Experimental Modal Analysis Method Research Articles

Crack localization in glass fiber composite beams by experimental modal analysis and multi variable Gaussian process regression method

PurposeEnsuring the early detection of structural issues in aircraft is crucial for preserving human lives. One effective approach involves identifying cracks in composite structures. This paper employs experimental modal analysis and a multi-variable Gaussian process regression method to detect and locate cracks in glass fiber composite beams.Design/methodology/approachThe present study proposes Gaussian process regression model trained by the first three natural frequencies determined experimentally using a roving impact hammer method with crystal four-channel analyzer, uniaxial accelerometer and experimental modal analysis software. The first three natural frequencies of the cracked composite beams obtained from experimental modal analysis are used to train a multi-variable Gaussian process regression model for crack localization. Radial basis function is used as a kernel function, and hyperparameters are optimized using the negative log marginal likelihood function. Bayesian conditional probability likelihood function is used to estimate the mean and variance for crack localization in composite structures.FindingsThe efficiency of Gaussian process regression is improved in the present work with the normalization of input data. The fitted Gaussian process regression model validates with experimental modal analysis for crack localization in composite structures. The discrepancy between predicted and measured values is 1.8%, indicating strong agreement between the experimental modal analysis and Gaussian process regression methods. Compared to other recent methods in the literature, this approach significantly improves efficiency and reduces error from 18.4% to 1.8%. Gaussian process regression is an efficient machine learning algorithm for crack localization in composite structures.Originality/valueThe experimental modal analysis results are first utilized for crack localization in cracked composite structures. Additionally, the input data are normalized and employed in a machine learning algorithm, such as the multi-variable Gaussian process regression method, to efficiently determine the crack location in these structures.

Dynamic field load testing of a horizontally curved longspan LRT Kuningan bridge using eccentric mass vibrator and experimental modal analysis

Light Rail Transit (LRT) infrastructure in Indonesia is developing at a rapid pace. The LRT challenging construction is the Kuningan-Longspan Curved bridge with a span of 148 meters and the radius of curvature R = 115 meter. Therefore, Kuningan LRT Bridge is considered as one of the longest concretes curved balanced cantilever LRT Bridge in the world. The implementation of bridge regulations in Indonesia requires a functional feasibility test before the bridge is operational. In the case of the Kuningan LRT bridge, functional feasibility tests were carried out in the form of static and the dynamic tests. The dynamic load test aim is finding the structure natural frequency in the vertical, Longitudinal and Transverse direction. There are 3 methods that being used to measure the dynamic parameters of the train bridge structure in Indonesia. The first method is the Impulsive method using the moving train with the speed of 25 Km/hour as a load. The second method is the usage of The Experimental Modal Analysis and the third method is the combination method of Experimental Modal Analysis with a vibrating instrument in the form of an Eccentric Mass Vibrator (Exciter). The experiment results and the modal fem from the designer is compared and presented in this paper.

Strain experimental modal analysis of an Euler–Bernoulli beam based on the thermoelastic principle

The strain mode shapes can be utilized as an indicator of vibration fatigue-hotspots and are utilized for predicting the distribution of damage intensity. However, the conventional approach for measurement, which involves using strain sensors, does not offer the necessary high spatial density required for accurately identifying critical locations or creating a comprehensive map of damage intensity. Non-contact methods have been employed to indirectly determine the full-field strain shapes, but when measuring kinematic quantities, a relation between kinematics and stress/strain must be known. For Euler–Bernoulli beam, the double spatial derivative is required which introduces a significant uncertainty. In contrast, by leveraging the thermoelastic principle, the full-field stress/strain response of an arbitrary structure can be directly measured using a high-speed infrared (IR) camera. The thermoelastic principle has not been extensively researched for strain experimental modal analysis (EMA). In this study, the hybrid EMA (based on one high-dynamic range sensor) was researched for thermoelastic identification of an Euler–Bernoulli beam. The minimum stress/temperature variation required to achieve accuracy comparable to scanning-laser kinematics-based strain mode shapes was investigated. The findings demonstrate that even when the noise floor is significantly higher than the signal, full-field strain mode shapes can be identified using IR cameras and the hybrid EMA method. By considering the minimum stress/temperature variation determined in this research (for aluminum and steel), the accuracy of thermoelasticity-based strain shapes can be evaluated during the experiment-design stage. While this research is theoretically and experimentally based on Euler–Bernoulli beam, generalization of the thermoelastic principle to arbitrary structure is feasible.

Single-degree-of-freedom experimental modal analysis method using phase data of frequency response function

Single-degree-of-freedom experimental modal analysis method using phase data of frequency response function

A hybrid approach to derive macro- and meso-mechanic cell models for vibrational investigations of lithium-ion pouch cells

Lithium-ion batteries are the core component of every energy storage system in modern electric vehicles. In order to represent the multi-physical processes in these battery systems in simulations, different modeling approaches are needed depending on the application area. In this work, two methods are presented to derive state-of-charge dependent material models for lithium-ion pouch cells suitable for modal analysis using the finite elements method. As a starting point, the non-destructive measurement method of experimental modal analysis is performed at different states of charge. Using the Dakota optimization framework, material models are derived by minimizing the deviations between measured and calculated natural frequencies. On a meso-mechanic level, a homogenization approach is presented, which makes it possible to use material parameters from tensile and compression tests of the individual cell layers to derive material models for the calculation of natural frequencies at cell level. A method is described to perform state-of-charge dependent modal calculations on pouch cells. Thus, a practical approach was created to derive models for vibrational investigations from low-cost, standardized tests.

A novel identification technique of machine tool support stiffness under the variance of structural weight

The preload-dependent stiffness of machine tool support was investigated in this study. A novel identification method of support stiffness has been proposed through the experimental modal analysis and finite element method. The support stiffness was identified with different machine weight during the assembling process of a machining center. Specifically, the structure weight increase of a machine tool in the assembly process causes its center of gravity to shift. Accordingly, the variance of support reaction affects the support stiffness. To explore the variance of support stiffness, the researchers of this study collaborated with a machine tool manufacturer. Impact testing was performed on each assembly stage. Additionally, finite element analysis was used to establish equations between the reaction force versus stiffness of supports under the structural weight variance. The obtained equations were used to predict the natural frequency and vibration mode of structures in various assembly stages. The maximum error between the experimental and simulated natural frequencies was 7.1%, and the minimum modal assurance criterion was 0.77. Finally, a modal analysis model that updates support stiffness automatically, which could be adopted by machine builders to develop new machine tool, is proposed.

Joint modeling for the analytical estimation of dynamic behaviors of beam-coupled structures

In this study, analytical method is applied for the estimation of dynamic behaviors of beam-coupled structures. Mathematical expressions are given with terms of shape factors, material information and assembly angles of each sub-component. Based on Euler-Bernoulli beam theory, entire formulation is built with compatibility of system dynamics. The coupled structures are divided into two types, point coupling and mass coupling, related with the properties of coupling points. Point coupling is commonly used assumption that two sub-components are combined with lumped spring or damping, and mass coupling has undeformable rigid joint which has mass and inertia like welded structures. Dynamic properties of coupled structures are predicted in forms of frequency response functions and spectral responses about given forces. The verification process is conducted for assessing the accuracy of the estimation formula by using modal frequencies and mode shapes of beam-coupled structures. Extracted modal parameters from experimental modal analysis and finite element method are adopted as reference values for verification.

Experimental Validation of Finite Element Models for Reinforced Concrete Beams with Discontinuities That Form Dowel-Type Joints

Earthquakes have the highest rate of mortality among the natural disasters and regularly lead to collapsed structures with people trapped inside them. When a reinforced concrete building collapses due to an earthquake, many of the concrete elements (i.e., beams and columns) are damaged and there are large sections where the concrete is missing and the steel reinforcement is exposed (i.e., concrete discontinuities). The prediction of vibration transmission in collapsed and severely damaged reinforced-concrete buildings could help decisions when trying to detect trapped survivors; hence there is need for experimentally validated finite element models of damaged concrete elements. This paper investigates the dynamic behaviour of damaged reinforced concrete beams using Experimental Modal Analysis (EMA) and Finite Element Methods (FEM). FEM models are assessed using two beams with one or more concrete discontinuities that form dowel-type joints. These models used either beam or spring elements for the exposed steel bars and were experimentally validated against EMA in terms of eigenfrequencies and mode shapes. Improved agreement was achieved when using springs instead of beam elements in the FEM model. The comparison of mode shapes used the Partial Modal Vector Ratio (PMVR) as a supplement to the Modal Assurance Criterion (MAC) to confirm that spring elements provide a more accurate representation of the response on all concrete parts of the beams.

Analysis of the Creeping Phenomenon of Linear Feed System Based on the Rigid-Flexible Coupling Model

A mathematical model of the creeping phenomenon based on the mechanical model of the linear feed system was established. The dynamic characteristic parameters of each fixed joint were obtained by Yoshimura’s integral. Using the method, only the dynamic characteristic parameters of the joint surface per unit area with simple structure need to be studied, and then, the dynamic characteristic parameters of the whole joint surface can be obtained by integration. Based on the principle of the half-power bandwidth method and the frequency response function identification, the dynamic parameters of each moving joint were solved by the method of experimental modal analysis. Through the parameters of the fixed and moving joints, a rigid body model of the feed system and a flexible body model including the power transmission parts (ball screw pair) and the motion guide parts (guide slide pair and rolling bearing) were, respectively, established. And then, a rigid-flexible coupling dynamic model of the feed system was obtained through the constraint relationships between joints. The influence of both the external load and the feed rate on the fluctuation of motion speed of the system was analyzed from this model. The difference between the experimental results and the simulation results on a feed system platform is not greater than 10%, which verifies the creeping phenomenon. This conclusion can provide a basis for the optimization of the dynamic performance of the ball screw linear-feeding workbench.

Domestic Software Developed for Updating of Finite Element Models and Experimental Modal Analysis of Structures

Reinforced concrete structures used in many areas of our daily life constitute an important part of the building stock in the construction sector. There are many buildings such as reinforced concrete buildings, bridges, tunnels, mosques and dams, and the construction of new buildings in line with the need continues. Many uncertainty factors play a role in the design phase of these structures from the dimensioning as a result of the analysis performed under the required loadings to the implementation phase in the field. Many unpredictable factors such as errors in the analysis, defects in materials and workmanship affect the success rate of the project of the structure. For this purpose, Experimental Modal Analysis method, which is widely used in the literature, is used to determine the success rate of new structures, to determine the dynamic characteristics and damage conditions of existing structures and structural health monitoring. Natural frequencies, which are the dynamic variables of the structure obtained by experimental modal analysis techniques, and mode shapes and damping ratios corresponding to these frequencies are used in the examination of the current state and structural properties of the structures. However, this experimental data can be obtained by with foreign-source software by allocating large budgets. The results of the native experimental modal analysis and finite element model update software developed within the scope of doctoral thesis are compared with the results of the existing software in the literature. As the application, raw signal data of Gülburnu Bridge and scaled Type-1 Arch Dam constructed in laboratory environment were used. The experimental results of the developed software and the existing software were found to be closely related to each other.

Experimental Modal Analysis and Structural Health Monitoring of the Double Curvature Deriner Arch Dam

Arch dams have delicate sections thanks to their curvature. The fact that these dams are large, costly and construction takes many years increases the importance of the structure. Mistakes and / or accidents that may occur during the construction of such structures may occur major loss of life and property. Considering the volumes, masses and slenderness of arch dams, they can be significantly affected by dynamic forces such as changing water pressure, temperature, wind and earthquakes. The level of these effects and to what extent they affect the dam can be determined by the analysis to be made to finite element model created by computer. Since Finite Element Analysis is based on certain assumptions, the results obtained should be compared and / or verified with the results obtained by experimental methods. One of the most suitable methods preferred in many engineering structures is the experimental modal analysis method. Within the scope of the study, experimental vibration tests were carried out in order to evaluate and determine the structural behavior of the double curvature Deriner Arch Dam, which has a body height of 249m and a crest length of 720m. Experimental measurements were carried out with accelerometers placed in appropriate places in order to obtain the mode shapes of the dam. The dynamic characteristics of the dam were determined using OMA software. The first seven natural frequencies of the Deriner arch dam were obtained in the range 1.60-4.10Hz. As a result of the negotiations with the DSI 26th Regional Directorate, the acceleration data obtained from the existing accelerometer system of the dam was instantly taken and a continuous monitoring process was initiated. This data was transferred to the web-based monitoring site and a structural condition monitoring platform was created.

Quantifying damping coefficient and attenuation at different frequencies for graphene modified polyurethane by drop ball test

In this study, polyurethane (PU) was modified by direct mixing of carboxyl functionalised graphene (GNP–COOH) referred to as f-GNP, without using any solvent, during in-situ polymerization. In a further attempt, the neat PU was modified with f-GNP and a hydrophobic silica-based solution (SG) during in-situ polymerization. The damping coefficient and attenuation capacity of neat polyurethane (PU), f-GNP based PU nanocomposite (PU + f-GNP), and f-GNP and hydrophobic silica-based solution PU nanocomposite (PU + f-GNP + SG), together with polytetrafluoroethylene (PTFE), high-density polyethylene (HDPE), ultra-high molecular weight polyethylene (UHMWPE), polyethylene terephthalate (PET), polyvinyl chloride (PVC) and NYLON have been obtained by the drop ball tests under controlled and consistent conditions. The results show that among the tested materials, polyurethane modified with carboxyl functionalised graphene and silica-based Sol-Gel (PU + f-GNP + SG) displays the greatest attenuations and PTFE the least.The attenuation of the various materials has been identified with the SVD-QR method. This experimental modal analysis method has been used to analyse the free response signal of the system during the drop ball test and identify the modal parameters such as damping ratio and frequency of the modes of deformation of the system. The drop ball test results show that the damping coefficient of polyurethane modified with 0.5 wt% carboxyl functionalised graphene (PU + f-GNP) increased by 37% at frequency range 200–300 Hz, by 34% at frequency range 500–600 Hz and by 32% at frequency range 700–1000 Hz. The developed nanocomposite materials have great potential for protecting leading edge erosion (LEE) of wind turbine.

Analytical and experimental modal analysis of model wind tunnel using microtremor excitation

In this study was investigated of possibility using the recorded micro tremor data on ground level as ambient vibration input excitation data for investigation and application Experimental Modal Analysis (EMA) on the bench-scale earthquake simulator (The Quanser Shake Table) for model wind tunnel. As known EMA methods (such as EFDD, SSI and so on) are supposed to deal with the ambient responses. For this purpose, analytical and experimental modal analysis of a model wind tunnel for dynamic characteristics was evaluated. 3D Finite element model of the building was evaluated for the model wind tunnel based on the design drawing. Ambient excitation was provided by shake table from the recorded micro tremor ambient vibration data on ground level. Enhanced Frequency Domain Decomposition is used for the output only modal identification. From this study, best correlation is found between mode shapes. Natural frequencies and analytical frequencies in average (only) 2.5% are differences.

Vibration stability analysis of cantilever structure based on symbolic regression algorithm and modal analysis method

The vibration stability of cantilever mechanism under high-speed rotation directly affects the positioning accuracy. Modal analysis method is usually used to study the vibration stability. However, the traditional experimental modal analysis (EMA) method needs to measure the impulse excitation, while the operational modal analysis (OMA) method needs to satisfy the assumption of white noise. Therefore, the existing modal analysis methods cannot be applied to the study of vibration stability of high-frequency cantilever mechanism. In this paper, the symbolic regression (SR) algorithm is combined with the EMA method, and the robustness analysis and feasibility verification are carried out under the condition of adding noise. The validation of the new method is divided into two parts. In the first part, a three degree of freedom (DOF) linear model is constructed, and the modal parameters identified by SR method and state space method are compared. In the second part, the method is applied to identify the modal parameters of stepped bar. The results are compared with the results of LMS (Siemens’ Testlab). Based on the time-domain response signal only, the modal parameters are extracted by SR, and the main vibration frequency is extracted from the response signal. The system simulation and experimental results show the method provides a possibility to analyze the vibration stability of cantilever structure.

The Planar Wide-Frequency Vibration Characteristics of Heavy-Load Radial Tires

This paper investigates the planar wide-frequency vibration characteristics of heavy-load radial tires with a large aspect ratio. A proposed tire model with a piecewise flexible beam on an elastic foundation is investigated and validated using experimental modal analysis and theoretical modeling method. The reproducibility of frequency response functions below 400 Hz is discussed. The experimental modal analysis particularly assesses the coupling of features across the circumferential and cross-sectional directions of heavy-load radial tire carcass. Piecewise circumferential modal characteristics were investigated experimentally, leading to the suggestion of a piecewise flexible beam on an elastic tire foundation. Using a genetic algorithm (GA), the structural parameters EI, ρ A , and kr and damping coefficients η and cr for the proposed tire model are identified, and the piecewise transfer functions and the planar transfer functions for a heavy-load radial tire are compared with planar hammer test. Experimental and theoretical results show the following: (1) the sectional vibration characteristics for a heavy-load radial tire with a large aspect ratio result from the cross-sectional vibration of the tire carcass; (2) the piecewise transfer function is mainly influenced by the circumferential vibration of the flexible carcass, and this is consistent with a model where a flexible beam is placed on an elastic tire foundation; (3) the analytical transfer functions calculated for the proposed tire model, drawing on the identified structural parameters and damping coefficients, agree well with the experimental results.

On passive damping in machine tool hybrid structural parts

Hybrid materials combining steel or cast iron with fibre or particle composites have a good potential for lightweight machine tool structural design with high damping ratio. These materials are analyzed in the paper with a focus on damping improvement of structural components and machine tool assemblies. Fibre composites and particle composites were selected as the lightweight elements for the hybrid machine tool structure. The fibre composites were designed as low-density, high stiffness-oriented reinforcements, which were bonded to build metal structural parts conventionally. The particle composites were applied as filler materials into the hollows of the metal structural parts. Both composite structures presented a possibility to reduce the mass of the component due to the reduction of wall thickness (fibre composite) or removal of heavy ribbing (particle composites) and to influence the parts’ static and dynamic stiffness. Hybrid structures, combining the light-weight elements with cast iron or welded steel, were designed and tested in case studies using experimental modal analysis methods. Experimental modal analysis was used as the main approach for identification of the damping ratio on a basic coupon level, followed by testing of structural parts in a stand-alone configuration and ending with a structural part assemblies testing. Both particle composites and fibre composites were successful in improving the damping ratio of single structural parts. However, the damping ratio of the hybrid component mounted into an assembly configuration shows only less significant improvement. The presented results demonstrate importance of the damping caused in the connecting interfaces.

Validation of Modal Analysis of Two-Storey Reinforced Concrete Frame

The aim of this paper is to perform experimental modal analysis of two-storey reinforced concrete frame which designed using BS 8110 without seismic load and validate the experimental result with model using finite element analysis software. Experimental Modal Analysis (EMA) is the process of determining the modal parameters such as natural frequencies, damping factors, modal vectors and mode shape of a structure from a set of frequency response functions. The experimental work was conducted on half-scale of two-storey reinforced concrete frame at Heavy Structural Laboratory. Moreover, the Impact Modal Testing and response accelerometer are employed to determine the modes of vibration of a structure during experiments without imposed any in-plane lateral force. The experimental natural frequencies, which are extracted from measurements, exhibit good agreement with analytical model predictions. It shows that experimental modal analysis method can be usefully employed to investigate the dynamic behaviour of reinforced concrete frame due to the minimum percentage error between experimental modal analysis and computer software analysis.

Structural dynamic analysis of a musical instrument: Tibetan singing bowl

Operational Modal Analysis (OMA) of Tibetan singing bowl is performed to extract natural frequencies and mode shapes without measuring excitation data. It is kept free on a rigid surface, which is a common way of playing this musical instrument. OMA results are validated using Experimental Modal Analysis (EMA) and Numerical Methods using FEA. Numerical simulations using ANSYS® software establishes a benchmark for EMA results. The input and response data for 144 response points are collected using instrumented hammer and accelerometer, connected to a four-channel FFT analyser. A self-generated MATLAB® code processes the response signals for EMA and OMA. For natural frequencies, the absolute error lies within 6%, except for the first mode. For mode shapes, the Modal Assurance Criteria (MAC) value is more than 70%, except for the fourth mode. Thus, OMA is the best available method compared to the EMA and Numerical method using FEA for structural analysis under actual performance conditions.

Effects of different poses and wind speeds on wind-induced vibration characteristics of a dish solar concentrator system

In order to investigate the anti-vibration characteristics of a dish solar concentrator (DSC) system with wind-induced vibration, based on fluid-solid interaction method, a simulation model of a DSC system is developed and verified by experimental modal analysis method, and the anti-vibration characteristics (including natural frequency, mode shape and maximum deformation, moment and force) of the DSC system with wind-induced vibration are investigated and the useful results are concluded and obtained. Actually, the wind loads will cause a decrease in its lower-order natural frequencies of the DSC system, but the moment and force of the DSC system will be increased due to the wind loads increase under the same azimuth and pitching angle. When natural frequency at different wind speeds mainly concentrated in the range of 0.8396–4.135 Hz, no resonance can be caused by wind-induced vibration, but the maximum deformation of the mode shape for the DSC system is 2.5055 mm so that the local stiffness should be checked in the design process. Moreover, the percentage that the maximum stress of DSC system is less than the yield limit of carbon steel (Q345) is 4.03%, and the DSC system is of good safety during its normal working condition. The obtained results is useful for enhancing the anti-vibration performance of the DSC system.

DIC‐Based Operational Modal Analysis of Bridges

A new method has been proposed to identify the natural frequencies and mode shapes of a bridge model, in which the digital image correlation (DIC) technique is used to track the dynamic displacement. A key issue in vibration‐based damage detection for a bridge is to determine its modal parameters. It is difficult to use traditional acceleration sensors to obtain the accurate mode shapes of bridges as the sensors are only deployed on a few measurement points of the bridges. In this article, the DIC technique is used to capture the movement of the entire experimental bridge model. A steel truss is used as a bridge model and stimulated by a hammer; its dynamic displacement is recorded by using a digital video camera. The correlation analysis is used to track the displacement of the points of interest, and their displacement time histories are inputted into a modal analysis system; the natural frequencies and mode shapes of the bridge model were obtained by both operational modal analysis (OMA) and traditional experimental modal analysis (EMA) methods. (1) The DIC results are compared with those obtained by a traditional acceleration sensor‐based method; the natural frequencies obtained by the two measurement methods are very close. (2) The DIC results are sensitive to the amplitude of the measured displacement and the shooting distance; small displacement amplitudes and long shooting distance may result in the low quality of the measured time‐history curves, and low‐frequency noise signals might be observed in their power spectral density (PSD) curves, while they can be easily solved by the filtering method in this article. (3) In addition, the first frequencies obtained by EMA and OMA are very close, which validates the applicability of the DIC measurement under ambient excitation. The research has illustrated the feasibility of the DIC method for obtaining the modal parameters of the bridges.