Changes In Mode Shapes Research Articles

In-situ piezoresponse force microscopy cantilever mode shape profiling

The frequency-dependent amplitude and phase in piezoresponse force microscopy (PFM) measurements are shown to be a consequence of the Euler-Bernoulli (EB) dynamics of atomic force microscope (AFM) cantilever beams used to make the measurements. Changes in the cantilever mode shape as a function of changes in the boundary conditions determine the sensitivity of cantilevers to forces between the tip and the sample. Conventional PFM and AFM measurements are made with the motion of the cantilever measured at one optical beam detector (OBD) spot location. A single OBD spot location provides a limited picture of the total cantilever motion, and in fact, experimentally observed cantilever amplitude and phase are shown to be strongly dependent on the OBD spot position for many measurements. In this work, the commonly observed frequency dependence of PFM response is explained through experimental measurements and analytic theoretical EB modeling of the PFM response as a function of both frequency and OBD spot location on a periodically poled lithium niobate sample. One notable conclusion is that a common choice of OBD spot location—at or near the tip of the cantilever—is particularly vulnerable to frequency dependent amplitude and phase variations stemming from dynamics of the cantilever sensor rather than from the piezoresponse of the sample.

Analysis of stationary roving mass effect for damage detection in beams using wavelet analysis of mode shapes

One of the main challenges in damage detection techniques is sensitivity to damage. During the last years, a large number of papers have used wavelet analysis as a sensitive mathematical tool for identifying changes in mode shapes induced by damage. This paper analyzes the effect of adding a mass to the structure at different positions. Depending on the location and severity of damage, the presence of the mass affects the natural frequencies and mode shapes in a different way. The paper applies a damage detection methodology proposed by the authors, although it has been modified in order to consider the addition of the mas. This methodology is based on a wavelet analysis of the difference of mode shapes of a damaged and a reference state. The singular behavior of a normalized weighted addition of wavelet coefficients is used as an indicator of damage. The presence of damage is detected by combining all the information provided by mode shapes and natural frequencies for different positions of the roving mass. A continuous wavelet transform is used to detect the difference between the response of a healthy state and a damaged one. The paper shows the results obtained for a beam with different cracks. The paper analyzes the sensitivity to damage of the proposed methodology by considering some practical issues such as the size of the crack, the number of measuring points and the effect of experimental noise.

Damage assessment through changes in mode shapes due to non-proportional damping

Modal parameters are often used for the structural damage assessment in the dynamic field. Usually, the changes in the modal parameters between different states are assumed as measures of damage. The frequencies are easy to identify, but in some circumstances they are not sensitive to damage and moreover they are mainly a global measure. On the contrary, the mode shapes are more suited for damage localization, but they are generally hard to identify accurately. The energy dissipation, and hence the damping, increases with damage. This feature is stable and has a monotonic behaviour, therefore, damping can be confidently used as an alternative or complementary measure for damage assessment in spite of the accuracy of its identification. However, the damping by itself suffers of the same drawbacks as the frequencies. The joint use of damping and mode shapes is an effective procedure for the damage identification. In the real world the damping is of nonproportional type and the measured mode shapes are complex. It is assumed that an increase of damage causes a modification of non-proportional damping and a variation of the modal complexity. The extent of modal complexity between two different structural states can be used to identify the damage through appropriate indicators. A number of such indicators is introduced and discussed. The effectiveness and sensitivity of the damage indicators are tested on theoretical and pseudo-experimental data.

Performance of rotational mode based indices in identification of added mass in beams

This study investigates the identification of added mass and its location in the glass fiber reinforced polymer (GFRP) beam structures. The main emphasis of this paper is to ascertain the importance of inclusion of rotational degrees of freedom (dofs) in the introduction of added mass or damage identification. Two identification indices that include the rotational dofs have been introduced in this paper: the modal force index (MFI) and the modal rotational curvature index (MRCI). The MFI amplifies damage signature using undamaged numerical stiffness matrix which is related to changes in the altered mode shapes from the original mode shapes. The MRCI is obtained by using a higher derivative of rotational mode shapes. Experimental and numerical results are compared with the existing methods leading to a conclusion that the contributions of the rotational modes play a key role in the identification of added mass. The authors believe that the similar results are likely in the case of damage identification also.

Fault detection of composite beam by using the modal parameters and RBFNN technique

The detection of transverse cracks in terms of their location and intensity by using the radial basis function neural network (RBFNN) technique is analyzed in the current research and validated with experimental investigation. The glass fiber-reinforced epoxy composite is used in this research because of its valuable features, such as high stiffness and strength-to-weight ratios, good fatigue and wear resistance, and damage tolerance capability compared with isotropic material. The theoretical and numerical investigations are performed to obtain a relationship between the change in natural frequencies and mode shapes for the cracked and noncracked composite beam. Numerical analysis is performed by using the finite element software ANSYS on cracked and noncracked composite beams to measure the modal parameters, such as natural frequencies and mode shapes. These parameters are used to design an artificial intelligent controller based on the RBFNN-type neural network for predicting crack severity and its intensity. The relative natural frequencies and mode shapes (First, second, and third modes) of vibration are used as input data to the RBFNN controller, and the relative crack locations and crack depths are the output of RBFNN. Results from theoretical and numerical analysis are compared with the experimental results, and a good agreement is observed between them.

Dynamic Characteristics Recovery of Delaminated Composite Structure

본 논문에서는 복합재 구조물에 손상이 있을 경우, 손상에 의해 변화된 구조물의 동적특성을 손상이 없는 상태로 회복하여, 전체 시스템의 안정성을 유지할 수 있도록 하였다. 층간 분리가 있는 구조물의 유한요소모델 구축을 위하여 향상된 층간 변위장 모델을 적용하였으며, 유한요소해석을 진행하여 구조물의 고유 진동수와 모드 형상을 관찰하였다. 능동제어 알고리즘과 압전 작동기를 적용하여 구조물의 진동 응답특성을 확인하였으며, 이를 바탕으로 손상된 구조물의 동적특성을 손상이 없는 상태로 회복할 수 있음을 확인하였다.In this paper, feasibility of dynamic characteristics recovery of delaminated composite structure is numerically studied by using active control algorithm and piezoelectric actuator. Macro-fiber composite(MFC), which has great flexibility and high actuating force, is considered as an actuator in this work. After construction of finite element model for delaminated composite structure based on improved layerwise theory, modal characteristics are investigated and changes of natural frequencies and mode shapes, caused by delamination, are observed. Then, active control algorithm is realized and implemented to system model and control performances are numerically evaluated. Dynamic characteristics of delaminated composite structure are effectively recovered to those of healthy composite structure.

English

The objective of this paper is to update its readers the various vibration based Crack/damage diagnosis techniques presented by various researchers for a cracked structures. These methods use finite element analysis techniques, together with experimental results, to detect damage in a fibre reinforced composites, laminated composites and non composite structures for its vibration analysis. Damage in structure alters its dynamic characteristics. It results in reduction of natural frequencies and changes in mode shapes, stiffness of the beam. An analysis of these changes makes it possible to determine the position and depth of cracks.

Identification of crack characteristics in beams by using modal frequencies and inverse problem

Detection of cracks in mechanical components as early as possible enables monitoring structural health and scheduling efficiently the maintenance tasks such as replacing the critical parts just in time. Vibration analysis based techniques for crack detection have been largely considered in the framework of beam-like structures. This methodology relies essentially on the observed changes of beam frequencies and mode shapes induced by the presence of damage. In the present work, using an explicit analytical model assessing the effect of a crack on beam strain energy, the beam first resonance frequencies as they depend on a single crack defect characteristics were evaluated. The crack equations were obtained by means of fracture mechanics approach. Variations of the first beam frequencies and modes shapes were then related explicitly to the location and depth of the crack. Measuring the beam frequency changes and monitoring their variations can be used to perform identification of the crack defect parameters by solution of an inverse problem.

Damage assessment from curvature mode shape using unified particle swarm optimization

A two-step procedure to detect and quantify damages in structures from changes in curvature mode shapes is presented here. In the first step the maximum difference in curvature mode shapes of the undamaged and damaged structure are used for visual identification of the damaged internal-substructure. In the next step, the identified substructures are searched using unified particle swarm optimization technique for exact identification of damage location and amount. Efficiency of the developed procedure is demonstrated using beam like structures. This methodology may be extended for identifying damages in general frame structures.

An improved CSS for damage detection of truss structures using changes in natural frequencies and mode shapes

Non-destructive structural damage identification can be carried out using the difference between a structure’s characteristics before and after a catastrophic event. An approach is to formulate the problem as an inverse optimization problem, in which the amounts of damage to each element are considered as the optimization variables. The objective is to set these variables such that the characteristics of the model correspond to the experimentally measured characteristics of the actual damaged structure. Since the structures are usually symmetric, this is an optimization problem with several global optimal solutions each representing a probable state of damage, where unlike many other optimization problems, it is not enough to merely find one of these optimal solutions; it is important to capture all such possible states and to compare them. In this paper, structural damage detection of planar and spatial trusses using the changes in structures’ natural frequencies and mode shapes is addressed. An improved Charged System Search algorithm is developed and utilized to tackle the problem of finding as many global optimal solutions as possible in a single run. A 10-bar planar truss and a 72-bar spatial truss are considered as numerical examples. Experimental results show that it is important to incorporate mode shapes in order to determine the actual damage scenario among other possibilities.

Features of Large Hinge-Bending Conformational Transitions. Prediction of Closed Structure from Open State

We performed a detailed analysis of conformational transition pathways for a set of 10 proteins, which undergo large hinge-bending-type motions with 4–12 Å RMSD (root mean-square distance) between open and closed crystal structures. Anisotropic network model-Monte Carlo (ANM-MC) algorithm generates a targeted pathway between two conformations, where the collective modes from the ANM are used for deformation at each iteration and the conformational energy of the deformed structure is minimized via an MC algorithm. The target structure was approached successfully with an RMSD of 0.9–4.1 Å when a relatively low cutoff radius of 10 Å was used in ANM. Even though one predominant mode (first or second) directed the open-to-closed conformational transition, changes in the dominant mode character were observed for most cases along the transition. By imposing radius of gyration constraint during mode selection, it was possible to predict the closed structure for eight out of 10 proteins (with initial 4.1–7.1 Å and final 1.7–2.9 Å RMSD to target). Deforming along a single mode leads to most successful predictions. Based on the previously reported free energy surface of adenylate kinase, deformations along the first mode produced an energetically favorable path, which was interestingly facilitated by a change in mode shape (resembling second and third modes) at key points. Pathway intermediates are provided in our database of conformational transitions (http://safir.prc.boun.edu.tr/anmmc/method/1).

Crack Assessment in Frame Structures Using Modal Data and Unified Particle Swarm Optimization Technique

The present paper deals with the application of unified particle swarm optimization (UPSO) technique for solving crack assessment problems in frame like structures. UPSO is a scheme for improving performance of standard particle swarm optimization (SPSO) by harnessing its exploration and exploitation ability simultaneously. The objective function formulated for crack assessment purpose uses the changes in natural frequencies and mode shapes as the damage indicators. The efficiency of present crack assessment algorithm is demonstrated by conducting several studies. First, a numerical study conducted among several PSO variants, such as global best SPSO, local best SPSO, PSO with constriction factor, PSO with time varying acceleration coefficient and UPSO for accessing their performance in solving inverse problem for crack assessment. Secondly, the performance of UPSO based algorithm is validated with experimental results. Finally, numerical studies are conducted to investigate the performance of UPSO based algorithm in crack assessment using noisy modal data. The results of these studies indicate that the developed method is capable for crack detection and quantification with satisfactory precision.

Generalised local entropy analysis for crack detection in beam-like structures

Generally, cracks would lead in local discontinuity and sudden change in mode shape, and the local entropy of beam mode will change with the discontinuity of mode shape. Based on this property, cracks can be detected without using a healthy mode shape serving as the baseline. This paper presents a generalised local entropy (GLE) analysis method for crack detection in beam structures, which is a non-baseline mode shape-based damage detection algorithm for beam-type structures. The fundamental and the second-order vibration modes of a cracked cantilever beam are analysed with the presented method. The proposed prediction scheme is validated by simulations and experiments. Based on the results obtained in this paper and the qualities of simplicity and efficiency of GLE method, a mode shape-based crack identification approach is developed as an alternative damage index for structural health monitoring and non-destructive testing.

Alternation of Flex Cable Vibration Modes in High Precision Hard Disk Drives

For fast and accurate data accessing operations, flex cable's vibratory response has been identified to be the key development focus for magnetic hard disk drives to meet near nanometer precision accuracy. Dampening the cable's dynamics with damper layers and revising the seek servo designs have been the common approaches found in the literature to reach the requirement. In this paper, vibrations of nonuniform flex cable, which is composed of baseline flex cable layers and addition of piezoelectric layer such as polyvinylidene fluoride film, are investigated through experiments and non-classical, reduced-order finite element analysis. It is found that the addition of the piezofilm changes the cable's natural frequencies only within 3% error range but alters the cable's bending vibration mode shapes significantly. The change in the cable's mode shapes leads to change of the known cable/actuator dynamic coupling reported in the literature. Results presented in this paper establish mechanical framework for active control of the flex cable onto the rotary actuator.

Determination of the Shape Function of a Multiple Cracked Beam Element and Its Application for the Free Vibration Analysis of a Multiple Cracked Frame Structure

Assessment of the behavior of damaged structures as well as determination of the locations and the depths of cracks in multiple cracked structures are very important and attractive for many researchers. This article presents some results on the determination of the vibration shape function of a multiple cracked elastic beam element, which is modeled as an assembly of intact sub-segments connected by massless rotational springs. Algorithms and computer programs to analyse changes of natural mode shapes of multiple cracked beams have been determined. Numerical analysis of natural mode shapes of cracked simple support beams using the obtained expression shows a good agreement in comparison with the well-known analytical methods. The methodology approach and results presented in this article are new and the basis for building an efficient method to identify cracks in frame structures using wavelet analysis of mode shapes.

3A12 Effectiveness of TPA based on change in mode shape(The 12th International Conference on Motion and Vibration Control)

This paper presents new techniques for vibration transmission analysis on the finite element (FE) model using Transfer Path Analysis (TPA). The techniques are 1) a contribution calculation technique for structure with manifold and continuous transfer paths, and 2) a visualization technique of contributions for efficient derivation of measures to reduce vibration. Taking advantage of the characteristics of the numerical model, the cross section whose contributions are calculated is changed sequentially between input point and output point. This contribution of each node and each DOF is converted to influence degree, which is a new indicator and expresses vibration characteristics effectively. The magnitude of the influence degree is visually expressed by deformation of the FE model to support understanding of vibration transmission characteristics. First, the authors applied the proposed techniques to the simple vehicle body FE model for the purpose of reducing vibration at the position on the panel. The parts that are responsible for vibration at the target position were shown as characteristic diagrams. On the basis of these diagrams, the authors modified the structure of the body. As a result, the panel vibration in the focused-on frequency was reduced, and the relationship was obtained by which the measures based on influence degree change the mode shape of vibration to reduce the vibration response. Next, the authors applied this approach to the W/B FE model that represents the actual vehicle body, which is complicated in the same way. As a result, the vibration at the target position was reduced. From this result, the effectiveness and usefulness of the proposed approach was demonstrated.

509 モード変化に基づいた車体骨格の振動伝達分析(GS-10,19 車両と運動)

509 モード変化に基づいた車体骨格の振動伝達分析(GS-10,19 車両と運動)

Damage Detection of Cantilever Beams Based on Derivatives of Mode Shapes

For the small crack detection (crack ration less than 5%), the derivatives of mode shapes of cantilever beams were used for crack detection in the beams. These derivatives consist of the slope, curvature and rate of curvature, which are the first, second and third derivatives of the displacement mode shape respectively. The presence of a crack results in a slight change in the mode shape of a structure which is manifested as a small discontinuity in the response at the crack location. It is hard to detect small cracks in beams using the direct data of mode shape change. But when the first, second and third derivatives of the displacement mode shape, that is the slope, curvature and rate of curvature, respectively, of the cracked cantilever beam provide a progressively better indication of the presence of a crack. However, `noise' effects due to the difference approximation error also begin to be magnified at higher derivatives so that it is not advantageous to go beyond the third derivatives of mode shapes. For the intact beam, these derivatives are smooth curves. So the local peaks or discontinuity on the slope, curvature and rate of curvature modal curves can be used to indicate abnormal mode shape changes at those positions. In this way, these local peak positions can be used to detect and locate cracks in the structure. The modal responses of the damaged and intact cantilever beams used were computed using the finite element method.

Vibration Analysis of a Simply Supported Beam with Multiple Breathing Cracks

Abstract The dynamic characteristics of a beam with multiple breathing cracks are studied in this paper. A systematic approach has been adopted in the present investigation to develop theoretical expressions for evaluation of natural frequencies and mode shapes. A simple elastic simply supported beam with two breathing cracks is considered for the dynamic analysis. The stiffness of the cracked beam is found out by using influence coefficients. The influence coefficients are calculated by using castigiliano's theorem and strain energy release rate (SERR). The equation of motion of the beam was derived by using Hamilton's principle. The stiffness and natural frequencies for the multiple cracked beam calculated using eigen value approach. It is seen that due to presence of cracks, the stiffness and natural frequency changes. The mode shapes and the FRF for the uncracked, cracked and breathing cracked cantilever beam also obtained and compared. The mode shape changes considerably due to the presence of crack.

Crack Investigation of Rotating Cantilever Beam by Fractal Dimension Analysis

Abstract Cracks reduce the service life of structures. A crack in a structural member introduces local flexibility that would affect vibration response of the structure. Both the mode shape and frequency change significantly due to the presence of crack. The objective of this paper is to obtain information about the location and depth of transverse open multiple cracks in a rotating cantilever beams. Vibration parameter in the form of mode shape of damaged rotating beam is obtained using finite element simulation. Using fractal dimension of mode shape profile, damage is detected. It is also shown that this method can produce satisfactory results with some limitation based on profile.