Experimental Modal Damping Identification of a Mechanical Structure Using Video Magnification Technique

Vibration can be introduced in all mechanical fields in our life. Engineers try to avoid its negative effect leading in some cases to deformation in the machines. Many researches are dedicated to study the identification of damping especially in multi degree of freedom systems with particular attention to the source of energy dissipation. They focus on developing new tools or methods which may be used in real problems to obtain accurate results about the amount (or value) and the location of energy dissipation in the structure. The aim of this paper is to present an original procedure aims to experimentally determine the modal damping ratio of a mechanical structure. The proposed procedure consists of extracting the Frequency Response Function of the vibrating system using the video magnification method and then calculate the modal damping ratio using the 3-dB method. These experimental measurements are carried out by giving an external force on a cantilever beam, then the modal damping ratios are extracted using motion magnification. The obtained results show a relative error less than 4.2% between the experimental measurements and the analytical calculation for the Frequency Response Function (FRF) curves. The novelty of the paper is to combine the video magnification technique and the 3dB method in a procedure that aims to experimentally measure the modal damping of a mechanical structure. The proposed procedure in this paper represents the damping identification as a simple and easy engineering application.     

USING THE CROSS-CORRELATION TECHNIQUE TO EXTRACT MODAL PARAMETERS ON RESPONSE-ONLY DATA

Modal parameter identification is used to identify those parameters of the model which describe the dynamic properties of a vibration system. Classical modal parameter extractions usually require measurements of both the input force and the resulting response in laboratory conditions. However, when large-scale operational structures are subjected to random and unmeasured forces such as wind, waves, or aerodynamics, modal parameters estimation must base itself on response-only data. Over the past years, many time-domain modal parameter identification techniques from output-only have been proposed. Among them, the natural excitation technique (NExT) has been a very powerful tool for the modal analysis of structures excited in operating environment. This issue reviews the theoretical development of natural excitation technique (NExT), which uses the cross-correlation functions of measured responses coupling with conventional time-domain parameter extraction under the assumption of white-noise random inputs. Then a frequency-domain poly reference modal identification scheme by coupling the cross-correlation technique with conventional frequency-domain poly reference modal parameter extraction is presented. It uses cross-power spectral density functions instead of frequency response functions and auto- and cross-correlation functions instead of impulse response functions to estimate modal parameters from response-only data. An experiment using an airplane model is performed to investigate the effectiveness of the cross-correlation technique coupled with frequency-domain poly reference modal identification scheme.     

Nonlinear finite element model updating of an infilled frame based on identified time-varying modal parameters during an earthquake

A model updating methodology is proposed for calibration of nonlinear finite element (FE) models simulating the behavior of real-world complex civil structures subjected to seismic excitations. In the proposed methodology, parameters of hysteretic material models assigned to elements (or substructures) of a nonlinear FE model are updated by minimizing an objective function. The objective function used in this study is the misfit between the experimentally identified time-varying modal parameters of the structure and those of the FE model at selected time instances along the response time history. The time-varying modal parameters are estimated using the deterministic–stochastic subspace identification method which is an input–output system identification approach. The performance of the proposed updating method is evaluated through numerical and experimental applications on a large-scale three-story reinforced concrete frame with masonry infills. The test structure was subjected to seismic base excitations of increasing amplitude at a large outdoor shake-table. A nonlinear FE model of the test structure has been calibrated to match the time-varying modal parameters of the test structure identified from measured data during a seismic base excitation. The accuracy of the proposed nonlinear FE model updating procedure is quantified in numerical and experimental applications using different error metrics. The calibrated models predict the exact simulated response very accurately in the numerical application, while the updated models match the measured response reasonably well in the experimental application.     

Extended Kalman filter for modal identification of structures equipped with a pendulum tuned mass damper

Pendulum tuned mass dampers (PTMDs) have been employed in several full-scale applications to attenuate excessive structural motions, which are mostly due to wind. Conducting periodic condition assessments of the devices to ascertain their health is necessary to ensure their continued optimal performance, which involves identifying the modal parameters of the underlying (bare) structure to which they are tuned to. Such an identification is also necessary for the design of control systems such as adaptive tuned mass dampers. Existing methods of arresting the motion of the damper to estimate the modal properties are expensive, time-consuming, and not suitable for online tuning. Instead, in this paper, parameter estimation using the Extended Kalman Filter (EKF) is proposed to undertake this task. The central task accomplished here is to estimate the dynamic characteristics of the bare structure (structure without the PTMD) from response measurements of the coupled main structure and PTMD system. The proposed methodology relies on ambient acceleration measurements of TMD-attenuated responses to estimate the bare structural modal frequencies, damping, and mode shapes, which can then be used either for condition assessment or for control. The application of EKF to modal parameter estimation is not new. However, a methodology to address the problem in wind engineering arising from stochastic disturbances present in both the measurement and state equations, and unknown process and noise covariances arising due to ambient excitations, is presented for the first time. Extensively studied for synthetic data, these two challenges have limited thus far the application of Kalman filtering to practical wind engineering parameter estimation problems using experimentally obtained measurements. In this paper, a detailed methodology is presented to address these challenges by using a modified form of the standard EKF equations, together with an algorithm to estimate the unknown disturbance and measurement noise covariances. Numerical simulations and an experimental study are both presented. Results demonstrate that the method proposed provides reliable estimates for the modal parameters required to perform condition assessment and control tasks for pendulum tuned mass dampers.     

Mode shape expansion using perturbed force approach

A new approach for expanding incomplete experimental mode shapes is presented which considers the modelling errors in the analytical model and the uncertainties in the vibration modal data measurements. The proposed approach adopts the perturbed force vector that includes the effect of the discrepancy in mass and stiffness between the finite element model and the actual tested dynamic system. From the developed formulations, the perturbed force vector can be obtained from measured modal data and is then used for predicting the unmeasured components of the expanded experimental mode shapes. A special case that does not require the experimental natural frequency in the mode shape expansion process is also discussed. A regularization algorithm based on the Tikhonov solution incorporating the generalized cross-validation method is employed to filter out the influence of noise in measured modal data on the predictions of unmeasured mode components. The accuracy and robustness of the proposed approach is verified with respect to the size of measured data set, sensor location, model deficiency and measurement uncertainty. The results from two numerical examples, a plane frame structure and a thin plate structure, show that the proposed approach has the best performance compared with the commonly used existing expansion methods, and can reliably produce the predictions of mode shape expansion, even in the cases with limited modal data measurements, large modelling errors and severe measurement noise.     

IDENTIFICATION OF MODAL PARAMETERS FROM MEASURED OUTPUT DATA USING VECTOR BACKWARD AUTOREGRESSIVE MODEL

In this paper, a modal identification system that is based on the vector backward autoregressive (VBAR) model has been developed for the identification of natural frequencies, damping ratios and mode shapes of structures from measured output data. The modal identification using forward autoregressive approach has some problems in discriminating the structure modes from spurious modes. On the contrary, the VBAR approach provides a determinate boundary for the separation of system modes from spurious modes, and an eigenvalue filter for the selection of physical modes is existent in the proposed method. For convenience of application, the backward state equation established from VBAR model is transformed into a forward state equation, which is termed as transformed VFAR model in this paper. In addition, the extraction of equivalent system matrix of state equation of motion for structures from the transformed VFAR model has been developed, and then the normal modes can be calculated from the identified equivalent system matrix. Two examples of modal identification are carried out to demonstrate the availability and effectiveness of the proposed backward approach: (1) Numerical modal identification for a three-degree-of-freedom dynamic system with noise level in 20% of r.m.s of measured output data; (2) experimental modal identification of a cantilever beam. Finally, to show the advantage of the proposed VBAR approach on the selection of physical modes, the modal identification by stochastic subspace method was performed. The results from both methods are compared.     

Application of a multivariable input-output subspace identification technique in structural analysis

In this paper a multivariable subspace-based identification method is applied to experimental modal analysis. The method shows its efficiency in the identification of data which is contaminated by a great amount of external noise. Numerical simulation is used to present the main characteristics of the method and compare its performance against other techniques currently used in experimental modal analysis. The subspace identification method is also applied to data from a modal test of a practical engineering structure.     

Structural damage evolution assessment using the regularised time step integration method

This paper presents an approach to identify both the location and severity evolution of damage in engineering structures directly from measured dynamic response data. A relationship between the change in structural parameters such as stiffness caused by structural damage development and the measured dynamic response data such as accelerations is proposed, on the basis of the governing equations of motion for the original and damaged structural systems. Structural damage parameters associated with time are properly chosen to reflect both the location and severity development over time of damage in a structure. Basic equations are provided to solve the chosen time-dependent damage parameters, which are constructed by using the Newmark time step integration method without requiring a modal analysis procedure. The Tikhonov regularisation method incorporating the L-curve criterion for determining the regularisation parameter is then employed to reduce the influence of measurement errors in dynamic response data and then to produce stable solutions for structural damage parameters. Results for two numerical examples with various simulated damage scenarios show that the proposed method can accurately identify the locations of structural damage and correctly assess the evolution of damage severity from information on vibration measurements with uncertainties.     

Use of speckle interferometry and modal assurance criterion for identification of component modes

One of the problems encountered in performing modal analysis is the identification of different modes occurring at close natural frequencies. This paper proposes to face such a problem by an original application of the modal assurance criterion (MAC) that is typically used to verify the reliability of numerical structural models by evaluating the correspondence between numerical and experimental mode shapes. To properly apply the MAC, experimental mode shapes must be retrieved acquiring data at a high number of experimental points suitably distributed on the surface of the structure. Using usual modal analysis techniques based on pointwise transducers, difficulties can be encountered to retrieve mode shapes with the required spatial resolution. In order to overcome such difficulties, Speckle interferometry techniques can be used. This paperproposes a procedure based on the application of a highly reliable MAC evaluated by time average Speckle interferometry for recognising the modes contributing to the stationary vibration patterns. The results obtained from the modal analysis of a thin square plate have shown that the proposed procedure is capable of pointing out the component modes.     

Dynamic holographic modal analysis for NDT

This paper describes crack and defect detection in structures through modification of the vibrational modal patterns and surface responses to stress. Features are made visible with dynamic holographic interferometery combined with parameter estimation. The procedure involves an unconventional, optimized, laser-illumination method. The methods are especially applicable to large structures and could prove pivotal to improved designs, monitoring and maintenance. Components and structures could be designed to better withstand operating stresses, and existing structures could be analysed to predict their response to stress. Since the modal characterization of a structure can act as a type of fingerprint, holographic interferometry can also be used to monitor structural degradation due to operating and aging. Modal characterization includes identification of resonant frequencies and also the corresponding mode shapes. Holographic interferometry provides for direct modal characterization of a structure as well as measuring its small loading dynamic response. The project demonstrated that a wide variety of defects can be located in structural components, vessels and pipes. An analytical exercise also demonstrates the ability to use global modal characteristics to determine the presence of local corrosion and erosion.     

Modeling and optimization of local constraint elastomer treatments for vibration and noise reduction

This paper presents the vibroacoustic study of a constrained elastomer treatment used in the industry for reducing noise. It can be trimmed and bonded conveniently to vibrating structures for reducing radiated noise. First, an identification of the elastomer viscoelastic characteristics is carried out with a program that models damped vibrations, a conjugate gradient search technique and experimental data extracted rom two contact-free modal analyses. The first modal analysis, adapted to dissipation characterization, is made on a partially covered suspended plate. The second modal analysis, adapted to identifying the elastomer stiffness behavior, concerns a cantilever beam that has almost been covered by a large treatment. The complete dynamic characterization is finally deduced from an iterative procedure that combines information from both experiments. The procedure highlights the influence of the treatment bonding quality on the achieved elastomer damping. Second, practical rules are deduced from a number of parametric studies on beams with baffled radiation conditions. In particular, a design criterion is introduced to help positioning patches where the elastomer damping can be maximized. A threshold, for which an optimal acoustic performance with a minimum of elastomer can be fulfilled, is also identified.     

HEALTH-MONITORING METHOD FOR BRIDGES UNDER ORDINARY TRAFFIC LOADINGS

A method for damage estimation of a bridge structure is presented using ambient vibration data caused by the traffic loadings. The procedure consists of identification of the operational modal properties and the assessment of damage locations and severities. An experimental study is carried out on a bridge model with a composite cross-section subjected to vehicle loadings. Vertical accelerations of the bridge deck are measured while vehicles are running. The modal parameters are identified from the free-decay signals extracted using the random decrement method. The damage assessment is carried out based on the estimated modal parameters using the neural networks technique. As input to the neural networks, the ratios of the resonant frequencies between before and after damages and the mode shapes after the damages are used to take into account the mass effect of the traffic on the bridge. The identified damage locations and severities agree reasonably well with the inflicted damages on the structure.     

Complex dynamics of a nonlinear aerospace structure: Experimental identification and modal interactions

Nonlinear system identification is a challenging task in view of the complexity and wide variety of nonlinear phenomena. The present paper addresses the identification of a real-life aerospace structure possessing a strongly nonlinear component with multiple mechanical stops. The complete identification procedure, from nonlinearity detection and characterization to parameter estimation, is carried out based upon experimental data. The combined use of various analysis techniques, such as the wavelet transform and the restoring force surface method, brings different perspectives to the dynamics. Specifically, the structure is shown to exhibit particularly interesting nonlinear behaviors, including jumps, modal interactions, force relaxation and chattering during impacts on the mechanical stops.     

Experimental and Numerical Study of Structural Identification Using Non-Linear Resonant Decay Method

One of the practical approaches in identifying structures is the non-linear resonant decay method which identifies a non-linear dynamic system utilizing a model based on linear modal space containing the underlying linear system and a small number of extra terms that exhibit the non-linear effects. In this paper, the method is illustrated in a simulated system and an experimental structure. The main objective of the non-linear resonant decay method is to identify the non-linear dynamic systems based on the use of a multi-shaker excitation using appropriated excitation which is obtained from the force appropriation approach. The experimental application of the method is indicated to provide suitable estimates of modal parameters for the identification of non-linear models of structures.     

Regularised finite element model updating using measured incomplete modal data

This paper presents an effective approach for directly updating finite element model from measured incomplete vibration modal data with regularised algorithms. The proposed method is based on the relationship between the perturbation of structural parameters such as stiffness change and the modal data measurements of the tested structure such as measured mode shape readings. In order to adjust structural parameters at detailed locations, structural updating parameters will be selected at critical point level to reflect the modelling errors at the connections of structural elements. These updating parameters are then evaluated by an iterative or a direct solution procedure, which gives optimised solutions in the least squares sense without requiring an optimisation technique. In order to reduce the influence of modal measurement uncertainty, the Tikhonov regularisation method incorporating the L-curve criterion is employed to produce reliable solutions for the chosen updating parameters. Numerical simulation investigations and experimental studies for the laboratory tested space steel frame structure are undertaken to verify the accuracy and effectiveness of the proposed methods for adjusting the stiffness at the joints of structural members. The results demonstrate that the proposed methods provide reliable estimates of finite element model updating using the measured incomplete modal data.     

Identification and updating of loading in frameworks using dynamic measurements

This paper is concerned with the effect of structural loading on dynamic performance. This topic is recognised as being of importance when validating finite element (FE) models with experimental data. A strategy for including axial load effects in a model updating procedure is developed. The method can be used to identify loading in structural frameworks using measured dynamic data.The effectiveness of the new method is demonstrated by means of case studies involving both simulated and experimental data. The theoretical study allows aspects of the sensitivity of the method to realistic levels of experimental noise to be studied as well as the way in which dynamic load identification can be enhanced with static measurements. The experimental case study proves the practical success of the technique. Updated axial load parameters are compared with static measurements of the same quantities.     

Force identification by means of in-operation modal models

In-operation modal analysis has become a valid alternative for structures where a classic forced-vibration test would be difficult if not impossible to conduct. The modelling of output-only data obtained from naturally excited structures is particularly interesting because the test structure remains in its normal in-operation condition during the test. One of the drawbacks of in-operation analysis is that part of the modal parameters can no longer be estimated. Consequently, the applicability of in-operation modal models remains somewhat restricted. For some in-operation applications, interest lies in the identification of the forces that gave rise to the measured response signals. In order to solve this ill-conditioned problem, a complete modal model of the structure is required. Recently, a sensitivity-based method was proposed for the normalization of operational mode shape estimates on the basis of in-operation modal models only. This method allows the reconstruction of complete modal models from output-only data. In this paper, the possibility of using such re-completed in-operation modal models for the identification of localized forces is explored.     

Pulsed TV-holography recording for vibration analysis applications

TV-holography is a well-known tool for vibration analysis. Using the so-called time-average method, this technique allows to record interferograms showing the mode shapes of a structure submitted to vibration excitation and is currently used for modal identification.Within the frames of a BRITE-EURAM program called vibration intensity processing using full-field multi-pulse laser technique (VIP), a TV-holography equipment has been developed, working with a 25 Hz pulsed laser and allowing easy on-site measurements. A measurement procedure has been defined and a specific data processing has been developed for the determination of structural intensity fields, which give transfer path of the vibration energy within a structure.The measurement of these quantities is possible the using classical means (accelerometers, stress gauges, etc.) but the data processing is complex and require a lot of accurate sensors because it is based on spatial derivatives of high order. The optical techniques (laser vibrometry, holography, etc.) are more suited for that purpose because of the high density of measuring points and because of the well-known advantages of these methods: reduced measurement time and no modification of the mass parameters of the structure as it is the case when using contact sensors.Different kinds of output data are then given: operational deflection shape, amplitude and phase, structural intensity field and its divergence through a further step of data processing. The complete procedure with the associated data processing has been tested (for various configurations of excitation and damping) first on a clamped plate, then on a cylinder and at the end on several industrial components.This paper describes the general measurement procedure and the equipment used. The data processing is also presented and various measurement results are shown. The conclusion gives the main advantages and limitations of the method and evaluates the application possibilities.     

Measurement of relevant elastic and damping material properties in sandwich thick plates

An easy-to-implement method to measure relevant elastic and damping properties of the constituents of a sandwich structure, possibly with a heterogeneous core, is proposed. The method makes use of a one-point dynamical measurement on a thick-plate. The hysteretic model for each (possibly orthotropic) constituent is written generically as “E(1+jη)” for all mechanical parameters. The estimation method of the parameters relies on a mixed experimental/numerical procedure. The frequencies and dampings of the natural modes of the plate are obtained from experimental impulse responses by means of a high-resolution modal analysis technique. This allows for considerably more experimental data to be used. Numerical modes (frequencies, dampings, and modal shapes) are computed by means of an extended Rayleigh-Ritz procedure under the “light damping” hypothesis, for given values of the mechanical parameters. Minimising the differences between the modal characteristics yields an estimation of the values of the mechanical parameters describing the hysteretic behaviour. A sensitivity analysis assesses the reliability of the method for each parameter. Validations of the method are proposed by (a) applying it to virtual plates on which a finite-element model replaces the experimental modal analysis, (b) some comparisons with results obtained by static mechanical measurements, and (c) by comparing the results on different plates made of the same sandwich material.     

Dynamic response of a monorail steel bridge under a moving train

This study proposes a dynamic response analysis procedure for traffic-induced vibration of a monorail bridge and train. Each car in the monorail train is idealized as a dynamic system of 15-degrees-of-freedom. The governing equations of motion for a three-dimensional monorail bridge-train interaction system are derived using Lagrange's formulation for monorail trains, and a finite-element method for modal analysis of monorail bridges. Analytical results on dynamic response of the monorail train and bridge are compared with field-test data in order to verify the validity of the proposed analysis procedure, and a positive correlation is found. An interesting feature of the monorail bridge response is that sway motion is caused by torsional behavior resulting from eccentricity between the shear center of the bridge section and the train load.