Operational Modal Analyses Research Articles

Enhancing reliability in estimating modal parameters for automotive disk Brakes: A comprehensive approach using the Eigensystem Realization algorithm and additional criteria

This paper investigates the challenges in accurately identifying and assessing vibration characteristics in automotive disk brakes, which, due to their geometric symmetry, exhibit closely spaced vibration modes. Understanding the damping characteristics is crucial due to their significant impact on dynamic stability and the potential onset of brake squeal, as damping directly influences the stability threshold and its uneven distribution can destabilize the system. Therefore, this study primarily focuses on the identification of modal parameters with an emphasis on the damping of disk brakes. Traditional Experimental Modal Analysis (EMA) techniques, which rely heavily on Frequency Response Function (FRF) measurements, encounter challenges in distinguishing closely spaced modes, thereby affecting the reliability of parameter estimation, particularly damping. These algorithms are primarily based on FRF measurements and are of multi-input – single-output type (MISO). In comparison to Operational Modal Analyses (OMA) algorithms, which are widely used in civil engineering and are of the multi-input − multi-output type and contain statistical tools for assessing the uncertainty of the estimate, EMA provides limited possibilities to assess the quality of estimating parameters. The primary contribution of this work is demonstrating that the Eigensystem Realization Algorithm (ERA), supplemented with indicators such as Extended Modal Amplitude Coherence (EMAC), Modal Phase Collinearity (MPC), and the Consistent Mode Indicator (CMI), offers a robust tool for accurate damping estimation. Additionally, the application of ERA to data originally acquired for frequency-based methods, specifically the Rational Fraction Polynomial (RFP) method, allows for a direct comparison of these two EMA algorithms using the same dataset. The results demonstrate that the proposed identification process effectively distinguishes system modes from those influenced by noise, providing a pathway to optimize test data acquisition and improve the accuracy of modal parameter estimation, especially in systems with closely spaced modes. The method can also serve as a tool for optimizing the acquisition of test data to improve the estimation of modal parameters, by varying the positions of input (SIMO) or by transitioning to MIMO identification to enhance the observability and controllability of closely spaced modes of disk brake.

Development and Validation of a New Type of Displacement-Based Miniatured Laser Vibrometers.

Developing a miniatured laser vibrometer becomes important for many engineering areas, such as experimental and operational modal analyses, model validation, and structural health monitoring. Due to its compact size and light weight, a miniatured laser vibrometer can be attached to various mobilized platforms, such as an unmanned aerial vehicle and a robotic arm whose payloads can usually not be large, to achieve a flexible vibration measurement capability. However, integrating optics into a miniaturized laser vibrometer presents several challenges. These include signal interference from ghost reflectance signals generated by the sub-components of integrated photonics, polarization effects caused by waveguide structures, wavelength drifting due to the semiconductor laser, and the poorer noise characteristics of an integrated laser chip compared to a non-integrated circuit. This work proposes a novel chip-based high-precision laser vibrometer by incorporating two or more sets of quadrature demodulation networks into its design. An additional set of quadrature demodulation networks with a distinct reference arm delay line length can be used to conduct real-time compensation to mitigate linear interference caused by temperature and environmental variations. A series of vibration measurements with frequencies ranging from 0.1 Hz to 1 MHz were conducted using the proposed laser vibrometer to show its repeatability and accuracy in vibration and ultrasonic vibration measurements, and its robustness to test surface conditions. The proposed laser vibrometer has the advantage of directly measuring the displacement response of a vibrating structure rather than integrating its velocity response to yield the measured displacement with a conventional laser Doppler vibrometer.

Effects of Ambient Temperature and Magnitude of the Vibration on the Dynamics of Pre-Stressed Precast Isolated Pedestrian Bridges

The dynamic properties of structures are known as inherent properties dependent on the mass and stiffness parameters. However, recent studies showed that the temperature and the magnitude of the vibration affect them. This study aims to reveal how the ambient temperature and human-induced vibrations alter the modal characteristics of pre-stressed precast isolated pedestrian bridges. For this aim, operational modal analyses have been applied to the Istanbul Medeniyet University pedestrian bridge. Three-bay pre-stressed precast and isolated bridge has been connecting the two campuses of the university for six years and its dynamic properties were investigated during its construction. In this study, the dominant frequencies of the bridge have been determined to see if they changed or not for its service life. Secondly, the dynamic response of the longest bay of the bridge has been evaluated under different temperatures and human-induced vibrations. Through a year, twelve acceleration measurements have been gathered in a temperature range of 5 – 33 °C and representing the different levels of human-induced vibrations, some jumping actions were applied and its response was recorded. While the performed analyses proved that, the dominant frequencies are dependent on the ambient temperature, no significant correlation was obtained between the amplitude of the vibration and the dominant frequencies of the bridge. High-amplitude vibrations have been used for the vibration serviceability check of the bridge, and it is seen that it satisfies the requirements set by different codes.

Operational modal analysis for supporting the retrofit design of bridges

AbstractAmbient vibration tests and operational modal analysis are commonly adopted worldwide to identify the dynamic behaviour of structures because they offer several advantages such as the use of portable light equipment, the possibility to be performed without interruptions of the structure serviceability, and the use of ambient noise to globally excite the construction. Ambient vibration tests are also usually adopted in structural health monitoring systems to control changes in the dynamic behaviour of structures over the time. In this paper the dynamic identification of two multi‐span simply supported prestressed RC deck bridges in Central Italy is presented. The modal parameters of the structures are identified adopting operational modal analyses based on in‐situ ambient vibration measurements. The experimentally identified dynamics is adopted to assess the bridges' seismic retrofitting works and to investigate their dynamic behaviour in the retrofitted state.

Dynamic identification and vibration serviceability assessment of a wooden cable‐stayed footbridge

AbstractThis paper discusses the dynamic characterization of a 3 spans wooden cable‐stayed footbridge newly built in Italy. The footbridge is 235 m long and consists of a 2‐girder wooden deck. The edge spans are simply supported, while the mid one (about 150 m long) is sustained by 16 stays linked to 2 pillars. Ambient vibration tests and operational modal analyses are performed to identify the global dynamic behaviour of the structure and 17 stable vibration modes are identified in the frequency range 0‐6 Hz. Moreover, the vibration serviceability is assessed performing in situ pedestrian load tests following the load protocols provided by Hivoss and Sètra technical guidelines, and verifying the recorded accelerations with the maximum ones suggested by codes (fib bulletin 32 and EN1990:2002).

Operational Modal Analysis as a Support for the Development of Digital Twin Models of Bridges

Many transportation infrastructures all around the world are facing new challenges in terms of ageing and loss of performance. The infrastructural asset managers are required to perform scrupulous control of the health condition of the infrastructures over time and to execute the required maintenance works. In this context, digital twin models of the infrastructures should have a key role to simplify and speed up the procedures for proper maintenance. This paper discusses the advantages of developing digital twin models for the management of infrastructures, with a focus on bridges. In particular, the role of dynamic tests performed on bridges for the development of digital twin models is addressed, paying attention to test procedures and requirements. Issues such as the quality of instrumentation, the numerosity, and layout of sensors, and the acquisition and post-processing procedures are addressed through applications to two real bridge case studies. Both infrastructures are multi-span pre-stressed RC bridges that were dynamically tested after the restoration and seismic upgrading works. Results of ambient vibration tests and operational modal analyses are described, providing an idea of dynamic test requirements, as well as their use within the framework of the digital twin model creation.

Structural health monitoring of South America's first 6-Story experimental light-frame timber-building by using a low-cost RaspberryShake seismic instrumentation

A low-cost seismic instrumentation system (LCSIS) has been implemented and validated for the structural health monitoring of South America's first experimental 6-story light-frame timber building (Peñuelas Tower). Furthermore, coupling the LCSIS with relative humidity and temperature measuring system has allowed for investigating the ambient-induced variations of the building's dynamic properties. The LCSIS has been accomplished using six accelerographs RaspberryShake® R4SD (R4SD), which were interconnected using a local network controlled by an auxiliary Raspberry Pi3 (RPi3). The RPi3 performs the following activities: (i) it works like an NTP server that allows the synchronization between the seismic instruments; (ii) it is connected to the internet to provide remote control and communication; (iii) it has internal subroutines to periodically estimate the dynamic properties of the building by using the FDD method from hourly ambient vibration tests based on the velocity data obtained from the vertical geophones included in R4SD instruments. The LCSIS was electrically supplied using a 55A battery and a battery charger to ensure operability during power outages. The building's natural frequencies and mode shapes were identified from operational modal analyses of five integrated ambient vibration tests, measured by a conventional seismic instrumentation system (Episensors ES-U2), showing consistent dynamic properties. The LCSIS was validated from shake table tests, observing a good agreement for signal frequencies smaller than 25–30 Hz in comparison with conventional measuring systems as well as measuring the response during an earthquake of low-intensity Mw = 4.6. Once the LCSIS was validated, a BME280 sensor was added to continuously monitor the temperature and relative humidity inside the building, which allowed for the implementation of a structural health monitoring system to track the ambient-induced variations of three principal natural frequencies. It was found a high sensitivity of the building's natural frequencies due to ambient variations, exhibiting peak-to-peak daily variations of 9.5–10.9 % and overall variations of 24.7–29.2 % during an eleven-month period, thus evidencing that timber structures could be more susceptible to temperature and relative humidity variations than other structural systems. Unexpectedly, the timber structure was found to be stiffer under moist conditions, which may be attributed to the tightening of timber assemblies due to wood swelling. A 48-hour state-space model was built to accurately compute the estimated natural frequencies as a function of the recorded temperature and relative humidity, showing that this procedure could be used to effectively disaggregate the ambient-induced variations from changes generated by damage or other unknown sources.

Operational Modal Analyses of Brush Seals and Seating Load Simulations

Abstract Brush seals are one of the most effective sealing technologies in turbomachinery since they enable contact-type operation for close clearance control. Brush seal bristles must interact under turbine conditions, and the minimum pressure load to initiate proper contact between fibers is called seating load. Seating load evaluation is essential for the durability and stability assessment of bristles since unseated fibers may flutter and cause seal failure. Even with proper seating, brush seal critical modes may still be excited by flow-induced fluctuations or bucket tip excitations. In this study, a finite element-based methodology was developed to determine the seating load and identify the critical modes of brush seals. Under pressure load, brush seal nonlinear contact simulations are followed by frequency-based analysis to determine bristle and seal pack critical modes. To determine the seating load of the brush seal, the change in modal response is examined. In this paper, the modeling methodology, parameter correction procedures, geometric inspection of test seals, correlation of transient analyses with dynamic tip force measurements, operational modes of brush seals and seating load evaluation methods are detailed.

Multi-Variant Modal Analysis Approach for Large Industrial Machine

Power generation technologies are essential for modern economies. Modal Analysis (MA) is advanced but well-established method for monitoring of structural integrity of critical assets, including power ones. Apart from classical MA, the Operational Modal Analysis approach is widely used in the study of dynamic properties of technical objects. The principal reasons are its advantages over the classical approach, such as the lack of necessity to apply the excitation force to the object and isolate it from other excitation sources. However, for industrial facilities, the operational excitation rarely takes the form of white noise. Especially in the case of rotating machines, the presence of rotational speed harmonics in the response signals causes problems with the correct identification of the modal model. The article presents a hybrid approach where combination of results of two Operational Modal Analyses and Experimental Modal Analysis is performed to improve the models’ quality. The proposed approach was tested on data obtained from a 215 MW turbogenerator operating in one of Polish power plants. With the proposed approach it was possible to diagnose the machine’s excessive vibration level correctly.

Structural identification of the dynamic behavior of floor diaphragms in existing buildings

The deformability of floor diaphragms plays a primary role in the structural behavior of existing buildings. Nonetheless, few structural identification procedures are available to investigate this matter from in-situ experimental measurements. Ambient vibration tests can be very useful to the purpose, allowing to assess the importance of the floor deformability in operational modal analyses through model-driven approaches. This information is particularly valuable for unreinforced masonry buildings, often characterized by deformable diaphragms whose effective stiffness is commonly unknown and hard to be evaluated. Based on these motivations, in this paper, a discrete linear model of deformable diaphragm is formulated in a novel fashion. The modal properties governing the free undamped dynamics are analytically determined through a fully general perturbation technique (direct problem). Therefore, a model-based structural identification procedure is proposed to analytically assess the inertial and elastic properties of the deformable diaphragm (inverse problem), assuming the outcomes of experimental modal analyses as known input. Consistently with the perturbation approach, explicit formulas are determined for low-order minimal models and higher-order model updating, accounting for mass and inertial eccentricities. Among the other identifiable mechanical parameters, the focus is put on the first and second-order identification of the in-plane shear stiffness of the diaphragm. The theoretical developments are successfully verified on pseudo-experimental and experimental bases, by applying the identification procedure to (i) the computational model of a prototypical steel frame structure, (ii) the large scale laboratory model of a two-story composite structure with mass eccentricities, (iii) a permanently monitored masonry building recently struck by the 2016-2017 Central Italy earthquake sequence.

Ambient vibration based-simplified frequency formulas for historical masonry stone mosques with timber truss roofs

ABSTRACT Historical masonry stone mosques with timber truss roofs were widely constructed all over the world. Due to the complex structural behaviors of this type of building, it is difficult to determine natural frequencies during the seismic safety evaluations numerically. The article aims to develop simplified natural frequency formulas based on ambient vibrations for the historical masonry stone mosques with timber truss roofs. Fourteen masonry stone mosques with timber truss roofs built in the Eastern Black Sea Region of Turkey are selected for the study. Experimental natural frequencies, mode shapes and damping ratios of the selected mosques under ambient vibrations are determined using the Operational Modal Analyses. Ambient vibration-based simplified natural frequency formulas based on the geometrical dimensions for the masonry stone mosques with timber truss roofs are obtained by using the statistical regression analysis. The proposed formulas for the first three frequencies are verified with the control data.

A simplified frequency formula for post-tensioned balanced cantilever bridges

The aim of this study is to develop a simplified natural fundamental frequency formula for the post-tensioned balanced cantilever bridges using the Operational Modal and Finite Element Analyses results. For this purpose, experimental and numerical studies were carried out on the five post-tensioned balanced cantilever bridges constructed in the city of Artvin, Turkey. First, the experimental and theoretical dynamic characteristics of the selected five bridges were determined using the ambient vibration-based Operational Modal Analysis and Finite Element Method, respectively. Then, the bridge model, which is given the highest correlation between the experimental and theoretical frequencies, was selected to determine the most important parameters that affected the modal behavior of the bridges. The most important parameters were determined as bridge length and pier height. Theoretical modal analyses were carried out for a series of bridge models with different lengths and heights. Finally, a simplified fundamental frequency formula was developed for the post-tensioned balanced cantilever bridges using the method of least squares considering the frequency values obtained from the theoretical modal analyses of the bridge models. The developed formula was checked with the experimentally obtained values, and it was observed that both sets of results were close to each other.

Restoration effects on experimental dynamic characteristics of masonry stone minarets

Masonry minarets are sensitive to wind and earthquake forces due to their slenderness and supporting structural system. They are restored in order to safely transfer to future generations. This paper investigates the restoration effects on the dynamic characteristics of masonry stone minarets using ambient vibrations tests. Three historical masonry stone minarets restored by the Regional Directorate of Foundation in Trabzon, Turkey are selected for this purpose. Restorations works such as re-pointing of joints, renewing spoiled stones, scraping cement-based plaster layer coating, rebuilding upper part wall of the minaret balcony, wall surface cleaning and renewing wooden cone were implemented in the selected three minarets. The experimental dynamic characteristics of the selected minarets before and after restoration are determined by Operational Modal Analyses Method using the ambient vibrations. The natural frequency, mode shapes and damping ratios obtained before and after restorations are compared with each other. It has been shown that the dynamic characteristics of the three minarets are positively and negatively affected depending on the restoration works.

Intense vibration mechanism analysis and vibration control technology for the combustion chamber of a liquid rocket engine

High-amplitude vibration in the combustion chambers of large-thrust liquid rocket engines (LREs) has been the main concern of aerospace structural engineers in China for many years. Excessive vibration poses a serious threat to the structural safety of engine and the reliability of system operation. In this study, the structural vibration and gas pulsation data of an LRE during an intense-vibration test condition were analysed in detail. The coupling characteristics between the sound pressure and the vibration signal of a combustion chamber were determined. A 3D dynamic model of the combustion chamber structure was then established with the modelling method of the corrugated composite sandwich plate. The accuracy of the model was verified by the results obtained from operational modal analyses of an engine hot test. Moreover, a novel vibro–acoustic coupling analysis method was proposed, and a vibro–acoustic coupling model for the combustor was established. By examining the acoustic and structural dynamic characteristics and acoustic–solid coupling relationship of the combustor, we were able to show the mechanism of intense vibration under the coupled resonance of acoustics and vibration. Finally, an engineering solution for suppressing the intense vibration of combustion chamber structures was proposed. We found that the intense vibration of the combustion chamber was caused by the ‘rough combustion’ or ‘oscillatory combustion’ in the combustor. The first-order longitudinal acoustic mode coupled with the three-node diameter structure mode, and thus formed a coupled resonance and generated a high dynamic gain because of the chamber pressure pulsation. The most effective and economical means of intense vibration suppression in combustion chamber structures is to decouple the acoustic–vibration coupling mode through structural improvements. In this way, the anti-resonance margin of the improved structure became larger than 7.5%. With the improved design, the vibration acceleration of the combustion chamber was reduced by two-thirds, and the effectiveness of the improvement measures was verified.

Assessing the impact of retrofitting on structural safety in historical buildings via ambient vibration tests

Historical structures are generally vulnerable to damages under earthquakes over the course of their life and are subject to be retrofitted to preserve the heritage against any possible extreme loads, particularly earthquakes. This process is handled via analysis by taking into account existing condition of the buildings, however, there are few studies focusing on the effectiveness of the applied retrofitting solutions. Therefore, there is a growing need to understand and compare the earthquake behavior of historical structures before and after retrofitting states. This paper aims at investigating the structural behavior of a historical timber/masonry building for conditions both before and after the retrofitting of the building. To enable a comparison for conditions, firstly theoretical finite element models were developed and then experimental operational modal analyses of the historical building were performed. Secondly, the experimental data regarding the dynamic response of the structure was obtained by ambient vibration tests and finite element models were updated. Two final updated models representing before and after the retrofitting states were developed. The final models selections were based on the convergence between the experimental and analytical natural frequencies, and the mode shapes. The updated final models enable to assess the earthquake behavior of the structure for both before and after retrofitting states. Furthermore, updated finite element models of the building for both before and after the retrofitting states were analyzed by a recorded earthquake in Turkey. Dynamic responses of the structure including principal stresses and displacements before and after retrofitting were compared and the impact of retrofitting is evaluated. The results show that the stiffness of the retrofitted structure has increased 3 times compared to its initial condition. The finding of this study will be beneficial to develop FEM models for a wide range of possible future retrofitting solutions.

Dynamical analysis of stroke induced vibrations in tennis racket

Tennis rackets are mostly designed disregarding the boundary condition managed by the player's hand on the handle. This process leads to a lack of accuracy in the mechanical parameters the manufacturers provide to their rackets in order for them to be reliable and comfortable to the player. Our work aimed at providing a better understanding of the effect of the tennis player's hand on the racket's dynamical behavior. For this purpose, a dedicated experimental procedure involving 14 tennis players and 5 tennis rackets has been carried out. Vibrations propagated from the racket toward the upper-limb have been collected synchronously with kinematic and electromyographic data during forehands of various intensities. Additionally, an analytical model of the hand/racket interaction has been designed based on operational modal analyses. This model provides a straightforward tool to predict changes in the dynamical behavior of a tennis racket under playing conditions. Results indicated that tennis players adjust their grip-force to tune the vibrational content entering into his upper-limb. Besides, a noteworthy outcome is that grip-force induces modifications in the racket's dynamical behavior that are at least as important as the differences observed under free boundary conditions due to the rackets' own mechanical parameters.

The effects of player grip on the dynamic behaviour of a tennis racket

ABSTRACTThe aim of this article is to characterise the extent to which the dynamic behaviour of a tennis racket is dependent on its mechanical characteristics and the modulation of the player’s grip force. This problem is addressed through steps involving both experiment and modelling. The first step was a free boundary condition modal analysis on five commercial rackets. Operational modal analyses were carried out under “slight”, “medium” and “strong” grip force conditions. Modal frequencies and damping factors were then obtained using a high-resolution method. Results indicated that the dynamic behaviour of a racket is not only determined by its mechanical characteristics, but is also highly dependent on the player’s grip force. Depending on the grip force intensity, the first two bending modes and the first torsional mode frequencies respectively decreased and increased while damping factors increased. The second step considered the design of a phenomenological hand-gripped racket model. This model is fruitful in that it easily predicts the potential variations in a racket’s dynamic behaviour according to the player’s grip force. These results provide a new perspective on the player/racket interaction optimisation by revealing how grip force can drive racket dynamic behaviour, and hence underlining the necessity of taking the player into account in the racket design process.

Damage evaluation in high-rise buildings using one modal eigenpair

A development of the ‘first-order storey pseudo-stiffness-based damage index’ of high-rise buildings is presented in this article. The proposed damage index is based on identification of an input set of one modal eigenpair, consisting of one modal frequency and the corresponding mode shape, overcoming the need and the difficulties of identifying multiple sets of eigenpairs in operational modal analyses of multistorey buildings. The calculation of first-order storey pseudo-stiffness-based damage index is expressed as a simple numerical procedure for comparison between the dynamic parameters of undamaged and damaged structures. The accuracy of the proposed damage assessment approach has been verified in two different tests – numerical and experimental. The numerical tests are based on the calculation of first-order storey pseudo-stiffness-based damage index in numerical models in which the structural damage is simulated with previously defined storey stiffness degradation. The experimental test consists of first-order storey pseudo-stiffness-based damage index accuracy test on the structure of the Urban Disaster Prevention Research Center, located in Tsukuba, Japan, and comparison to the results obtained by previously proven accurate damage detection method. The test results have shown that the proposed first-order storey pseudo-stiffness-based damage index index, based on the first modal eigenpair, can be applied as an instant damage detection method in structural health monitoring of multistorey buildings, providing the location and severity of structural damage.

Structural Health Monitoring of Major Danube Bridges in Bratislava

The paper presents some of the intermediate results obtained in the framework of the research program APVV No. 0236-12 granted by the Slovak Research and Development Agency entitled “Bridge Structural Health Monitoring via Repeated Dynamic Tests”.The paper describes initial structural health monitoring (SHM) tests of the Port Bridge and of the Slovak National Uprising Bridge across the Danube River in Bratislava, Slovakia. The first one is a highway and railway continuous steel truss bridge with 4 spans and a total length of 460.8 meters (largest span 240.8 m). The second one is an asymmetric cable-stayed steel bridge with an orthotropic 2-box beam supported in one plane by cables from an inclined pylon. The total length is 431.8 meters (largest span 303 m). The paper is aimed at different topics: the description of the test setups, the measuring accelerometer polygons synchronized by Wi-Fi connection, synchronization of the video footage with the measurements, etc. Some natural frequencies and mode shapes have been identified from the operational modal analyses.

Investigation of a historic masonry structure by numerical and operational modal analyses

SummaryThis paper presents the results of model calibration conducted on a historical mosque called Hafsa Sultan in Manisa, Turkey. The finite element model of the mosque was calibrated by the use of the results obtained from ambient vibration tests of the structure. In order to develop a solid model of the structure, the dimensions of the structure, defects such as cracks and material degradations in the structure, and the materials used in different parts were identified. For the evaluation of the material properties of the structure, nondestructive and destructive testing methods were used. The numerical and experimental modal parameters of the structure were obtained by finite element method (FEM) and Operational Modal Analysis (OMA), respectively. The natural frequencies and corresponding mode shapes were obtained from both FEM and OMA and compared with each other. While a good compatibility was achieved between mode shapes, some differences between natural frequencies occurred. It was thought that the differences resulted from variations in the Young's modulus of masonry, cracks in elements or boundary conditions. Therefore, the finite element model was calibrated by changing material parameters. Finally, a more realistic numerical model of the mosque was put forward and the results were discussed in detail. Copyright © 2015 John Wiley & Sons, Ltd.