Showing papers on "Modal testing published in 1999"

Vibration: Fundamentals and Practice

Abstract: VIBRATION ENGINEERING Introduction Study of Vibration Application Areas History of Vibration Organization of the Book Problems TIME RESPONSE Introduction Undamped Oscillator Heavy Springs Oscillations in Fluid Systems Damped Simple Oscillator Forced Response Problems FREQUENCY RESPONSE Introduction Response to Harmonic Excitations Transform Techniques Mechanical Impedance Approach Transmissibility Functions Receptance Method Problems VIBRATION SIGNAL ANALYSIS Introduction Frequency Spectrum Signal Types Fourier Analysis Random Vibration Analysis Other Topics of Signal Analysis Order Analysis Machine Monitoring and Fault Diagnosis Problems MODAL ANALYSIS Introduction Degrees of Freedom and Independent Coordinates System Representation Modal Vibrations Orthogonality of Natural Modes Static Modes and Rigid Body Modes Other Modal Formulations Forced Vibration Damped Systems State-Space Approach Problems DISTRIBUTED-PARAMETER SYSTEMS Introduction Transverse Vibration of Cables Longitudinal Vibrations of Rods Torsional Vibration of Shafts Flexural Vibration of Beams Damped Continuous Systems Vibration of Membranes and Plates Problems VIBRATION DAMPING Introduction Types of Damping Representation of Damping in Vibration Analysis Measurement of Damping Interface Damping Problems VIBRATION INSTRUMENTATION Introduction Vibration Exciters Control System Performance Specification Motion Sensors and Transducers Torque, Force, and Other Sensors Problems SIGNAL CONDITIONING AND MODIFICATION Introduction Amplifiers Analog Filters Modulators and Demodulators Analog-Digital Conversion Bridge Circuits Linearizing Devices Miscellaneous Signal Modification Circuitry Signal Analyzers and Display Devices Problems VIBRATION TESTING AND HUMAN RESPONSE Introduction Representation of a Vibration Environment Pre-Test Procedures Testing Procedures Some Practical Information Vibration Excitations on Humans Human Response to Vibration Regulation of Human Vibration Problems EXPERIMENTAL MODAL ANALYSIS Introduction Frequency Domain Formulation Experimental Model Development Curve Fitting of Transfer Functions Laboratory Experiments Commercial EMA Systems Problems VIBRATION DESIGN AND CONTROL Introduction Specification of Vibration Limits Vibration Isolation Balancing of Rotating Machinery Balancing of Reciprocating Machines Whirling of Shafts Design through Modal Testing Passive Control of Vibration Active Control of Vibration Control of Beam Vibrations Problems APPENDIX A: DYNAMIC MODELS AND ANALOGIES Model Development Analogies Mechanical Elements Electrical Elements Thermal Elements Fluid Elements State-Space Models Response Analysis and Simulation APPENDIX B: NEWTONIAN AND LAGRANGIAN MECHANICS Vector Kinematics Newtonian (Vector) Mechanics Lagrangian Mechanics APPENDIX C: REVIEW OF LINEAR ALGEBRA Vectors and Matrices Vector-Matrix Algebra Matrix Inverse Vector Spaces Determinants System of Linear Equations Quadratic Forms Matrix Eigenvalue Problem Matrix Transformations Matrix Exponential APPENDIX D: LAPLACE TRANSFORM Introduction Laplace Transform Response Analysis Transfer Function APPENDIX E: DIGITAL FOURIER ANALYSIS AND FFT Unification of the Three Fourier Transform Types Fast Fourier Transform (FFT) Discrete Correlation and Convolution Digital Fourier Analysis Procedures APPENDIX F: SOFTWARE TOOLS SIMULINK MATLAB Control Systems Toolbox LabVIEW APPENDIX G: RELIABILITY CONSIDERATIONS FOR MULTI-COMPONENT UNITS Failure Analysis Bayes' Theorem INDEX

EXPERIMENTAL MODAL ANALYSIS By

Abstract: Experimental modal analysis has grown steadily in pop ularity since the advent of the digital FFT spectrum analyzer in the early 1970’s. Today, impact testing (or bump testing) has become widespread as a fast and economical means of finding the modes of vibration of a machine or structure. In this paper, we review all of the main topics associated with experimental modal analysis (or modal testing), including making FRF measurements with a FFT analyzer, modal excitation techniques, and modal parameter estimation from a set of FRFs (curve fitting).

Modal analysis and testing

Abstract: An Overview of the Fundamentals of Modal Analysis.- to Signal Processing.- 1: Fundamentals of Signal Processing.- 2: Advanced Signal Processing.- Rules for the Exchange and Analysis of Dynamic Information.- I: Basic Definitions and Test Scenarios.- II: Numerically Simulated Results for a Deterministic Excitation with no External Loads.- III: Numerically Simulated and Experimental Results for a Deterministic Excitation with External Loads.- IV: Numerically Simulated and Experimental Results for a Random Excitation.- V: Q-Transmissibility Matrix vs. Single Point Transmissibility in Test Environments.- PartVI: Current Practice and Standards.- Theoretical Models for Modal Analysis.- Fundamentals of Time Domain Modal Identification.- Modal Identification Methods in the Frequency Domain.- Parametric Identification Based on Pseudo-Tests.- Updating of Analytical Models - Basic Procedures and Extensions.- Model Quality Assessment and Model Updating.- Damage Detection and Evaluation I.- Damage Detection and Evaluation II Field Applications to Large Structures.- Structural Modification.- Damping: an Introduction to Viscoelastic Models.- Description of Damping and Applications.- Existence and Normalization of Complex Modes for Post Experimental Use in Modal Analysis.- Active Control of Structures.- Acoustic Modal Analysis.- Neural Networks for Modal Analysis.- Advanced Optimisation Methods for Model Updating.- Modal Analysis for Rotating Machinery.- Nonlinearity in Modal Analysis.

Design, Manufacture and Testing of A Bend-Twist D-Spar

Abstract: Studies have indicated that an adaptive wind turbine blade design can significantly enhance the performance of the wind turbine blade on energy capture and load mitigation. In order to realize the potential benefits of aeroelastic tailoring, a bend-twist D-spar, which is the backbone of a blade, was designed and fabricated to achieve the objectives of having maximum bend-twist coupling and fulfilling desirable structural properties (031 & GJ). Two bend-twist D-spars, a hybrid of glass and carbon fibers and an all-carbon D-spar, were fabricated using a bladder process. One of the D-spars, the hybrid D-spar, was subjected to a cantilever static test and modal testing. Various parameters such as materials, laminate schedule, thickness and internal rib were examined in designing a bend-twist D-spar. The fabrication tooling, the lay-up process and the joint design for two symmetric clamshells are described in this report. Finally, comparisons between the experimental test results and numerical results are presented. The comparisons indicate that the numerical analysis (static and modal analysis) agrees well with test results.

The contribution of non-structrual components to the overall dynamic behaviour of concrete floor slabs

Abstract: Prestressing and the advent of high strength materials enable the construction of more slender floor slabs with lower values of natural frequency and damping. Under certain circumstances, the vibrations due to forcing frequencies of normal human activities can be annoying to the occupants. Since the occupants are both the source and the sensor, the vibration cannot be isolated and must be controlled by the structural system. At present, there is a limited knowledge about the overall dynamic characteristics of such concrete slabs, including contributions from individual structural and non-structural components. An extensive programme of modal testing on a slender one-way spanning 50% scaled post-tensioned concrete slab is described. Testing was performed using electromagnetic shaker, instrumented hammer, heeldrop, and walking excitations, to determine full floor dynamic characteristics. The tests investigated the effect on vibration performance of the level of prestress, and of various non-structural additions, including vibration absorbers and effect of occupants. It was found that an increase in prestressing force increases natural frequency and decreases damping due to closing up of microcracks. A model is presented to reflect these changes in terms of effective second moment of area. Cantilever partition tests showed energy to dissipate by swaying, and full-height partitions were seen to act as line supports leading to a significant stiffening of the slab. Analytical models are derived for both forms of partitions. Tests with false floors showed a significantly higher increase in slab damping when the floor panels rested on the pedestals, as opposed to being rigidly fixed to them. Although the addition of viscoelastic screed layers were not seen to have great effect in damping, an analytical model is derived which shows the advantages of using such layers. A TMD system was designed and installed on the floor, using plywood sheets, which led to a reduction in vibration response by as much as 80%. A theoretical model is derived to represent the TMD results and a design criterion is suggested. Finally, the effect of human-structure interaction is investigated. An analytical model shows the natural frequency of the body to be 10.43Hz with a damping of 50%. Results are also reported of tests on a full-scale field slab, confirming some of the findings of the model slab experiments. Broadly, the results show that contrary to popular belief, merely the presence of non-structural components does not necessarily enhance the dynamic behaviour of the system. The design of these components and nature of their installation are important factors affecting their contribution to the overall floor vibrational behaviour.

Effective ambient vibration testing for validating numerical models of concrete dams

Abstract: Ambient vibration tests were conducted on a 56 metre high concrete gravity dam to measure its modal properties for validating a finite element model of the dam–reservoir–foundation system. Excitation was provided by wind, by reservoir water cascading down the spillweir, and by the force of water released through outlet-pipes. Vibrations of the dam were measured using accelerometers, and 3-hour data records were acquired from each location. Data were processed by testing for stationarity and rejecting non-stationary portions before Fourier analysis. Power spectra with low variance were generated from which natural frequencies of the dam were identified clearly and modal damping factors estimated. Modal analysis of the frequency response spectra yielded mode shapes for the six lowest lateral modes of vibration of the dam. The finite element model for the dam was analysed using EACD-3D, and the computed mode shapes and natural frequencies compared well with the measured results. The study demonstrates that ambient vibration testing can offer a viable alternative to forced vibration testing when only the modal properties of a dam are required. Copyright © 1999 John Wiley & Sons, Ltd.

Modal sensing of circular cylindrical shells using segmented piezoelectric elements

Abstract: In this computational study, we investigate the use of thin piezoelectric films to detect the vibration of circular cylindrical shells. Rather than use complicated sensor shapes for modal filtering, we consider simple rectangular shapes and leave the measurement filtering and reconstruction of the system dynamics to full order modal observers. Simulations indicate that decreasing the magnitude of the real part of the observer gain leads to slower convergence but to the desired mode. Larger values lead to faster convergence but to the actual sensor measurements, indicating the occurrence of minimal signal filtering. Increasing the number of sensors can improve observer performance provided that they are placed intelligently on the shell. If a sensor cannot adequately detect the mode which it was intended to sense, sensor output cancelation may affect the behavior of all modal observers. In addition to the signal measurement analysis, the contribution of different mode types within different frequency bands is also investigated, as well as the determination of an adequate number of vibrational modes to include in the simulations.

The scanning laser Doppler vibrometer applied to impact modal testing

Abstract: Previous-described continuous-scanning laser Doppler vibrometer (LDV) test techniques involved, generally, sinusoidal testing of structures. They are here extended to be applicable to impact testing. In an impact test a scanning LDV's response has peaks in the frequency domain, spaced at multiples of the scan frequency, on both sides of each natural frequency, to which standard modal analysis can be applied. The resulting modal constants can be processed to give, depending on the type of scan, mode shapes, or angular vibration, or (three) translational components of vibration at a point. The methods appears to be comparable with normal impact testing in speed and effectiveness - and have considerable advantages in modal testing.

Vibration and actuation characteristics of composite structures with a bonded piezo-ceramic actuator

Abstract: For the design of vibration control systems of composite structures using piezo-ceramic actuators, it is necessary to obtain an accurate system model. Especially, the information related to natural modes, damping ratios and modal actuation forces appears in the governing state space equations. A refined finite element analysis based on the layerwise displacement plate theory has been performed to obtain the system parameters of composite plates with piezoelectric actuators. In this study, the present finite element method has the capability to take account of the stepped effect due to partly bonded piezo-ceramics. Also modal testing techniques have been applied to identify the system parameters experimentally. Through the comparison of numerical results with experimental data, the validity of the numerical procedures has been proved.

Vibration serviceability of long-span cast in-situ concrete floors

Abstract: This thesis describes an investigation into the vibration serviceability of long-span and slender in-situ concrete floors, which are typically post-tensioned. The motivation for the research is the present trend towards increased slenderness of post-tensioned floors supporting open-plan high- quality offices where vibration serviceability may easily become the governing design criterion. The vibration serviceability issue in post-tensioned floors is now also recognised by the UK Concrete Society which proposed, for the first time, guidelines for performing a vibration serviceability check when designing office floors. The guidelines were published in Concrete Society Technical Report 43 (CSTR43) in 1994 and its publication prompted the initialisation of this research project. There were two reasons for this. Firstly, problems were reported with the reliability and practical application of these guidelines, and, secondly, the guidelines were not experimentally verified which is unusual for any design provision related to vibration serviceability. In order to improve understanding of the dynamic performance of a rather specific group of office floors which are long-span and made of cast in-situ concrete, a combined experimental and analytical approach has been adopted. A state-of-the-art facility comprising hardware and software suitable for field modal testing and dynamic response measurements of prototype floor structures was commissioned as a part of this research. The facility is built up around the instrumented sledge hammer, which served as the main excitation source in modal testing, and multi-degree-of-freedom vibration parameter estimation procedures utilising measured floor frequency response functions. The main testing programme consisted of modal testing of four prototype floor structures of varying complexity weighing between 13 and 1000 tonnes. All four slab structures were slender and made of in-situ concrete. These tests were complemented by measurements of the floors' acceleration responses to a single person walking excitation tuned to create as large as realistically possible responses. The modal testing experimental data (measured natural frequencies, mode shapes and modal damping ratios) were used to validate numerical finite element (FE) models representing each floor structure. To do this, advanced FE model correlation and manual updating procedures were employed. Results of these exercises highlighted a number of important issues related to the dynamic behaviour of the concrete floors investigated. Firstly, the bending stiffness of in-situ concrete columns and walls contributed significantly to overall floor bending stiffness and must be considered. Secondly, higher modes of vibration which are close to the fundamental frequency appear in concrete floors, and should not be neglected as they can be easily excited by walking leading to dynamic responses greater than those associated with the fundamental mode. Thirdly, the width of band beams contributes significantly to the lateral stiffness of post-tensioned floors, which, in turn, may be very beneficial for their vibration serviceability. The validated numerical FE models were then used to check the performance of three representative walking excitation models available in the literature. It was shown that, in general, all three models overestimated the measured response to the third harmonic of the walking excitation, which is particularly important for low-frequency office floors. Only one of the models did so in a way which is not overly conservative. This model is recommended for use in vibration serviceability assessment of post-tensioned floors. Finally, gross oversimplification of these important issues is identified as the principal reason for the failure of the current CSTR43 vibration serviceability guidelines to predict reliably vibration response of a wide range of post-tensioned in-situ cast concrete floors.

Generalized modal space drive control system for a vibrating tube process parameter sensor

Abstract: A drive system is taught for controlling the modal content of any number of drive signals used to excite any number of drives on a vibrating conduit such as is found in a Coriolis mass flowmeter or a vibrating tube densimeter. One or more motion signals are obtained from one or more spatially distinct feedback sensors. The motion signals are preferably filtered using a multi-channel modal filter to decompose the motion signals, each of which contain modal content at a plurality of vibration modes, into n single degree of freedom modal response signals. Each modal response signal corresponds to one of the vibration modes at which the vibrating conduit is excited. The n modal response signals are input to a drive channel having a separate processing channel for each of the n modal response signals. Within each drive controller channel, the respective modal response signal is compared to a desired modal response setpoint and the resulting mode error signal is amplified by a modal gain to produce a modal excitation signal for each mode. The modal excitation signal represents the modal excitation necessarily applied to the vibrating conduit to cause the modal response to match the modal setpoint for the given mode. The modal excitation signals are transformed from the modal domain back to the physical domain and mapped to the physical locations of the drives. The resulting drive signals are applied to the drives to excite the conduit.

Modal Characteristics of a Flexible Smart Plate Filled with Electrorheological Fluids

Abstract: This paper presents modal characteristics of a flexible smart plate filled with an electrorheolo gical fluid. First, an oscillatory test is undertaken to extract the electric field-dependent complex shear modulus of the employed starch/silicone oil-based electrorheological fluid. A dynamic model of the smart plate associated with the measured modulus is then developed by adopting a finite element approach to predict field-dependent modal characteristics. Following the construction of a four-partitioned smart plate, an extensive modal test is empirically conducted to identify natural frequencies and mode shapes with respect to both the intensity and the area of the applied field to the fluid domains. Consequently, the measured natural frequencies and mode shapes are compared with the predicted ones to validate the proposed dynamic model. In addition, the control effectiveness for different field-energizing areas under the forced vibration is evaluated in the time domain.

Extraction of ritz vectors from vibration test data

Abstract: Modal parameters obtained from modal testing (such as modal vectors, natural frequencies, and damping ratios) have been used extensively in system identification, finite element model updating, and structural health monitoring. As an alternative to modal vectors, load-dependent Ritz vectors have been shown useful in various areas of structural dynamics such as model reduction and damage detection. The applications of Ritz vectors, however, have been mainly limited in analytical and numerical analyses because of the difficulty to identify them from vibration tests. This paper presents a procedure to extract load-dependent Ritz vectors using a complete flexibility matrix constructed from measured vibration test data. The proposed method cannot only construct the Ritz vectors corresponding to the actual load pattern employed in vibration tests, but also generate Ritz vectors from arbitrary load patterns. Experimental data obtained from the vibration test of a grid-type bridge structure are employed to validate and illustrate the proposed extraction procedure.

Damage localization in reinforced concrete beams by dynamic stiffness determination

Abstract: In the framework of developing a non-destructive vibration testing method for monitoring the structural integrity of constructions in civil engineering, it is important to be able to determine the dynamic stiffness in each section of the structure from measured modal characteristics. From the dynamic stiffnesses, one obtains directly an idea of the extension of the cracked zones in the structure. In an experimental program, a concrete beam of 6 meter length is subjected to an increasing static load to introduce cracks. After each static preload the beam is tested dynamically in a free-free set-up. The change in modal parameters is then translated into damage in the beam. The technique to predict the damage location and intensity that will be presented in the paper, is a direct stiffness derivation from measured modal displacement derivatives. Using the bending modes, the dynamic bending stiffness can be derived from modal curvatures. Using the torsional modes, the dynamic torsion stiffness can be derived from modal torsion rates.

The SMAC modal parameter extraction package

Abstract: The objective of many modal testing programs is to identify modal parameters of complex systems for model validation purposes. Often this objective is difficult to achieve in an efficient manner due to the complexity of the system being tested. Traditional modal extraction techniques perform well under certain conditions; however, when moderately damped modes and/or high modal density is characteristic of the system response, accurate identification of the modal parameters is challenging. A modal extraction package, called Synthesize Modes and Correlate or SMAC, has been developed to address these concerns. This extraction technique calculates reciprocal modal vectors based on frequency response function (FRF) measurements. The FRFs are multiplied by a reciprocal modal vector to synthesize a single degree-of-freedom (SDOF) FRF. The correlation coefficient compares the synthesized SDOF FRF against an analytical SDOF FRF. Frequency and damping values are optimized to obtain the maximum correlation coefficient, which corresponds to the true system root. A quadrature fit algorithm is then used to generate shapes based on the SMAC modal parameters. Examples are provided utilizing the SMAC package on experimental data from a moderately damped system and one with high-modal density.

Comparison between modal analysis and finite‐element modeling of a marimba bar

Abstract: The sound spectrum of low‐tuned marimba bars contains many components that cannot be explained by a simple one‐dimensional model of flexural vibrations A modal analysis has thus been performed on a bass marimba bar C3 with a fundamental frequency of 130 Hz [outer dimensions: 46×6×235 cm (x,y,z), material: rosewood], taking into account two spatial components of vibration The 20 lowest modes were extracted from this analysis (modal frequencies and mode shapes) A 3‐D finite‐element analysis of this bar, based on an orthotropic model for the material, has been conducted in parallel Modal analysis and finite‐element modeling yield very similar mode shapes and modal frequencies for the first 12 modes, between 130 and 4000 Hz, which confirms the experimental results and validates the theoretical approach The discrepancies between measured and calculated frequencies are less than 4% in this frequency range For higher frequencies, between 4000 and 8000 Hz, the main flexural modes along 0x, such as the (7,0) and the (8,0) modes, are still correctly predicted In this range, the three components of the bar motion become significant and the finite‐element modeling shows a number of modes which were not detected in the modal analysis