Modal Test Data Research Articles

Damage identification of reinforced concrete slabs using experimental modal testing and finite element model updating

Condition assessment and health monitoring of reinforced concrete structures is an essential part of their effective maintenance throughout their service life. Vibration-based damage detection and health monitoring is one of the most popular global approaches where experimentally measured modal parameters, such as frequencies, mode shapes, etc. are compared to their corresponding finite element counterparts to estimate possible stiffness loss. The present investigation implements a vibration-based parameter estimation algorithm for updating a finite-element (FE) model for damage assessment of reinforced concrete slabs using measured frequency response functions (FRF) data through a mixed numerical-experimental technique. An inverse eigen-sensitivity algorithm has been implemented to minimize the error function realized as the weighted differences in the mode shapes and frequencies of the FE model and the modal test data. Three reinforced concrete slabs were subjected to real physical damage conditions to verify the efficacy of the proposed methodology. The technique is found to be resilient in the presence of modal and coordinate sparsity. In general, damage can be assessed even if the portions of the structure are inaccessible to the users, thereby extending the possibility of its application to most of the practical configurations of reinforced concrete slabs.

Advancing Mistuning Identification and Dynamic Modeling of Blisks Through Blade Detuning Tests

Blisks extensively used in advanced aeroengines are vulnerable to vibration problems due to the high sensitivity of the blisk’s forced response to blade mistuning. This paper proposes an emerging mistuning identification technique based on blade detuning tests (BDTID) for predictive dynamic modeling of blisks. The conventional frequency-mistuning modeling approaches relying on blade mistuning identification by reduced-order model techniques and modal test data of the full blisk are also adopted to construct different mistuned models of a blisk test piece for comparison purposes. A complete assessment of these blisk models is achieved through the forced response tests in a stationary traveling wave excitation test rig. The BDTID consists of blade-detuning tests followed by a correction procedure. The detuning tests enable us to approximately evaluate the “blade-alone” frequencies through blade-by-blade impact testing in combination with a mass detuning mechanism. The correction procedure is able to evaluate the detuning test quality by the quantification of the residual interblade coupling due to mass detuning. More importantly, a robustness investigation demonstrates that this procedure is able to capture the “true” blade mistuning even in cases of poor blade detuning test quality. The resultant mistuned blisk model exhibits high accuracy in the modal correlation and forced response validation results. Compared with conventional methods, BDTID takes advantage of easy implementation with less experimental effort and has proven robust performance. It is therefore recommended for blade mistuning identification and predictive blisk dynamic modeling in a wide variety of scenarios.

Dynamic modeling and analysis of the rotor–stator coupling system of a coaxial contra-rotating gearbox

In this paper, a main gearbox using an encased differential gear train to achieve coaxial contra-rotating is considered, and a dynamic modeling method of the rotor–stator coupling system of the gearbox based on box model updating is introduced. The transverse torsional dynamic model of the gear transmission subsystem is established based on the lumped parameter method. The finite element model of the box is updated according to the modal test data, and the reduced dynamic parameters of the box are obtained. According to the displacement coordination condition, the dynamic model of the rotor–stator system of the gearbox is established. The vibration response of the transmission components with or without the coupling box is calculated by numerical integration, and the response of the box caused by the dynamic support reaction force is analyzed by the finite element method. The results show that the vibration peak and fluctuation range of the transmission parts with coupling box are smaller than those without coupling box. The box response at the support of the input bevel gear pair is large, while that at the support of the output shaft is small.

Research on Modal Test Method for Civil Aircraft Structure

In the process of civil aircraft development, it is of great significance to carry out a modal analysis of aircraft component structures and obtain modal parameters to verify whether the dynamic characteristics of aircraft structures meet the design requirements. This paper takes the structural modal of aircraft components as the research object and proposes the modal test method of aircraft structure, which provides effective modal test data support for the design and optimization of aircraft component structure.

Defect identification in electro-mechanical assembly using finite element method and modal assurance criterion

Globally automotive industry is going through a critical transition from gasoline vehicle to electric and hybrid electric vehicle. These changes have challenged industry with completely different vehicle driveline architecture. These systems have more electro-mechanical components which need to be critically designed for the vibration, thermal, structural and shock related requirements. Design for vibration endurance has been a major requirement and robust matured design of these systems may take several design iterations. Finite element models give us freedom to simulate and analyze design performance before actual prototype building. Simulation results can be predicted more accurately if model fidelity is strong enough. To have strong model fidelity, modal test data correlation is an important step towards robust design. In this paper, study on Test-FE model correlation has been performed for an electro-mechanical assembly using Modal Assurance Criterion. During the entire correlation study, it was assumed that the DUT was undamaged and entire focus of the work was towards improving FE model fidelity. But obtained results pointed the inconsistency between the FE model and test results at a specific region which later has been captured as a defect in the DUT. The results of this paper can help in identifying anomalies in actual product samples and in taking decision on testing other samples.

Flow-Induced Vibration Hybrid Modeling Method and Dynamic Characteristics of U-Section Rubber Outer Windshield System of High-Speed Trains

The flow-induced vibration characteristic of the U-section rubber outer windshield structure of high-speed train is the key factor to limit its high-speed movement. Accurate and effective flow-induced vibration analysis of windshield structures is an important topic. In this paper, a hybrid modeling method for the analysis of flow-induced vibration of windshield structure is innovatively proposed for the U-section rubber windshield system of high-speed train. The method uses the external aerodynamic load obtained by aerodynamic simulation as the input condition of the flow-induced vibration model, and maps the aerodynamic load to the structural dynamics model characterized by the modal test data of the windshield structure. The flow-induced vibration model is established by means of modal superposition method and the time-domain response is effectively integrated by Runge Kutta method with variable step size. The results show that this method can effectively simulate the flow induced vibration of the wind baffle structure, and the real-time relationship between the aerodynamic load and the modal characteristics of the structure and the response of displacement and velocity can be obtained. On this basis, the comprehensive dynamic performance of the windshield system of high-speed trains at 400 km/h under external aerodynamic load is studied, that is, the force, displacement and velocity variation rules of the flexible structure are examined. It is determined that the displacement and velocity response curve of the measuring point near the lower side of the U-section rubber outer windshield is significantly higher than that of other parts. Moreover, the contribution of the first mode to the dynamic response of the structure is very obvious. This method provides an efficient calculation method for analyzing the flow-induced vibration characteristics of complex flexible structures.

Transient response of fluid-surrounded core barrel under earthquake excitations bearing different frequency contents

Seismic evaluation of nuclear reactor components plays an important role in enhancing the seismic safety of nuclear reactor components. The frequency content in earthquakes has a significant impact on the response. This paper reports the numerical research with regard to the response of Hualong Pressurized Reactor (HPR) core barrel surrounded by fluid and suffering from earthquakes bearing different frequency contents. A newly developed added mass formula is utilized to model the effect of fluid on the core barrel, and three earthquakes including low, intermediate and high frequency contents are used to excite the core barrel. After model validation by using modal test data, a transient finite element procedure is carried out to obtain the displacement, velocity and stress intensity responses. Collectively, the results indicate that the core barrel exhibits forced vibration behavior. Contrary to expectations, the earthquakes bearing intermediate frequency content causes the strongest displacement and stress intensity responses (the maximum stress intensity and maximum displacement are 1.286 times and 1.297 times those of the earthquakes bearing low frequency content). These findings indicate that the use of earthquakes bearing intermediate frequency content in the design stage allows higher conservation of the HPR core barrel.

基于模态试验的揉碎机振动特性分析

Aiming at the problems of large vibrations and noise of a working stalk rubbing machine, this paper took the 9R-60 rubbing machine as the research object and used the B&K modal test system and the vibration test system to analyse the modal and no-load conditions of the whole machine. Through analysing modal test data, it was concluded that the first five natural frequencies of the machine were 95.262 Hz, 144.386 Hz, 288.198 Hz, 313.719 Hz and 326.140 Hz. The results showed that spindle rotation had a more significant effect on the vibration than the feed chain rotation; the maximum vibration acceleration occurred at the small motor frame at a spindle speed of 1700 r·min-1 and a feed chain speed of 0.65 m·s-1, which was 135.539 m·s-2. The distribution of the amplitude statistical characteristics of the vibration signals follows the normal distribution and belongs to the stationary random process. The vibration was a self-excited vibration of the rotating machinery caused by the rotation of the main shaft and a forced vibration excited by the rotation of the same shaft. The research provides a direction for further research on the vibration characteristics of the rubbing machine under load conditions, and provides a theoretical basis for the subsequent vibration reduction design.

Research on Load Reverse Engineering and Vibration Fatigue Analysis Technology of Rapid Box Wagon

The overall stiffness and modal frequency of the car body of a rapid box car are reduced by the design of the full-side open movable side door structure. The vibration fatigue performance of the welded structure in this car body needs to be verified. The rigid-flexible coupling model of the rapid box wagon was established first, and the model was verified by modal test data. By the application of the virtual iteration method on this model, the displacement excitation loads of this vehicle were acquired. The effectiveness of the load reverse obtaining technology was verified through the comparison between calculated data and the experimental data. Based on the rigid-flexible coupling model and the load obtained by reverse engineering, the fatigue life of the welded structure in the car body was evaluated through the modal structural stress method. The calculated results show that the car body structure obtains obvious modal vibration, which leads to short fatigue life in several weld lines. According to the application requirements of this wagon, the local improvement scheme was proposed, and the effect of the improvement program was evaluated. In this paper, a new fatigue evaluation technology based on the load reverse method of test data was proposed, which provides a theoretical basis for the structural design and program improvement of railway vehicles.

Gaseous Detectors for Field Applications: Quality Control, Thermal and Mechanical Stability

A cosmic muon imaging system is essentially a particle tracking detector as known from experimental High Energy Physics. The Multiwire Proportional Chamber (MWPC) once revolutionized this field of science, and as such it is a viable choice as the core element of an imaging system. Long term construction and operation experience was gathered from a Japanese–Hungarian collaboration that gave rise to the MWPC-based Muon Observatory System (MMOS), and is being used in Japan at the Sakurajima volcano. The present paper attempts to draw conclusions on the thermal and mechanical limits of the system, based on controlled measurements and detailed simulations. High temperature behavior and effects of thermal cycling and conditioning are presented, which appear to consistently allow one to propose quality control criteria. Regarding mechanical stability, the relation between gluing quality (tensile strength) and expected stress from vibration (during transportation) determines the safety factor to avoid damages. Both of these are presented and quantified in the paper using a conservative and austere approach, with mechanical simulations validated with experimental modal testing data. One can conclude that mechanical stress during industrial standard air freight shipping conditions is nearly a factor of three below the calculated maximum stress.

A direct method for the simultaneous updating of finite element mass, damping and stiffness matrices

This paper is mainly concerned with a model updating problem for damped structural systems, which can be described as the following inverse quadratic eigenvalue problem (IQEP) and an optimal approximate problem (OAP). Problem IQEP: Given matrices and with , for , , and both Λ and X being closed under complex conjugation, find real symmetric matrices M, D and K such that . Problem OAP: Given real symmetric matrices and , find such that , where is the solution set of Problem IQEP and is a weighted Frobenius norm. The representation of the general solution to Problem IQEP and the explicit formula for the optimal approximate solution of Problem OAP are given by applying the singular value decomposition. A given numerical example shows that the updated model can be in good agreement with the modal test data.

Modal testing and evaluation of cracks on cantilever beam using mode shape curvatures and natural frequencies

This paper presented the process of implementing and developing a novel damage detection approach on beam like-structure using modal parameters. In Theoretical Modal Testing (TMT), the mode shapes, mode shape curvatures and natural frequencies were extracted by formulating differential equations of motion of un-cracked and cracked beams. In Experimental Modal Testing (EMT), the transient excitation method of modal testing is performed by using an impact hammer test. EMT involves an extraction of natural frequencies through frequency response functions at various surface cracks on the beam in a virtual instrumentation environment. Cantilever beams of Aluminum 6061 is considered for analysis with crack position at the interval of 50 mm from fixed end to free end at varying crack depths 20%, 40% and 60% of the beam total depth. The modal data from experimental modal testing was validated with theoretical modal testing data. It was observed that there was a minor change in lower modes; major change in natural frequencies for higher modes with the variation of damage location/depths. To overcome the difficulty in crack detection of structures based on mode shapes and frequencies individually, both the parameters mentioned are collectively used in this work as Frequency-Modeshape Based Damage Detection Technique (FMBDD) to evaluate the crack location as well as crack depth easily and accurately.

Finite element model updating of metallic and composite structures-A state of the art review

<abstract> Finite element model updating (FEMU) is a technique to improve the analytical finite element (FE) model of any structure from its experimental modal test data. The main purpose to apply FEMU on structures is to remove the uncertainties or errors present in the analytical FE model. The main objective of this paper is to present a review on the various FEMU techniques which can be applied to remove the uncertainties present in the FE model of the actual engineering structures. Applications of various FEMU techniques on the metallic and the composite structures have been discussed in this review paper. FEMU is applied on the metallic and the composite structures to remove the error present in their FE models. The main objective of the FEMU is to accurately predict the modal analysis characteristics such as the spatial-model, modal-model and the response model of the structures. The uncertainties present in the analytical or simulated FE model of any structure may be due to its material properties, dimensions and most probably due to the uncertainties present in the boundary conditions of the structure. However, to provide a sufficient strength to this review paper, the different updating methods are applied on the three degree of freedom spring mass system, on a 1-D aluminum beam, 2-D aluminum panel and on a graphite-epoxy composite material laminate. It is found that the updating algorithms are fast and reliable enough to remove error present in the numerical or simulated FE model of the structures and deliver the accurate estimation of the spatial-model, modal-model and response model of the different material structures. </abstract>

Stability Improvement of Brake Disc to Mode Coupling at High Frequency Squeal

In this research study, the high-frequency squeal noise of a brake disc was found to occurred at a frequency of about 15 kHz. The potential root cause has been studied where mode frequency coupling and shape locking mechanism of brake disc and brake pads components are the main investigated topic. From the vehicle field test and the Dynamometer test, the braking condition, friction coefficient and braking pressure, have been confirmed to be used in numerical experiments. The updated finite element model (FEM) with the modal testing data of the existing brake components are formulated for the Complex Eigenvalue Analysis (CEA). In this study, the modification is based on in-board and out-board cheek thickness of the brake disc. Two of nine modifications of the brake disc cheek thickness are proposed with the method of separation the brake disc out-of-plane and in-plane modes and the method of avoiding shape locking between the brake disc and the brake pads modes. The constructed prototypes are verified with the vehicle field test and well agreed with the CEA.

Evaluation of two crack models for reinforced concrete one-way slabs subjected to bending by means of modal tests

Cracks can affect a reinforced concrete (RC) structure and the evaluation of damage related to them is a typical application of structural health monitoring systems. This way, two RC one-way slabs with different reinforcement ratios were tested in laboratory in a four-line static load test scheme, followed by modal testing. Using modal testing data, finite element models of the cracked structures were prepared and calibrated for several cracked stages, to evaluate which crack model would present a better performance when compared to the experimental counterparts. Cracks were simulated via a reduction of flexural stiffness by penalizing the elastic modulus. Two continuous crack models were evaluated: Model 1 which employs reduction factors based on the ratio of moment of inertia after the cracking moment is reached and the moment of inertia of the uncracked section; Model 2 which is based on the stiffness reduction in the region of influence of each crack. The evaluation of both models was made using natural frequencies and mode shapes (through Modal Assurance Criterion-MAC indicator) as indicators, and Model 2 presented better results. An additional approach to globally reduce stiffness in the early stages of load before visible cracks appear and also in uncracked regions was shown necessary, to take into account the reductions on natural frequencies observed in the tests. By employing the stiffness reduction factors obtained for Model 2 it was possible to evaluate the crack depth evolution along the load stages.

Correlating Finite Element Model of a Car Spot-welded Front-End Module in the Light of Modal Testing Data

Model updating methods can be adopted to improve the correlation level between the finite element model of a spot welded structure and its test model. However, in the presence of contact interfaces in the vicinity of the welded areas, improving the correlation level is problematic and challenging. An approach for correlating the finite element model of a welded structure with contact interfaces using finite element model updating and modal testing is proposed. The proposed approach was tested on a car front-end module structure that consisted of nine components and 76 resistance spot-welded joints used to assemble the components. CWELD and CELAS1 element connectors were used to represent the spot-welded joints and contact interfaces in the finite element modelling and updating. This approach was applied successfully to predict the modal parameters of the car spot-welded front-end module. The total error of the initial finite element model of the structure was reduced from 27.13% to 5.75%. The findings of this work suggest that the proposed approach has a great potential for use in investigating the dynamic behaviour of various spot-welded structures without a significant decline in accuracy.

A modified elastic contact stiffness model considering the deformation of bulk substrate

Establishing an accurate and effective stiffness model of the elastic contact surface is the basis for further modeling and analysis of machine tool dynamics. In this paper, a new elastic contact stiffness model is proposed that considers the bulk substrate deformation and modifies the Greenwood and Williamson microcontact model (GW model) of rough surfaces. Based on the Hertz contact theory and fixed-point iteration method, a single asperity contact model is created to analyze the effects of bulk substrate deformation and coating materials. To make the contact stiffness model more accurate and effective, two aspects are improved: One is to introduce the triangular distribution function to make the asperity heights distribution more consistent with the actual machined surface, and the other is to correct the defects in the micro-contact process. Comparing the finite element simulation results with the modal test data, the correctness of the proposed contact stiffness model is verified. The simulation results reveal the influence of distribution function, surface roughness and coating material on the contact characteristics of the joint surface.

Finite element model updating of a composite material beam using direct updating method

Finite element model updating is a technique to improve the simulated finite element model of a structure from its experimental modal test data. This paper utilizes the direct updating algorithm for a composite material beam to update its modal-model.In this paper, initially finite element model updating of the steel beam is carried out. There are different types of possible errors may in the finite element model of a steel beam such as in the geometry, material properties, boundary conditions, and in joints etc. The finite element model of the beam is carried out by assuming the uncertainty in the Young’s modulus of the beam, named as “un-correct model or a simulated model”. Another finite element model of the beam has built up with no uncertainty, named as “correct model or experimental model”. It is assumed that the experimental model is correct and represents the actual/real experimental conditions and properties of the steel beam structure. The objective of the direct updating method is to update or correct the simulated finite element model of a steel beam by using the experimental finite element model data.The main objective of this paper is to update the analytical finite element model of the composite beam by using direct updating method. The uncertainties in the simulated finite element model of the composite structures may be in the modulus of elasticity of the fibers and matrices, individual densities, modulus of rigidity, and most importantly in the fiber orientations. The simulated finite element model of the composite beam is carried out by taking all the above uncertainties and corrects it by using the direct updating method. It is found that direct updating method is simple and easy to apply for composite structures and can effectively correct the simulated finite element model from the experimental modal data.

Structural dynamic design optimization and experimental verification of a machine tool

Structural dynamic performance of a machine tool greatly affects machining precision and productivity. One effective approach in improving the dynamic performance is by applying topology design optimization to the machine tool structure. However, traditional topology optimization method is hard to implement and does not provide a clear stiffener layout. Furthermore, the topology optimization of certain components does not signify the performance improvement of a holistic machine tool. This paper suggests a new structural dynamic design optimization method for the holistic machine tool. The Adaptive Growth Method which is based on the growth mechanism of natural branch systems is adopted to design the inner stiffener layout of structures, and an optimization strategy for the holistic machine tool utilizing dynamic sensitivity analysis is studied. Both components and contact parts are considered. The dynamic sensitivities of the components are analyzed based on modal test data, and help to determine which components need to be optimized. Then, the headstock, column, and bed are optimized, and the weak contact stiffness is improved. The FEA (finite element analysis) results of an optimized machine tool show that the TCP (tool center point) harmonic displacement is decreased distinctly. To validate the effectiveness of the suggested method, an experiment of the manufactured machine tool structure is conducted, and the experimental results had shown great improvements in the holistic machine tool.

Lumped-Parametric Modeling Based on Modal Test and Analysis of Vibration Characteristics of the Hard-Coated Blisk

To apply the hard-coated damping technology on the blisk with more obvious effect, it’s indispensable to develop the dynamic model of the hard-coated blisk to realize the prediction and design of the damping effect of the coating. In this paper, a method of establishing a lumped-parametric model based on the modal test data of the blisk before and after coating was proposed. The stiffness and material damping of hard coating was described by complex stiffness, and a two-degrees-of freedom lumped-parametric model and the equation of motion were established. Meanwhile the method of solving the natural characteristics and vibration responses was provided. Then, the identification of parameters needed for dynamic modelling was realized using modal data obtained by experiment. A case study was carried out by taking the blisk with NiCrAlCoY + YSZ hard coating as an example, and the natural characteristics and vibration responses of the uncoated and coated blisks were calculated with the proposed lumped-parametric model. The results were contrasted with the experimental data and the FEM (finite element method) results, which proved the validity of the lumped-parametric model of the hard-coated blisk. In addition, the analysis results indicate that the hard coating has a significant effect on the vibration reduction of blisk.