Showing papers on "Modal testing published in 1997"

Variability of Modal Parameters Measured on the Alamosa Canyon Bridge

Abstract: A significant amount of work has been reported in technical literature regarding the use of changes in modal parameters to identify the location and extent of damage in structures. Curiously absent, and critically important to the practical implementation of this work, is an accurate characterization of the natural variability of these modal parameters caused by effects other than damage. To examine this issue, a two-lane, seven-span, composite slab-on-girder bridge near the town of Truth or Consequences in southern New Mexico was tested several times over a period of nine months. Environmental effects common to this location that could potentially produce changes in the measured modal properties include changes in temperature, high winds, and changes to the supporting soil medium. In addition to environmental effects, variabilities in modal testing procedures and data reduction can also cause changes in the identified dynamic properties of the structure. In this paper the natural variability of the frequencies and mode shapes of the Alamosa Canyon bridge that result from changes in time of day when the test was performed, amount of traffic, and environmental conditions will be discussed. Because this bridge has not been in active use throughout the testing period, it is assumed that any change in the observed modal properties are the result of the factors listed above rather than deterioration of the structure itself.

Is It a Mode Shape, or an Operating Deflection Shape?

Abstract: Mode shapes and operating "deflection" shapes are related to one another. In fact, one is always measured in order to obtain the other. Yet, they are quite different from one another in a number of ways. This article discusses the relationships between modal testing, modal analysis and operating deflection shape measurements.

Improved Damage Location Accuracy Using Strain Energy-Based Mode Selection Criteria

Abstract: Amethod is presented forselecting thesubsetofidenti® edstructural vibration modesto beusedin® niteelement model correlation for structural damagedetection. Themethod is based on a ranking of themodesusing measured modal strain energy and is a function of only the measured modal parameters. It is shown that a mode selection strategy based on maximum modal strain energy produces more accurate update results than a strategy based on minimum frequency. Strategies that use the strain energy stored by modes in both the undamaged and damaged structuralcon® gurationareconsidered.Itisdemonstratedthatmoreaccurateresultsareobtainedwhen themodes are selected using the maximum strain energy stored in the damaged structural con® guration. The mode selection techniques are applied to the results of a damage detection experiment on a suspended truss structure that has a large amount of localized modal behavior.

Signal versus Noise in Damage Detection by Experimental Modal Analysis

Abstract: Remote bridge-monitoring systems based on measured structural vibration have been perceived to be able to assist in bridge inspection for the future. Sensitivity of measured modal properties to potential damage is very critical for their practical application, which is examined here. Modal tests were conducted on a one-sixth scale multiple steel-girder model bridge and a fracture critical field bridge, including both intact and simulated damage states. Sensitivity of modal parameters to changes of structural condition was studied using statistical methods (for frequencies, damping ratios, mode shapes, and their derivatives). Results show that, even though modal frequencies and mode shapes may be used to identify the existence of commonly observed bridge damage with certain sensitivity, it is difficult to identify their locations.

Autonomous Modal Identification of the Space Shuttle Tail Rudder

Abstract: Autonomous modal identification automates the calculation of natural vibration frequencies, damping, and mode shapes of a structure from experimental data. This technology complements damage detection techniques that use continuous or periodic monitoring of vibration characteristics. The approach shown in the paper incorporates the Eigensystem Realization Algorithm (ERA)as a data analysis engine and an autonomous supervisor to condense multiple estimates of modal parameters using ERA''s Consistent-Mode Indicator and correlation of mode shapes. The procedure was applied to free-decay responses of a Space Shuttle tail rudder and successfully identified the seven modes of the structure below 250 Hz. The final modal parameters are a condensed set of results for 87 individual ERA cases requiring approximately five minutes of CPU time on a DEC alpha computer.

A Normalized Modal Eigenvalue Approach for Resolving Modal Interaction

Abstract: Modal interaction refers to the way that the modes of a structure interact when its geometry and material properties are perturbed. The amount of interaction between the neighboring modes depends on the closeness of the natural frequencies, the mode shapes, and the magnitude and distribution of the perturbation. By formulating the structural eigenvalue problem as a normalized modal eigenvalue problem, it is shown that the amount of interaction in two modes can be simply characterized by six normalized modal parameters and the difference between the normalized frequencies. In this paper, the statistical behaviors of the normalized frequencies and modes are investigated based on a perturbation analysis. The results are independently verified by Monte Carlo simulations.

Using Modal Analysis for Estimation of Anisotropic Material Constants

Abstract: A dynamic method is presented for the estimation of the in-plane elastic properties of structural panels modeled as thin orthotropic plates. The method utilizes the concept of modal analysis. Results from experimental modal testing are matched with theoretical modal analysis calculations for a set of plate bending modes and one in-plane mode of the compression type. The elastic constants \iE\d1, \iE\d2, and \iG\d1\d2 are estimated by minimizing the relative errors between corresponding experimentally and theoretically determined eigenfrequencies. A ratio of two chosen mode shape values of an in-plane compression mode yields an estimate of the Poisson ratio ν\d2\d1. The other in-plane Poisson’s ratio ν\d1\d2 is calculated on the basis of \iE\d1, \iE\d2, and ν\d2\d1 using Hooke’s generalized law. Some redundant information gained from the experimental modal testing is used to minimize possible errors in the test and evaluation process. The method is applied to one type of wood panel material, namely oriented strand board.

Distributed Piezoelectric Element Method for Vibration Control of Smart Plates

Abstract: A new method for active control of plates is presented that includes methods for designing piezoelectric modal sensors and modal actuators. The piezoelectric modal sensor and modal actuator are designed by cutting all of the piezoelectric layers into several independent elements. The modal coordinates and the modal velocities can be obtained from the charges and currents generated by the sensor elements, and the modal actuator is designed by modulating the spatial distribution of voltage applied on the piezoelectric actuator. A scheme for modal control of smart plates is given. Moreover, improvement of the controllabilty of the plates due to segmentation actuator lamina is discussed.

Feasibility analysis of using piezoceramic transducers for cantilever beam modal testing

Abstract: This paper presents a theoretical analysis of the application of piezoceramic transducers to cantilever beam modal testing. Four pairs of sensors and actuators, including accelerometer - point force, accelerometer - PZT, PVDF - point force and PVDF - PZT, are considered. The frequency response functions (FRFs) for the four pairs of sensors and actuators are first derived and written in the conventional modal format. The characteristics of modal parameters can thus be interpreted through the FRFs. A column of the FRF matrix can then be obtained based on the theoretical formulation. A curve-fitting algorithm is then applied to extract the modal parameters, such as natural frequencies, mode shapes and damping ratios. Results show that any sensor - actuator pair can successfully determine natural frequencies and damping ratios. Point types of transducer result in the displacement mode shapes, while piezoceramic transducers that are strip types and distributed in sense give the mode shapes of the slope difference between the edges of piezoceramic transducers. The paper provides the theoretical basis of applying piezoceramic transducers to experimental modal analysis and numerically supports the feasibility of cantilever beam modal testing using piezoceramic transducers.

Adaptive control of flexible structures using modal positive position feedback

Abstract: An adaptive modal positive position feedback (AMPPF) method is presented for controlling the vibration and shape of flexible structures. The proposed strategy combines the attractive attributes of the independent modal space control (IMSC) of Meirovitch and the positive position feedback (PPF) of Goh and Caughey. The controller is designed in the uncoupled modal space using only modal position signals to damp the vibration of undamped modes. The parameters of the AMPPF controller are also adjusted in an adaptive manner in order to follow the performance of an optimal reference model. In this way, optimal damping and zero steady state errors can be achieved even in the presence of uncertain or changing structural parameters. The adaptation laws governing the stable variation in the AMPPF controller parameters are derived using the Lyapunov stability theorem. The effectiveness of the AMPPF in controlling the vibration and shape of a variable mass cantilevered beam is demonstrated experimentally. The performance obtained with the AMPPF algorithm is compared with those of other classical control algorithms. The results obtained emphasize the potential of the AMPPF algorithm as an efficient means for controlling flexible structures with uncertainties in real time. © 1997 by John Wiley & Sons, Ltd

Experimental investigations on the stators of electrical machines in relation to vibration and noise problems

Abstract: All mechanical structures including electrical machine stators and rotors have many built-in mechanisms for dissipating the vibrational energy. Often damping prevents extraneously excited vibrations from being noticed, and the importance and need for damping is not recognised. As advances are made towards building efficient light-weight structures, some of the damping that was present in the structure is inadvertently eliminated. Hence the damping mechanisms need to be studied and efforts be made to incorporate more damping in these re-designed structures in a more reliable and cost-effective way. The authors describe an experimental method to achieve this using modal analysis. The distributed EM forces, and stator models are discussed. The vibration amplitudes at the resonances of two stator models and damping ratios at various resonances are also discussed.

Modal Analysis of Multi-reference Impact Test Data for Steel Stringer Bridges

Abstract: A comparative study on the postprocessing of experimental modal datafrom afull scale steel stringer bridge for damage identification is presented. The bridge was tested before and aJ2er removal of one of the bearing plates at one abutment Frequency Response Functions, measured cd different spatial locaiions, are used to post-process the data using a Complex Mode Indicator Furution(CMlF) algorithm. Dynamic properties of the bn’dge show major differences between the two cases. In addition, modal flexibility of the bridge is calculated for the measured degrees of freedom. Modal flexibility of the btidge shows good agreement with static instrumentation results under truck loading The induced damage is successfully quantified for this loading case. The “after-removal” condition doia was also post-processed a t Las Alamos N a t i o n a l Laborcdory u s i n g t h e Eigensystem Realization Algolithm (ERA) in order to provide a distant check and correlation for the results. T h i s p a p e r b r i e f l y desctibes t h e t w o d i f f e r e n t algorithms and presents the results in both modal and flexibility space. Further, the principal focus of this paper is the pas-processing algorithms and one damage index, although a number of different damage identifcaiion indices are being used for varying levels and types of damage as part of the ongoing research project

Low Strain Measurements Using Random Noise Excitation

Abstract: Low-strain wave propagation velocity and attenuation are effective measures of state in particulate media. The standard resonant column test procedure is modified to facilitate the study of wave propagation at low strains. The system uses band-limited random noise excitation in combination with signal averaging to control the signal-to-noise ratio. This procedure is efficiently implemented by replacing typical peripheral devices with a signal analyzer and computer control. The methodology permits testing at very low strains. The effect of non-linear system response on computed transfer functions is addressed. Other results include the analytical treatment of coupling between torsional and transverse modes, the evaluation of local low-strain shear parameters from solid specimens tested in torsion, and the use of multi-mode testing for the evaluation of field parameters.

Artificial boundary conditions for model updating and damage detection

Abstract: The updating of finite element models commonly makes use of measured modal parameters. The number of modal parameters measured in a typical modal test is small, while the number of model parameters to be adjusted can be large. In this paper, it is shown that the natural frequencies for the structure under a variety of boundary conditions are available from any square, spatially incomplete frequency response function data, without any actual physical alteration of the boundary conditions, hence the term "artificial boundary conditions." This approach can provide potentially a large number of additional and distinct mode frequencies from the same modal test. The simplest example of this approach is that the driving point antiresonance frequencies correspond to the natural frequencies obtained from the structure with the driving point DOF constrained to ground. This result is developed generally for multiple measured points, and is shown to be related to previous results concerning omitted coordinate systems and spatially incomplete test data. The approach is applied to sensitivity-based model updating and damage detection.

Extraction of Normal Modes and Full Modal Damping from Complex Modal Parameters

Abstract: A procedure for extracting the structural normal modes and nondiagonal damping matrix from damped system realization parameters is presented. The procedure utilizes the state-space realization of experimental data obtained using identification algorithms such as the Eigensystem Realization Algorithm and Polyreference. This realization is first decomposed into the complex damped modes of the system and each mode is then transformed into an equivalent real-valued approximation of a second-order system. The transformation yields an approximation of the normal mode frequencies, mode shapes, and damping ratios. The procedure then develops a corrective transformation that accounts for the modal coupling implicit in nonproportional damping, thus yielding the correct structural normal modes and a nondiagonal modal damping matrix for the realization. Solutions for the corrective transformation are shown to be subject to a displacement consistency criterion. The damping identification procedure is demonstrated for both overdetermined (more sensors than modes) and underdetermined (more modes than sensors) problems using simulated data.

Damage localization in a space truss model using modal strain energy

Abstract: A three-dimensional scale model of a hexagonal boom truss of the then space station Freedom was built and tested in the laboratory. The purpose of the tests was to extract complete high-quality data of the vibrational characteristics of the structure, before and after damage, to validate damage detection/evaluation theories. The vibration tests consisted of experimental modal analysis before and after the infliction of artificial damage. The structure was subjected to 18 different damage scenarios, at single and multiple locations, of three types: a) cut damage consisting of a cut through half the depth of the element, b) partial damage removing 50% of the area over the middle third of the element, and c) complete damage caused by completely cutting through the member. All damages were induced without changing the mass properties of the structure through specially designed clamping devices. This paper summarizes the experimental program, the modal test results, the extracted modal shapes and an analysis implemented to localize the damage via modal strain energy distribution. The modal test results consist of the vibrational signatures due to different damages on the structure. The extracted modal results are implemented in a global damage detection/evaluation theory based on modal strain energy distribution. The strain energy distributions due to the static shapes of the modes are computed before and after the inflicted damage. The differences from the normalized strain energy distributions are multiplied times element weight factors proportional to the strain energy distribution of the damaged structure. The weighted modal strain energy differences are lumped into the connecting nodes of the elements to provide indications of the location of the inflicted damage. The technique is able to locate the complete damage and the partial damage, but was not able to detect the cut damage.

Structural assessment by modal analysis in Western Canada

Abstract: Modal testing of a civil engineering structure is generally conducted when its complexity is such that the expense and effort required to obtain its experimental dynamic properties is justified. The need to use the experimental data as a bench mark for calibrating finite element models is a valid justification. Because of the underlying assumptions regarding boundary conditions and member properties and connectivities in finite element modeling, structural engineers often require ways to calibrate their models in order to develop some degree of confidence in the results from computer runs. Considering the significant effort and economic resources needed to conduct such tests, modal testing cannot be conducted on a regular basis. However, the information obtained from each test is invaluable for structural assessment. This paper presents a summary of recent projects for structural assessment of civil engineering structures in Western Canada by modal analysis. A chronological list of significant testing projects in the last two decades, with brief description of each, is presented.

Modal analysis of soft‐soil sites including radiation damping

Abstract: For the one-dimensional analysis of soft-soil layers on an elastic half-space, a general form of analytical solution is developed for converting radiation damping due to energy leaking back to the half-space into equivalent modal damping, allowing the modal analysis technique to be extended to a site where radiation damping has to be accounted for. Closed-form solutions for equivalent modal damping ratios and effective modal participation factors are developed for a single layer with a shear wave velocity distribution varying from constant to linearly increasing with depth. Compact and recursive forms of solutions for equivalent modal damping ratios are developed for a system with an arbitrary number of homogeneous layers on an elastic half-space. Comparisons with numerical solutions show that the modal solutions are accurate. The nominal frequency of a site, i.e. the inverse of four times the total shear wave travel time through the layers, is an important parameter for estimating the high mode frequencies. A parameter study shows that for the same impedance ratio of the bottom layer to the elastic half-space, a system of soil layers with an increasing soil rigidity with depth has, in general, larger peak modal amplifications at the ground surface than does a single homogeneous layer on an elastic half-space, while a system with a decreasing soil rigidity with depth has smaller modal peak amplifications. © 1997 by John Wiley & Sons, Ltd.

Modal parameter extraction from in-operation data

Abstract: In the classical modal parameter estimation approach, the baseline data which are processed are Frequency Response Functions measured in laboratory conditions However, in many applications, the real operating conditions may differ significantly from those applied during the modal test (suspension pre-strains of a car on the road, large motion of a running engine, aeroelastic interaction and wing/rotor pre-strain in air- and rotorcraft, strong environmental excitation in civil structures as traffic load, wind/wave excitation, ) Hence, the need arises to identify a modal model in these real operational conditions In most cases, only response data are measurable while the actual loading conditions are unknown A number of different estimation techniques have been evaluated for their applicability in such conditions They include the Polyreference Least Squares Complex Exponential method and an Auto-Regressive Vector model method The basic principles of these methods are reviewed and applied to an experimental case