Application Of Modal Analysis Research Articles

Two-dimensional optical coherence tomography for real-time structural dynamical characterization

We present a two-dimensional optical coherence vibration tomography (2DOCVT) system with an ultra-precision displacement resolution of ~0.1nm that is capable of in site real-time absolute displacement measurement of structural line vibrations. Experimental results of sinusoidal, sweep and impulse vibrations were reported. The key figures of merit such as the 2DOCVT system could obtain fast line vibration measurement without scanning and it also could be used to capture structural modal parameters in one single impulse excitation measurement without any vibration excitation input information, making it attractive for the application in low-frequency vibration measurement and response-only modal analysis.

Relationship between the shape and density distribution of the femur and its natural frequencies of vibration

It has been recently suggested that mechanical loads applied at frequencies close to the natural frequencies of bone could enhance bone apposition due to the resonance phenomenon. Other applications of bone modal analysis are also suggested. For the above-mentioned applications, it is important to understand how patient-specific bone shape and density distribution influence the natural frequencies of bones. We used finite element models to study the effects of bone shape and density distribution on the natural frequencies of the femur in free boundary conditions. A statistical shape and appearance model that describes shape and density distribution independently was created, based on a training set of 27 femora. The natural frequencies were then calculated for different shape modes varied around the mean shape while keeping the mean density distribution, for different appearance modes around the mean density distribution while keeping the mean bone shape, and for the 27 training femora. Single shape or appearance modes could cause up to 15% variations in the natural frequencies with certain modes having the greatest impact. For the actual femora, shape and density distribution changed the natural frequencies by up to 38%. First appearance mode that describes the general cortical bone thickness and trabecular bone density had one of the strongest impacts. The first appearance mode could therefore provide a sensitive measure of general bone health and disease progression. Since shape and density could cause large variations in the calculated natural frequencies, patient-specific FE models are needed for accurate estimation of bone natural frequencies.

Application of Classical and Operational Modal Analysis for Examination of Engineering Structures

Due to the types of construction (steel, concrete etc.), the type of excitation (caused by wind, rail and traffic etc.) in the measurement of engineering structures’ vibration different measurement techniques and different data processing techniques are used. The paper presents the comparison of Classical and Operational Modal Analysis on the basis of engineering structures. The results of vibration's measurements of selected engineering structures with the use of different methods of data processing are presented and discussed in the paper. Dynamic measurements of a structure were performed with the use of a multichannel PULSE system, produced by the Brüel & Kjær.

Application of modal analysis to the watermelon through finite element modeling for use in ripeness assessment

It is very difficult to judge watermelon ripeness by external characteristics. The laser Doppler vibrometer (LDV) is a new approach to determination of fruit quality. This optical-mechanical technique was utilized for nondestructive detection of the vibration response of watermelons to predict ripeness. Finite element modeling (FEM) was used to find the optimum location for excitation and response measurement and to analyze the mode shapes. The model was considered based on red, white, and green tissues and included individual properties such as density and elasticity modulus. Modal analysis of the finite element model showed acceptable agreement between experimental results and finite element simulation. According to the mode shapes of watermelon, optimum locations for applying input vibrations and detecting output vibrations were suggested. Then watermelons were excited and their responses were recorded by LDV at the determined locations. The phase shift between input and output signals were extracted over a wide frequency range. The firmness of cut fruits was measured with penetrometer as a ripeness indicator. A regression model was developed to predict the internal texture firmness using phase shifts at statistically selected frequencies. The determination coefficients (R2) of the calibration and cross validation models were 0.9998 and 0.994 respectively.

Artificial Neural Networks Application in Modal Analysis of Tires

Abstract The paper deals with the application of artificial neural networks (ANN) to tires’ own frequency (OF) prediction depending on a tire construction. Experimental data of OF were obtained by electronic speckle pattern interferometry (ESPI). A very good conformity of both experimental and predicted data sets is presented here. The presented ANN method applied to ESPI experimental data can effectively help designers to optimize dimensions of tires from the point of view of their noise.

Application of quantitative modal analysis for investigation of thermal degradation of microelectronic packages

The influence of high temperature storage on the properties of epoxy based materials in microelectronic packages was investigated by application of a quantitative modal analysis technique. An electromagnetic shaker in combination with scanning laser Doppler vibrometry was used to extract the alteration of the modal response of the components in relationship with the thermal aging time. Data analysis was accomplished by the error ratio (ER) method, modal assurance criterion (MAC) and determination of an aspect ratio (AR) using an image correlation technique. Increasing the storage time resulted in a higher degree of degradation which was reflected by an increase in the values of ER, MAC and the AR. Microstructural investigations confirmed that alteration of the modal response is related to the temperature dependent gradual degradation and modification of the properties of the packaging material which was supported by finite element analysis. This present work shows the feasibility of modal analysis as an efficient and quantitative non-destructive testing method for evaluation of degradation of electronic packages.

Parametric excitation of a thin ring under time-varying initial stress; theoretical and numerical analysis

Initial stress in rings is one of the destructive effects which is almost inevitable due to various reasons such as being subsystems of a shrink-fitted joint, imperfections in the manufacturing, assembly or misalignment of the supporting mounts, and unbalancing in rotating condition. So, in this paper we focus on the effect of the initial stress and its variation with time on the dynamics of the pre-stressed ring. For this purpose, the equation of motion for in-plane bending vibration of a thin ring is derived using Hamilton’s principle. It is assumed that the initial stress is due to the distributed radially time-varying pressure. By representing the dynamic initial stress in the coefficients of the equation of motion; the equation is converted to Mathieu’s equation. The strained parameters method has been used to obtain the stability regions of motion and transition curves. Furthermore, to validate the obtained stability regions, numerical solutions of the equation of motion and Floquet theorem are used in some selected values of the parameters of the initial stress (magnitude of static and dynamic components of the initial stress). The fourth-order Runge-Kutta algorithm is used for numerical analysis of the equation of motion. The results show that the parameters of initial stress have direct impact on the stability of dynamic response. The obtained results from theoretical and numerical methods which are notably consistent with each other demonstrate that the initial stress, which has been almost always neglected in dynamic models of the systems, has a significant effect on the dynamics of the system, and it may even lead to an unstable dynamic response, while the excitation frequency is far enough from resonance region. So this paper can present the other application of modal analysis to non-destructive measure of initial stress.

Application of Experimental Modal Analysis to Determine Damping Properties for Stacked Corrugated Boxes

Multilayer stacked corrugated packaging boxes are a common shipping mode in packaging distribution. This study discusses how to determine the damping properties of stacked corrugated boxes using experimental modal analysis (EMA). Prior to the calculation of damping properties, two MATLAB-based digital filters were applied to process the sampled original signals. Both the logarithmic method and the curve fit method are used to compute the multiple damping ratios from the acceleration and displacement response data after the excitation. The study found that the viscous damping and dry friction damping take place in a different time frame in stacked corrugated boxes. This study recommends using the curve fit method to determine damping properties for a multiple-degree-of-freedom system such as stacked corrugated boxes.

An Integrated Seismic Monitoring System for a Full-Scale Embedded Retaining Wall

Abstract Over the last 50 years, data from laboratory tests and post-earthquake reconnaissance have been used to gain knowledge about the dynamic and seismic behavior of geotechnical structures and to improve analysis and design procedures. The scarcity of reconnaissance data has pointed out the need for full-scale and near full-scale tests for research purposes in earthquake engineering. Structural health monitoring (SHM) systems have been applied to different kinds of structures, but although static control of displacements and pressures is quite common, dynamic monitoring is fairly limited in geotechnical engineering. In the present paper, an integrated structural and geotechnical monitoring program aimed at filling this knowledge gap is described with reference to a real flexible retaining wall. The objective of the research is to establish a combination of sensors, numerical analyses, and data processing procedures to turn the monitored retaining wall into a smart geotechnical structure. Attention is herein focused on two aspects related to the implementation of the monitoring system and the dynamic identification of the soil-structure system. Specifically, the paper describes an example of seismic monitoring system for full-scale flexible retaining walls based on sensors embedded in the reinforced concrete piles. Installation details are given together with a description of the monitoring system architecture in its current stage of implementation. Issues and requirements for the measurement chain are discussed, taking into account possible installation drawbacks (i.e., shocks) and the opportunity to monitor the response under operational conditions. Furthermore, a novel and successful application of operational modal analysis (OMA) to such a complex geotechnical system is reported. It allows for the identification of the fundamental modes of the soil-wall system in operation (but before the erection of a building on the excavated side). Implementation of the monitoring system prototype is still in progress, but some interesting results have already been outlined.

Modal parameter estimation by combining stochastic and deterministic frequency-domain approaches

The poly-reference Least squares Complex Frequency-domain (pLSCF) estimator—commercially known as the LMS PolyMAX estimator—is used intensively in modal analysis applications nowadays. pLSCF is non-iterative (deterministic) and relatively accurate modal parameter estimation algorithm. This algorithm has several advantages: it is polyreference, fast, numerically stable for large-bandwidth with high-model order analysis, and yields very clear stabilization diagrams even with highly noisy FRFs measurements. One drawback of the pLSCF-estimator is that it yields a poor damping estimates especially for highly damped and weakly excited modes when the FRFs are very noisy.In this contribution, an approach will be proposed to improve the accuracy of pLSCF estimator and in particular, the damping estimates in case of high noise level. The new proposed approach is a combined stochastic-deterministic frequency-domain algorithm. In this approach, a 2-step procedure is introduced to improve the damping estimates while maintaining the very clear stabilization diagrams. In the first step, a parametric Maximum Likelihood smoothing approach, which is the stochastic part, is used to remove the noise from the data and in the second step, the pLSCF estimator, which is the deterministic part, is applied to the smoothed data resulting in improved (damping) estimates.The presented algorithm is able to maintain the benefits of pLSCF and at the same time leads to an improvement of the damping estimates in highly damped and very noisy cases. In addition, the new procedure properly deals with uncertainty on the measurements where the data variance due to measurement noise is taken into account.The procedure is illustrated and tested by using simulated as well as experimental data. The presented procedure to process a highly damped noisy vibration data leads to very accurate estimates in comparison to the traditional pLSCF estimator.

Impacts of Epistemic Uncertainty in Operational Modal Analysis

AbstractField experimentation on constructed systems demands consideration of many mechanisms of epistemic and aleatory uncertainties as well as human errors and subjectivity. This is especially true in operational modal analysis (OMA) applications that aim to identify the dynamic properties of a structure. Although statistics and probability theory are sufficient for quantifying aleatory uncertainty and bounding the resulting errors in OMA results, there is much debate as to whether the same tools may also be used to quantify epistemic uncertainty. This study explored a framework for better understanding the distinctions and impacts of these two types of uncertainties in OMA and how human errors and subjectivity may be classified. A physical laboratory model was designed to simulate four key sources of epistemic uncertainty that represented the primary test variables: structural complexity (changing boundary conditions, nonlinearity), ambient excitation characteristics (magnitude, directionality, and ban...

Modal Characteristics Study of CEM-1 Single-Layer Printed Circuit Board Using Experimental Modal Analysis

Since the level of vibration always depends on the natural frequencies of the system, it is important to know the modal parameters of such system to control failure and provide prevention actions. The demand for structurally reliable Printed Circuit Boards (PCB) has increased as more functions are required from electronic products along with less weight and smaller size. This imposes certain limitations and critical requirements. The applications of Experimental Modal Analysis (EMA), together with Finite Element Method (FEM) allow structural modification and optimization of the PCB. However, the purpose of this paper will only investigate the dynamic characteristics of CEM-1 Single-layer PCB using Experimental Modal Analysis (EMA) method. The dynamic characteristics are extracted for free-free end condition. In EMA, a model is developed using ME'Scope and modal testing is carried out using dbFA Suite 4.9 to obtain the experimental natural frequencies and mode shapes. The understanding on dynamic behavior of this structure provides valuable insight into the nature of the response and remarkable enhancement of its model, strength and vibration.

Application of Modal Analysis in Local Damage Diagnosis of Steel Beam

For one cantilever steel beam, according to the stress concentration principle resulted from the small hole, four small holes were drilled at different positions to form the local damage of the steel beam. The modal tests including the displacement modal and the strain modal were conducted before and after the steel beam was damaged. The test results indicated: from the decreased frequency, one could only judge on the whole that the steel beam had been damaged, but could not determine the detailed damaged positions; the detailed damaged positions of the steel beam were also difficult to be determined by the displacement modal test whether by ripple technique or by hammering technique, but could be determined by the strain modal test by hammering technique, especially under the first order of modal. The research achievements can offer some references for the diagnosis of local damage of engineering structures by the strain modal analysis method.

An application of operational modal analysis in modal filtering

Modal filtration in the field of damage detection has many advantages, including: its autonomous operation (without the interaction of qualified staff), low computational cost and low sensitivity to changes in external conditions. However, the main drawback of this group of damage detection methods is its limited applicability to operational data. In this paper a method of modal filter formulation from the in-operational data is described. The basis for this approach is FRFs synthesis using knowledge of the operational modal model. For that purpose a method of operational mode shape scaling is described. This is based on the measurements of several FRFs of the object. The method is then applied to the construction of modal filters and modal filtration. Additionally, the study presents verification of the method using data obtained from simulation and laboratory experiments. Verification consisted of comparing the results of modal filtering based on classical experimental modal analysis with the results of the approach proposed in the work.

Study of the Applicability of Modal Pushover Analysis on Irregular Continuous Bridges

The influence of higher modes and their consideration in the pushover analysis of three irregular continuous bridges is discussed. Modal pushover analysis (MPA) is addressed and compared with inelastic time-history analysis (ITHA). In the operation process of MPA, each important mode is used to determine the distribution of forces for the pushover analysis separately, and the displacements of different parts of bridge are monitored to construct pushover curves for each important mode. When the analyses for all important modes of one bridge are completed, the results are combined and compared with the results of ITHA. The investigation shows, for each important mode, adopting different displacement-monitored points obtains different pushover curves. If reasonable pushover curves are selected as capacity spectra, MPA can give the results comparable with ITHA, or else MPA does not work well. Finally, how to choose reasonable displacement-monitored point to construct capacity spectrum of MPA is identified.

Applicability of Modal Pushover Analysis on Bridges

Taking one irregular continuous bridge as an example, modal pushover analysis (MPA) has been conducted to judge whether it would be applicable for seismic analysis of irregular bridge structures. The bridge’s seismic demand in the transverse direction has been determined through two different methods, inelastic time history analysis (ITHA) and MPA respectively. The comparison between those two results indicates that MPA would be suitable only for bridges under elastic or slightly damaged state. Finally, some modifications are used to improve the MPA’s scope of application, and the results illustrate that the adapted MPA will be able to estimate bridges’ seismic demands to some extent.

The Application of Modal Analysis in Hole-Defect in Lumber

Larch lumbers were tested by using modal analysis technology and Frequency response functions (FRF) were derived. Modal parameters, including first 4 intrinsic frequency and first 3 modal shape, were distinguished by single modal method. Research shows that the intrinsic frequency of hole-defect lumbers is little lower than standard lumbers’ and the change rate of frequency is becoming larger gradually with the diameter of hole-defect. However, it can not judge the position of the hole-defect by the change rate of frequency. The modal shape of the node near the hole-defect always jumps abruptly, so it can estimate the particular position of hole-defect in the lumber. The variation of modal shape is becoming larger gradually with the diameter of hole-defect. It can make qualitative and quantitative estimate to the hole-defect in the lumber by considering intrinsic frequency and modal shape together.

Global Linear Instability

This article reviews linear instability analysis of flows over or through complex two-dimensional (2D) and 3D geometries. In the three decades since it first appeared in the literature, global instability analysis, based on the solution of the multidimensional eigenvalue and/or initial value problem, is continuously broadening both in scope and in depth. To date it has dealt successfully with a wide range of applications arising in aerospace engineering, physiological flows, food processing, and nuclear-reactor safety. In recent years, nonmodal analysis has complemented the more traditional modal approach and increased knowledge of flow instability physics. Recent highlights delivered by the application of either modal or nonmodal global analysis are briefly discussed. A conscious effort is made to demystify both the tools currently utilized and the jargon employed to describe them, demonstrating the simplicity of the analysis. Hopefully this will provide new impulses for the creation of next-generation algorithms capable of coping with the main open research areas in which step-change progress can be expected by the application of the theory: instability analysis of fully inhomogeneous, 3D flows and control thereof.

Operational modal analysis by updating autoregressive model

This paper presents improvements of a multivariable autoregressive (AR) model for applications in operational modal analysis considering simultaneously the temporal response data of multi-channel measurements. The parameters are estimated by using the least squares method via the implementation of the QR factorization. A new noise rate-based factor called the Noise rate Order Factor (NOF) is introduced for use in the effective selection of model order and noise rate estimation. For the selection of structural modes, an orderwise criterion called the Order Modal Assurance Criterion (OMAC) is used, based on the correlation of mode shapes computed from two successive orders. Specifically, the algorithm is updated with respect to model order from a small value to produce a cost-effective computation. Furthermore, the confidence intervals of each natural frequency, damping ratio and mode shapes are also computed and evaluated with respect to model order and noise rate. This method is thus very effective for identifying the modal parameters in case of ambient vibrations dealing with modern output-only modal analysis. Simulations and discussions on a steel plate structure are presented, and the experimental results show good agreement with the finite element analysis.

Modal Parameter Identification using Ambient Vibration Testing with Introducing a new Software

The ambient vibration measurement is a kind of output data-only dynamic testing where the traffics and winds are used as agents responsible for natural or environmental excitation. Therefore an experimental modal analysis procedure for ambient vibration testing needs to base itself on output-only data. The modal analysis involving output-only measurements present a challenge that requires the use of special modal identification technique, which can deal with very small magnitude of ambient vibration contaminated by noise. Two complementary modal analysis methods are implemented. They are rather simple peak picking (PP) method in frequency domain and more advanced stochastic subspace identification (SSI) method in time domain. According to these methods Graphical User Interface (GUI) software developed in MATLAB. This program is called SIP and can be used in modal parameter identification of large civil structures such as bridges and towers. This paper presents the application of ambient vibration testing and experimental modal analysis on large civil engineering structures and also gives brief review of program. Also modal parameters of the Babolsar arch steel bridge are extracted using SIP and ambient vibration data from dynamic test carried out on this bridge.