Conventional Modal Testing Research Articles

Piezo sensor-based operational strain modal analysis of structures: Transition from lab to field application

This study evaluates piezo sensors for modal identification of a scaled-down prototype of a pedestrian foot-over bridge under pedestrian motions and further extends the application in real-life structures. The piezo sensors-based results are compared with the accelerometers-based displacement modal parameters. Pedestrian motions are adopted to simulate the operational conditions of a pedestrian footover bridge with different patterns of pedestrian motions. Piezo sensors are found to effectively capture the low amplitude dynamic strain response under pedestrian motions. Strain modal testing captures the modal parameters positively correlated with conventional acceleration modal testing. Staggered pedestrian motions are best suited for actuating the structure uniformly at all instrumented nodes. Piezo sensor-based modal testing is extended to modal testing of real-life footover bridges under low amplitude ambient pedestrian traffic. Piezo sensors successfully capture the bending and torsion modes with good correlation with accelerometers-based modes. The strain-based modal parameters are obtained with excellent repeatability and negligible deviation.

Modal testing with a pedestrian as a vibration exciter

A novel approach, for identification of modal properties using a dynamic excitation induced by a human walker, has previously been proposed to identify natural frequencies, damping ratios and modal masses. The developed approach is now expanded to also estimate vibration mode shapes, thus fully characterising the dynamic behaviour of a structure in a simple and affordable way. Additionally, the reliability of the method is parametrically analysed and validated against simulated and real world data of a footbridge. Results indicate that, given a reasonable initial estimate of the target modal properties values and with careful consideration of the number and location of measured responses, it is possible to estimate all modal properties of a structure in a reliable and simpler way than conventional modal testing methods: handheld impact hammer, electrodynamic shaker or ambient vibration tests.

Beat wave method for mode pair extraction of a bell type structure

This paper presents a mode pair extraction method for a bell-type structure that employs a generated beat response signal. Due to the occurrence of small asymmetries in the bell structure, a mode pair can be observed on the circumference. Each mode in the pair has very close frequencies and interference between these frequencies produces beats. Beats are a very interesting acoustics phenomenon in the bell sound. Controlling the beat characteristics requires extraction of a mode pair after the bell is cast. The conventional modal test needed excitation force and response signals at several points. On the contrary, the proposed method requires only the beat response measured at two points on the circumference. This method applied the theory of shell-of-revolution and measured the amplitude ratios of the beat wave’s peak and the valley. The position of the nodes and anti-nodes of the mode pair was determined using the amplitude ratio and the auto-spectrum. The validity of the new method was verified by comparing the experimental results with those of the multi-point test method. Moreover, this method is much simpler and faster than the conventional ones.

On the comparison between displacement modal testing and strain modal testing

The conventional modal testing (referred to as displacement modal testing (DMT)) is based on measurement of displacement, velocity or acceleration as well as excitation force. Though there exits an enormous literature with regard to DMT, on the contrary, a few papers address modal testing based on strain gauges or strain sensor (referred to as strain modal testing (SMT)). The main reason for this scenario is due to practical problems in the use of strain gauges as calibration procedure, ground loop sensitivity are not adequate at high frequency, bonding quality. In this work, a novel piezoelectric strain sensor is used for SMT. In this study it is demonstrated that this sensor overcomes the practical drawbacks related to the use of strain gauges. Thus, SMT based on piezoelectric strain sensors can be a valid alternative to DMT which is usually based on accelerometers. Comparisons between the modal testing results concerning brackets with different constraint conditions using both accelerometers and strain sensors are given in terms of modal parameters, highlighting their pros and cons.

Iterative Method for Exponential Damping Identification

AbstractExponential damping is a new potential damping model for dynamic analysis of systems. This article outlines a complex mode procedure for identifying the exponential damping model and discusses its applicability and limitations. A new iterative method for relaxation factor is proposed, without using the full set of modal data, which is simple, direct, and compatible with conventional modal testing procedures. Combined with the frequency response functions (FRFs)‐based model updating method, the finite element model with such nonviscous damping is updated. The proposed method and several related issues are illustrated by numerical examples. It is shown that the finite element model updated method for the systems with exponential damping can predict accurately not only the natural frequencies but also the FRFs of the systems.

Identification of Modal Properties of Composite Thin Plate Using OMA in Wind Tunnel Environment

Identification of modal parameters is crucial especially in aerospace applications whereby the interactions of airflow with aircraft structures can result in undesirable structural deformations. This structural deformation can be predicted with knowledge of the modal parameters. This can be achieved through conventional modal testing that requires a known excitation force in order to extract these dynamic properties. This technique can be experimentally complex because of the need for artificial excitation and it also does not represent actual operational condition. The current work presents part of research work that address the practical implementation of operational modal analysis (OMA) applied to a cantilevered hybrid composite plate exposed to low speed airflow in a wind tunnel. A single contactless sensing system via a laser vibrometer is employed to measure the response. OMA technique applied in a wind-on condition succeeded in extracting the modal parameters of the hybrid composite plate which correlate well with modal testing using impact hammer excitation.

Identification of inertia properties from the results of output-only modal analysis

Accurate knowledge of the rigid body properties of a structure including the mass, the location of mass center and the moments of inertia is important in machine design, vibration analysis, optimization and modeling of mechanical systems. However, estimation of these properties through theoretical methods is difficult when the structure has a complicated shape. In practice, the inertia properties can be estimated using the conventional modal testing methods by extracting the rigid body modes when the structure is tested in free-free boundary condition. However, all the rigid body modes are not always detectable, due to this fact that the structure is not excited at all degrees of freedom. In order to obtain all of the rigid body modes, many activities have been conducted for selecting the type and location of excitation without much success. In operational modal analysis (OMA), the structure can be excited at any arbitrary point and in different directions. In this paper, a new approach is introduced for estimation of the inertia properties from OMA. The data from OMA are adequate to extract all the rigid body modes of structure. A modal method is used for estimating the inertia properties from the rigid body modes extracted from OMA. The suggested approach is applied to a numerical model of a two-dimensional steel beam as well as a numerical model of a 3D frame and the accuracy of results is evaluated. It is shown that OMA can provide enough data to extract the inertia properties. A real beam is also tested in order to evaluate the performance of the method in practice, needless of a complicated procedure as for conventional methods.

Improved Interpretation of Vibration Responses from Concrete Delamination Defects Using Air-Coupled Impact Resonance Tests

AbstractThe deteriorating national infrastructure demands improved nondestructive evaluation (NDE) and structural health monitoring methods for existing concrete structures. Vibration resonance tests offer an efficient NDE method to identify and characterize shallow (near-surface) delamination defects that afflict RC structures. However, efficient implementation of effective modal analysis methods for this purpose is hindered by practical testing limitations. This paper studies vibration resonance data from square, rectangular, and circular near-surface delamination defects in concrete using two testing configurations: a coupled source-receiver set configuration (driving point type), which is analogous to the impact-echo (IE) test, and a fixed-source moving sensor configuration, which represents a conventional modal analysis test. All data were collected using contactless air-coupled sensors, which enable efficient data collection from large structures from prepared laboratory samples. An approach to self...

Frequency response functions of shape features from full-field vibration measurements using digital image correlation

The availability of high speed digital cameras has enabled three-dimensional (3D) vibration measurement by stereography and digital image correlation (DIC). The 3D DIC technique provides non-contact full-field measurements on complex surfaces whereas conventional modal testing methods employ point-wise frequency response functions. It is proposed to identify the modal properties by utilising the domain-wise responses captured by a DIC system. This idea will be illustrated by a case study in the form a car bonnet of 3D irregular shape typical of many engineering structures. The full-field measured data are highly redundant, but the application of image processing using functional transformation enables the extraction of a small number of shape features without any significant loss of information from the raw DIC data. The complex bonnet surface on which the displacement responses are measured is essentially a 2-manifold. It is possible to apply surface parameterisation to ‘flatten’ the 3D surface to form a 2D planar domain. Well-developed image processing techniques are defined on planar domains and used to extract features from the displacement patterns on the surface of a specimen. An adaptive geometric moment descriptor (AGMD), defined on surface parametric space, is able to extract shape features from a series of full-field transient responses under random excitation. Results show the effectiveness of the AGMD and the obtained shape features are demonstrated to be succinct and efficient. Approximately 14 thousand data points of raw DIC measurement are represented by 20 shape feature terms at each time step. Shape-descriptor frequency response functions (SD-FRFs) of the response field and the loading field are derived in the shape feature space. It is seen that the SD-FRF has a similar format to the conventional receptance FRF. The usual modal identification procedure is applied to determine the natural frequencies, damping factors and eigen-shape-feature vectors from the SD-FRF. Natural frequencies and mode shapes from a finite element (FE) model are correlated with the experimental data using the cosine distance between the shape feature vectors with 20 terms. There are numerous benefits of using image decomposition to analyse 3D DIC measured data, including (1) representation of the raw measurement data with efficiency and succinctness; (2) determination of the FRF of any point on the specimen by the use of the full-field shape features; and (3) elimination of DIC measurement noise. Also, the SD-FRF is potentially ideal for cases of field excitation of structures.

MODAL ANALYSIS OF BRIDGE STRUCTURES BY MEANS OF FORCED VIBRATION TESTS / TILTO KONSTRUKCIJŲ MODALINĖ ANALIZĖ TAIKANT PRIVERSTINĖS VIBRACIJOS TESTUS

New modern bridges and older structures exposed to accelerated deterioration need permanent condition monitoring. The major tools used in bridge condition evaluation are based on the results of the experimental modal analysis of bridge structures. This paper focuses on the methodology of Forced Vibration Tests performed by means of mechanical exciters. A comprehensive testing system called MANABRIS, developed at Wroclaw University of Technology, is presented. The system is equipped with a rotational eccentric mass exciter and dedicated software for programming and controlling the tests and for acquiring and processing measurement data. The results of a Forced Vibration Test carried out on a typical railway bridge are compared with the results of a conventional modal test of the structure excited by trains. The precision of the considered testing techniques is evaluated and the range of their effective application is proposed. Santrauka Naujų šiuolaikinių tiltų ir senesnių konstrukcijų, kurias veikia greitesnio nusidėvėjimo procesai, būklę reikia nuolat stebėti. Pagrindinės priemonės, taikomos tilto būklei vertinti, pagrįstos tilto konstrukcijų eksperimentinės modalinės analizės rezultatais. Šiame straipsnyje pagrindinis dėmesys skiriamas priverstinės vibracijos testams (angl. Forced Vibration Tests), atliktiems naudojant mechaninio žadinimo generatorius. Pristatoma išsami bandymo sistema, pavadinta MANABRIS, kuri buvo sukurta Vroclavo technologijos universitete. Sistemoje yra sukamasis ekscentriškas masės sužadintuvas ir programinė įranga, skirta testams programuoti ir kontroliuoti, norint gauti ir apdoroti matavimų duomenis. Priverstinės vibracijos testo (angl. Forced Vibration Test), atlikto su įprastu geležinkelio tiltu, rezultatai lyginami su tradicinio modalinio testo rezultatais, gautais konstrukcijas veikiant traukiniais. Vertinamas testo tikslumas ir siūlomi jo efektyvaus pritaikymo būdai.

MULTI-POINT MEASUREMENT OF STRUCTURAL VIBRATION USING PATTERN RECOGNITION FROM CAMERA IMAGE

Modal testing requires measuring the vibration of many points, for which an accelerometer, a gab sensor and laser vibrometer are generally used. Conventional modal testing requires mounting of these sensors to all measurement points in order to acquire the signals. However, this can be disadvantageous because it requires considerable measurement time and effort when there are many measurement points. In this paper, we propose a method for modal testing using a camera image. A camera can measure the vibration of many points at the same time. However, this task requires that the measurement points be classified frame by frame. While it is possible to classify the measurement points one by one, this also requires much time. Therefore, we try to classify multiple points using pattern recognition. The feasibility of the proposed method is verified by a beam experiment. The experimental results demonstrate that we can obtain good results.

Modal analysis of mdof system by using free vibration response data only

Conventional modal testing requires the actuator and sensor to perform FRF measurement so as to determine the structural modal parameters. This paper presents a new idea of experimental modal analysis by only using the structural free vibration response due to initial conditions. If the structural displacement can be measured, the displacement response matrices that are the discrete-time-domain data for all measured dofs can be formulated. The velocity and acceleration response matrices can then be calculated by finite difference methods. With the input of these response matrices to the developed algorithm, the system natural frequencies and their corresponding mode shapes can be determined simultaneously. Numerical examples for a 3-dof and 10-dof systems are presented, to show, respectively, the feasibility and effectiveness of the developed method. Results show the proposed method is very promising. Only the structural displacement response in free vibration condition need to be measured and as the input to the modal parameter extraction algorithm such that all of the structural modal frequencies and mode shapes of the system can be determined successfully. The presented idea can also be extended and applied to the general structure with non-proportional damping case. The proposed methodology can therefore enhance the structural modal analysis technique.

Experimental modal analysis for microelectromechanical systems

The structural dynamics behavior of microelectromechanical systems (MEMS), which include moving, overhung, and compliant subcomponents, plays a pivotal role in determining their performance and reliability. Traditionally, experimental modal analysis is used to characterize the dynamic behavior of structures, as well as to derive, validate, update, and correct analytical and numerical models. Due to their small size, however, conventional modal testing methods cannot be directly applied to microstructures. In this paper we provide an overview of modal testing techniques for microsystems. A particular experimental modal analysis methodology that includes base excitation via a piezoelectric shaker and measurement through a laser interferometer is then described and evaluated. A distinguishing characteristic of the methodology is its simplicity, including its simple setup and off-the-shelf components. The modal model is derived for the base excitation of microcantilever beams. The effectiveness of the methodology is illustrated through various experiments on polysilicon microcantilevers for different geometries and ambient pressures. Analysis of the damping data for different pressures has confirmed the well-documented fact that the structural damping in microsystems can be considerably less than damping arising from interaction with the ambient gases.

Model Updating Using the Closed-Loop Natural Frequency

Parameter modification of a linear finite element model (FEM) based on a modal sensitivity matrix is usually performed through an effort to match FEM modal data to experimental ones. However, there are cases where this method cannot be applied successfully; lack of reliable modal data and ill-conditioning of the modal sensitivity matrix constitute such cases. In this research, a novel concept of introducing feedback loops to the conventional modal test setup is proposed. This method uses closed-loop natural frequency data for parameter modification to overcome the problems associated with the conventional method based on modal sensitivity matrix. The feedback loop changes the modal characteristics of the system, and the closed-loop natural frequencies can be used as additional information to solve the problem caused by lack of reliable modal data. Through proper selection of exciter and sensor locations and associated feedback gains, the condition number of the modal sensitivity matrix can be reduced, and a more reliable estimation result can be expected. A parameter modification scheme based on the closed-loop natural frequency data along with the modal sensitivity modification and controller design method is explained. Proposed controller design method is efficient in changing modes. Numerical simulation of parameter estimation based on time-domain input/output data is provided to demonstrate the estimation performance of proposed method.

폐루프 공진 주파수를 이용한 모델 개선법

Parameter modification of a linear finite element model(FEM) based on modal sensitivity matrix is usually performed through an effort to match FEM modal data to experimental ones. However, there are cases where this method can`t be applied successfully; lack of reliable modal data and ill-conditioning of the modal sensitivity matrix constitute such cases. In this research, a novel concept of introducing feedback loops to the conventional modal test setup is proposed. This method uses closed-loop natural frequency data for parameter modification to overcome the problems associated with the conventional method based on modal sensitivity matrix. We proposed the whole procedure of parameter modification using the closed-loop natural frequency data including the modal sensitivity modification and controller design method. Proposed controller design method is efficient in changing modes. Numerical simulation of parameter estimation based on time-domain input/output data is provided to demonstrate the estimation performance of the proposed method.

Force Equilibrium Approach for Linearization of Constrained Mechanical System Dynamics

The purpose of this study is to derive a linearized form of dynamic equations for constrained mechanical systems. The governing equations for constrained mechanical systems are generally expressed in terms of Differential-Algebraic Equations (DAEs). Conventional methods of linearization are based on the perturbation of the nonlinear DAE, where small amounts of perturbations are taken to guarantee linear characteristics of the equations. On the other hand, the proposed linearized dynamic equations are derived directly from a force equilibrium condition, not from the DAEs, with small motion assumption. This approach is straightforward and simple compared to conventional perturbation methods, and can be applicable to any constrained mechanical systems that undergo small displacement under external forces. The modeling procedure and formulation of linearized dynamic equations are demonstrated by the example of a vehicle suspension system, a typical constrained multibody system. The solution is validated by comparison with conventional nonlinear dynamic analysis and modal test results.

On the Modal Testing of Microstructures: Its Theoretical Approach and Experimental Setup

Small and lightweight structures have very high natural frequencies and small elastic displacement compared to ordinary structures. Due to limited excitation bandwidth and relatively large size of pick up devices, conventional modal testing facilities are not feasible for testing MEMS structures. A modal testing system based on the base excitation principle was developed in this research. In the meantime, the associated mathematical model for frequency response functions was derived as well. Testing structures are mounted on a rigid platform that can move essentially with only one translational degree of freedom. An electric discharge pulse strikes the platform to provide a very wide band excitation. Laser Doppler vibrometers are used to pick up both input and output signals. Since these signals are picked up without contacting structures, the structural dynamic characteristics remain intact without any distortion. With this system, modal parameters of a miniature structure can be extracted, and the receptance functions are synthesized successfully.

Scanning laser Doppler technique for model testing of distributed-parameter systems

IN conventional modal testing, accelerometers are used to sense structural response data that are processed to obtain the natural frequencies, damping, and mode shapes of the structure under test. In the case of lightweight structures like composites where mass loading and other local effects of these transducers are not eligible, optical instruments like the laser Doppler vibrometer (LDV) are used. The availability of realtime scanning LDVs has introduced many interesting measurement possibilities. In the method developed in this paper, we process the scanning LDV velocity output signal in the frequency domain to directly obtain the deflection shape of the vibrating structure in a functional (series) form. The technique is demonstrated through application to the problem of modal identification of a cantilever beam. The identified dynamic characteristics of the cantilever beam have been compared with analytical solutions. The method employs a noninvasive, noncontact procedure that avoids the problem of transducer mass loading on lightweight structures and makes possible measurements on hard-to-reach and hazardous surfaces. Contents In its basic form, the LDV is essentially a point velocity sensor, with the sensitivity direction being along or perpendicular to the line of sight, depending on the optical configuration. To extend the usefulness of the instrument, manufacturers now offer automatic scanning mechanisms so that the measurements can be performed at a sequence of locations without operator intervention. However, the sensor is stationary during each measurement and the automation has been only in terms of successively moving the sensor to the next measurement point. If we take the concept further along, our system employs a higher scanning rate so that the test data can be considered to be acquired in a simultaneous sense (the sensor is moving continuously while the measurements are in progress). Although high-speed real-time scanning has been reported previously, the data processing has been limited to sampling the scanning LDV output and relating the instaneous velocity to fixed spatial locations, assuming a nonoscillatory velocity field. Using harmonic scanning along a straight line on the surface of a solid test object, our system can be used to obtain the velocity profile along the scan line in a functional form for oscillatory velocity fields also. It is shown that the spatial velocity distribution modulates the velocity output signal from the LDV, and a Fourier analysis of this modulated signal can be used to derive this spatial distribution in a Chebyshev series form. The technique is applicable to systems where the space-time distribution of velocity is of a particular