base Motion Induced Excitations

Abstract: Transient response of rotor-bearing systems is of continuous interest to both researchers and designers of large rotating machinery. The paper develops a comprehensive approach to this study using the modal method and numerical FFT analysis. Equations of motion of the rotor-bearing system are solved in the modal coordinates such that the number of degrees of freedom can be largely reduced. The transient modal time functions for each mode and the nonlinear bearing forces are examined in both time and frequency domains using numerical FFT analysis. This eliminates the examination of transient motion at certain locations in the rotor system that may lead to erroneous conclusions. A comparison of the overall transient motion, individual modal functions, unbalance excitations and the nonlinear bearing forces in frequency domain provides valuable information for the overall performance of the rotor-bearing system. A typical multimass rotor-bearing system is used as an example for this approach, and design conclusions are drawn from the results obtained.

System identification of civil engineering structures

Abstract: The comparison of measured dynamic characteristics or response of large structures with that of an appropriate finite element model with all its underlying assumptions often reveals discrepancies. This may be due to improperly determined parameters, such as interstory stiffness, mass of different stories, and the modulus of elasticity of the concrete, as well as the inadequacies of the model.The measured dynamic response generally occurs in one of three forms: time response, frequency response, and modal data. For time response data, either in free vibration or for a known input, parameters are estimated by proper adjustments to match more closely the measured motion. For steady-state frequency response, a sinusoidal load (or synchronized loads) is input mechanically and the response, both in amplitude and in phase, is measured for different frequencies of excitation. Damped resonant frequencies, the associated modal damping ratios, and the corresponding mode shapes are the measured quantities for modal d...

Modal Testing using Multiple References

Abstract: With the increased availability of multi-channel FFT analyzers, more emphasis has been placed in recent years on the development of new methods for modal testing using multiple references. In the case of shaker testing, this means the use of two or more shakers. In the case of hammer (impact) testing, this means the use of two or more reference transducers. This paper presents the results of our recent experiences in both the collection of FRF data, and the curve fitting of it to obtain the modal parameters of a structure. The key difference between these results and those of a more traditional mo dal test is that multiple rows or columns of the structure's FRF matrix are not only collected simultaneously, but are also curve fit in a simultaneous manner. In this paper, the advantages offered by multiple reference modal testing and curve fitting are addressed. The theory and usefulness of a frequency domain curve fitting algorithm are extended to account for the effects of “out -of-band” modes, which always occur in practical applications. Verifications of the method and its implementation using both analytical and experimental FRF data are also presented in the paper. NOMENCLATURE n = number of DOFs of the model m = number of modes r = number of reference points of the FRF measurements f = number of frequency points used from FRF

Modal test/analysis correlation for the Centaur G prime launch vehicle

Abstract: A modal test was performed on the Centaur G Prime launch vehicle for the purpose of verifying the loads analysis model. This paper describes the procedure by which modal parameters obtained in this test were correlated with the corresponding analytical predictions. Based on this correlation the stiffness model of the shuttle trunnion system has been modified. The evolution of the model updating and the final results are described.

A comparative overview of modal testing and system identification for control of structures

Abstract: This paper presents a comparative overview of the disciplines of modal testing used in structural engineering and system identification used in control theory. A list of representative references from both areas is given and the basic methods are briefly described. Recent progress on the interaction of modal testing and control disciplines is discussed. It is concluded that combined efforts of researchers in both disciplines are required for unification of modal testing and system identification methods for control of flexible structures.

Modal testing the EOLE

Abstract: Modal testing an immense and flexible wind turbine poses a number of problems. It requires innovative excitation techniques since the modal frequencies of this type of structure are quite low. Also, substantial energy must be input to the structure to obtain reasonable levels of response. In this paper, the results of the modal test of the 110 m tall EOLE wind turbine are presented which had a number of modal frequencies below 1.0 Hz. Step-relaxation and wind were used to excite the structure. 5 refs., 14 figs., 2 tabs.

Modal sensitivity for structural systems with repeated frequencies

Abstract: Repeated or closely packed modal frequencies are common physical occurrences for vibrating structures which are complex or possess multi-planes of symmetry. The computation of the sensitivity to structural modifications for these frequencies and mode shapes is made difficult by the fact that the mode shapes are not unique, since any linear combination of eigenvectors corresponding to a repeated eigenvalue is also an eigenvector. The work of Chen and Pan is extended, who used modal expansion techniques for accommodating the sensitivity analysis of structures with repeated eigenvalues. Starting with a discussion of the physical significance of sensitivity analysis for repeated frequency modes, a derivation is presented of the governing equations for the derivatives of a repeated eigenvalue. This is followed with a small example to illustrate the results. An efficient computation procedure, based upon an expansion of Nelson's ideas for large banded systems, is then proposed for systems with repeated or closely spaced eigenvalues.

Modal analysis of a Caribbean steel drum

Abstract: Modes of vibration and coupling between adjacent note areas in a double‐second steel drum are compared by several complementary techniques, including impact modal analysis, holographic interferometry, and recording sound spectra under varying conditions of damping. Each note has at least one overtone mode tuned to a harmonic of the fundamental frequency. Striking the A4b note area, for example, excites not only a second harmonic A5b in that same note area but also the strategically located A5b and A6b note areas adjacent to it. The coupling depends upon amplitude in a nonlinear way.

Model Parameter Estimation with Multi-reference Curve Fitting : Vibration, Control Engineering, Engineering for Industry

Abstract: Many kinds of curve fit techniques have been developed for the estimation of the modal parameters of a mechanical structure, using the theory of modal analysis. As one of the most popular curve fit techniques which correspond to the multiple input vibration test, Vold's method in the time domain (Poly-reference) is well-known and used extensively. In this paper, a new method which results from improving Vold's method in the time domain is proposed to obtain global modal parameters. In Vold's method, residues are determined by using every column of the transfer function matrix. Then, any two columns of residue matrix contradict each other. In the proposed method, the residues are obtained at the same time by using all of the transfer function matrix. And such contradiction can be solved. With this method, modal parameters of the fly wheel of an automobile are identified. Comparing this new method with former methods, the validity of the new method is confirmed.

Modal survey tests for high-frequency vibration analysis of the Space Shuttle Main Engine

Abstract: Variations in the modal characteristics of different Space Shuttle Main Engines (SSMEs) are presented herein to study their structural dynamics vibrations, especially under fluid/structure interaction. The results of extensive modal survey tests and analysis relative to significant features in the modal characteristics of different powerheads and components are discussed.

Centaur G Prime modal test

Abstract: The Centaur G Prime modal test resulted in sets of modes (frequencies, mode shapes and damping) with an accuracy similiar to or better than that normally obtained from the modal testing of linear structures with no backlash and small damping. In other words, performing the test at high level greatly minimized the backlash effect and provided a valid, simple linearization of the trunnion friction problem for the Centaur in the Shuttle Cargo Bay. All the most important modes (target modes) were measured and provided the data base for updating the finite element model for the pre-flight verification loads analysis.

Experimental Modal Analysis and Dynamic Component Synthesis. Volume 4. System Modeling Techniques

Abstract: : This report reviews the theoretical basis for the current methods used to predict the system dynamics of a modified structure or of combined structures based upon a previously determined, modal or impedance, model of the structure(s). The methods reviewed were: Modal modeling Technique: Local eigenvalue modification, Coupling of Structures Using Eigenvalue Modification, and Complex Mode Eigenvalue Modification; Sensitivity Analysis; and Impedance Modeling Technique: Building Block Approach, Dynamic Stiffness Method, and Frequency Response Method. The effects of measurement errors, modal parameter estimation error, and truncated modes in the application of modal modeling technique are evaluated. Some of the experimental modal model validation method are also presented. Several methods to normalize the measured complex modes were reviewed including both the time domain and frequency domain techniques. A new component mode synthesis method (Super element Component Dynamic Synthesis) developed by the University of Dayton Research Institute is presented in Section 5 and Appendices. A complete literature search in the area of System Modeling was performed and is listed in the Bibliography.

Computer assisted noise and vibration analysis system--canvas

Abstract: A multipurpose program package developed by Nippon Kokan K.K. for noise and vibration analysis is described. The package, called CANVAS (Computer Assisted Noise and Vibration Analysis System), is modular, containing programs for experimental modal analysis, acoustic intensity analysis, signature analysis for rotating machinery, and underwater sound prediction.