Curvature Mode Research Articles

Detection of low-velocity impact-induced delaminations in composite laminates using Auto-Regressive models

In this paper, the detection of delaminations in carbon-fiber-reinforced-plastic (CFRP) laminate plates induced by low-velocity impacts (LVI) is investigated by means of Auto-Regressive (AR) models obtained from the time histories of the acquired responses of the composite specimens. A couple of piezoelectric patches for actuation and sensing purposes are employed. The proposed structural health monitoring (SHM) routine begins with the selection of the suitable locations of the piezoelectric transducers via the numerical analysis of the curvature mode shapes of the CFRP plates. The normalized data recorded for the undamaged plate configuration are then analyzed to obtain the most suitable AR model using five techniques based on the Akaike Information Criterion (AIC), the Akaike Final Prediction Error (FPE), the Partial Autocorrelation Function (PAF), the Root Mean Squared (RMS) of the AR residuals for different order p, and the Singular Value Decomposition (SVD). Linear Discriminant Analysis (LDA) is then applied on the AR model parameters to enhance the performance of the proposed delamination identification routine. Results show the effectiveness of the developed procedure when a reduced number of sensors is available.

Imprints of massive primordial fields on large-scale structure

Attention has focussed recently on models of inflation that involve a second or more fields with a mass near the inflationary Hubble parameter H, as may occur in supersymmetric theories if the supersymmetry-breaking scale is not far from H. Quasi-single-field (QsF) inflation is a relatively simple family of phenomenological models that serve as a proxy for theories with additional fields with masses m∼ H. Since QsF inflation involves fields in addition to the inflaton, the consistency conditions between correlations that arise in single-clock inflation are not necessarily satisfied. As a result, correlation functions in the squeezed limit may be larger than in single-field inflation. Scalar non-Gaussianities mediated by the massive isocurvature field in QsF have been shown to be potentially observable. These are especially interesting since they would convey information about the mass of the isocurvature field. Here we consider non-Gaussian correlators involving tensor modes and their observational signatures. A physical correlation between a (long-wavelength) tensor mode and two scalar modes (tss), for instance, may give rise to local departures from statistical isotropy or, in other words, a non-trivial four-point function. The presence of the tensor mode may moreover be inferred geometrically from the shape dependence of the four-point function. We compute tss and stt (one soft curvature mode and two hard tensors) bispectra in QsF inflation, identifying the conditions necessary for these to “violate” the consistency relations. We find that while consistency conditions are violated by stt correlations, they are preserved by the tss in the minimal QsF model. Our study of primordial correlators which include gravitons in seeking imprints of additional fields with masses m∼ H during inflation can be seen as complementary to the recent ``cosmological collider physics'' proposal.

Axial quasinormal modes of Einstein-Gauss-Bonnet-dilaton neutron stars

We investigate axial quasi-normal modes of realistic neutron stars in Einstein-Gauss-Bonnet-dilaton gravity. We consider 8 realistic equations of state containing nuclear, hyperonic, and hybrid matter. We focus on the fundamental curvature mode and compare the results with those of pure Einstein theory. We observe that the frequency of the modes is increased by the presence of the Gauss-Bonnet-dilaton, while the impact on the damping time is typically smaller. Interestingly, we obtain that universal relations valid in pure Einstein theory still hold for Einstein-Gauss-Bonnet-dilaton gravity, and we propose a method to use these phenomenological relations to constrain the value of the Gauss-Bonnet coupling.

Performance of Vibration Based Damage Detection Algorithms for Detection of Disbond in Stiffened Metallic Plates

Though vibration based health monitoring has been the focus of attention for quite some time, there exist a strong requirement for an extensive and comprehensive study on the relative performance of different damage detection algorithms under different damage scenarios. To fulfill this objective, a stiffened aluminium plate has been selected to make a comparative study on the performance of several vibration based damage detection techniques, namely, Modal Curvature, Gapped Smoothing Method/Modal Curvature, Generalized Fractal Dimension and Uniform Load Surface Curvature based on four different criteria: variation of damage intensity (i.e., disbond length), position of stiffener and disbond, the effect of noise and capability to detect multiple damage. In addition to this, a new approach, based on the curvature of wavelet coefficients, has been presented. It is found that this novel approach is extremely effective in determining the presence and location of damage under different situations. The entire numerical modelling is done in ANSYS 14.0 and the damage detection algorithms written in MATLAB codes have been used to generate the required damage indices using the modal data retrieved from ANSYS. The study ultimately enlightens inherent characteristics of the various damage detection algorithms under different damage conditions.

Vibration Based Methods For Damage Detection In Structures

Vibration based damage detection methods are among the most popular and promising approaches for health monitoring of structures. In this work a critical review of different methods for damage detection methods of structures is presented. The theoretical bases of the most popular methods based on the changes in the modal properties of the structures are deduced. The review includes the modal displacements, the mode shape slopes, the modal curvatures and the strain energy methods. The efficiency of all these methods is compared by using a finite element analysis of intact and damaged beams. The methods are tested experimentally by using a scanning laser vibrometer to measure the modal properties of specially prepared composite beams with defects. All this methods are compared with the damage detection method based on the analysis of the Poincaré maps of the motion of the structures). Conclusions concerning the advantages and the applicability of the considered methods are deduced.

Research on Calculation and Location of Defects in Derrick Tower

Having suffered from the serious environment for ages leads to a decline in the carrying capacity of the derrick as a result of different types of defects. Aiming at a certain derrick tower, finite element analysis software ANSYS was used to calculate and analyze the mode difference of curvature of derrick before and after the damage based on the theory of damage identification from changes in curvature mode shape. Then the conclusion is confirmed by experiments. It shows that local corrosion and bending will cause the change of first two order curvature mode of derrick, and the more is the local damage, the bigger is the mode difference of curvature.

Phonon-phonon interactions and phonon damping for the curvature modes in carbon nanotubes

We focus on the damping of the lowest-lying gapped modes with integer angular-momentum quantum number in carbon nanotubes (CNTs). These modes, called C modes simply, can be predicted within the framework of the continuum elasticity theory with the curvature term. Based on the phonon-phonon interactions due to the anharmonic effect, we obtain the three-phonon coupling coefficients of different damping processes of C modes. Applying perturbation theory, we calculate relaxation rates and upper bounds of quality factors for the long-wavelength C modes. In addition, we display the wave vector dependence of and show the importance of the C mode damping to thermal conductivity.

Damage detection for plate-like structures using generalized curvature mode shape method

Mode shape curvature-based method was originally developed to identify the damage in one-dimensional beam-like structures. In this paper, the method is generalized to fit for damage identification of plate-like structures, using two-dimensional mode shape curvatures. The modified method only requires the first few curvature mode shapes of the plate before and after damage, or only need modal information of the damaged plate if gapped smoothing technique is employed. To evaluate the effectiveness of the proposed method, numerical simulations considering various plate damage scenarios in terms of damage location, damage severity and multiple damages have been conducted, and experimental modal analysis on a steel plate with clamped and free edges is also performed to correlate with the numerical results. The final results show that the proposed method works well to detect the damage in a simple manner. For damaged structures, irregularities in their modal characterizations are induced at the places where local damages exist. Gapped smoothing technique takes advantage of smoothing functions and elevates the suggest method to be a reference-free approach. In the present study, a brief discussion has been performed and suggestions have been given concerning different smoothing functions used in the gapped smoothing technique.

STUDY ON DAMAGE DETECTION OF SQUARE PYRAMID SPACE GRID STRUCTURE CONSIDERING INITIAL RANDOM DEFECTS

Because of different types of load, material properties deviation and construction errors, structures have initial defects inevitably. Therefore structural damages emerge easily and have strong randomness. At the same time, the ideal design model often has difference with structure in service. To most structures, the initial testing dates cannot be obtained, while this initial model is very important to structural damage detection. So the ideal model needs to revise. In this paper, elastic modulus, Poisson ratio and link section area are given as initial random defects and these defects obey normal distribution which can be constructed by Monte Carlo probabilistic design method. Firstly, the sensitivity parameters to structural response will be received by PDS technology from Ansys. Next, the square pyramid space grid models with random defects were obtained. Finally, given link element damage, using the method combined curvature mode difference with wavelet transform, the link element damage can be determined. Through analysis, the effects about the initial defects to damage detection will be obtained.

Effect of damage on the vibration modal of a novel three-dimensional and four-directional braided composite T-beam

The effect of damage on the modal properties of a three-dimensional (3Dim) and four-directional (4Dir) braided composite T-beam was investigated by means of modal experiments and finite element analysis (FEA). The experimental tests on these damaged T-beams showed alteration of the vibration mode response. The damage obviously changed the mode shape curvatures. The influence of the damage upon the modal shape curvatures of the T-beam could be used to detect and localize the damage. Finite element modeling (FEM) of the damaged T-beam revealed that the damage affected the natural frequency of the T-beam but did not affect its modal shape.

Sparse sensing detection of impact-induced delaminations in composite laminates

The detection of delaminations in composite structures due to impacts is a critical issue for any structural health monitoring (SHM) programme. In this work, an experimental campaign is carried out to investigate the presence of delamination induced in carbon-fibre-reinforced-plastic (CFRP) plates by low velocity impacts (LVI). A reduced number of piezoelectric devices for actuation and sensing purposes are employed. The proposed study starts with the choice of the proper positions of the piezoelectric sensor and actuator through the analysis of the numerical curvature mode shapes of the composite laminated plate. A wavelet packet transform (WPT)-based algorithm is applied on the vibrating response of the plates to extract wavelet-based damage sensitive features. Linear Discriminant Analysis (LDA) is then applied on the extracted damage sensitive features to enhance the performance of the proposed delamination identification procedure. Results show the effectiveness of the developed SHM routine when a reduced number of sensors is either desirable or mandatory.

Non-linear curvature inhomogeneities and backreaction for relativistic viscous fluids

The non-perturbative curvature inhomogeneities induced by relativistic viscous fluids are not conserved in the large-scale limit. However, when the bulk viscosity is a function of the total energy density of the plasma (or of the trace of the extrinsic curvature), the relevant evolution equations develop a further symmetry preventing the nonlinear growth of curvature perturbations. In this situation the fully inhomogeneous evolution can be solved to leading order in the gradient expansion. Over large scales, both the acceleration and the curvature inhomogeneities are determined by the bulk viscosity coefficients. Conversely the shear viscosity does not affect the evolution of the curvature and does not produce any acceleration. The curvature modes analyzed here do not depend on the choice of time hypersurfaces and are invariant for infinitesimal coordinate transformations in the perturbative regime.

Impact damage identification in composite skin-stiffener structures based on modal curvatures

The feasibility of a vibration-based damage identification approach for impact damage in two advanced composite skin-stiffener structures is investigated in this paper. Mode shape curvatures combined with the modal strain energy damage index (MSE-DI) algorithm are utilized to identify the damage. Special attention is paid to the effective application of this vibration-based methodology by investigating the relation between the damage location, the structural design, and the dynamic behavior. The performance of a 1D and 2D formulation of the MSE-DI algorithm is compared for several damage scenarios. Experiments demonstrated the capabilities of the MSE-DI algorithm to detect, localize, and roughly quantify the size of barely visible impact damage in advanced composite structures. It is concluded that the method is particularly effective for health monitoring of skin-stiffener connections. The most effective results were obtained by considering the 1D formulation in the direction of the stiffeners for the stiffener mid-section and perpendicular to the stiffeners for the stiffener run-out. The method remained inconclusive in the case of pure skin-related damage. The results obtained in this study contribute to the development of guidelines for vibration-based structural health monitoring of advanced composite skin-stiffener structures. Copyright © 2015 John Wiley & Sons, Ltd.

Elastic Parameter Identification of Plate Structures Using Modal Response: An ECE Based Approach

AbstractThis article describes an inverse method for the identification of heterogeneous anisotropic elastic parameters of plate structure from an incomplete modal response. Many efforts in this area have shown that derivatives of the displacement mode shapes or curvature mode shapes are much more sensitive to the heterogeneous parameter distribution of the structure when compared with the mode shapes themselves. Thus, the curvature mode shapes are used widely to quantify the material profile. Following this observation, a strategy based on the error in constitutive equation (ECE) function, which naturally incorporates this fact seamlessly into the identification procedure, is proposed. The identification problem is posed as an optimization problem in that the cost function measures the discrepancy in the constitutive equation, which connects kinematically admissible curvature/strains and dynamically admissible couples/stresses. The resulting system becomes an extended system with primary and Lagrangian v...

Damage detection on framed structures: modal curvature evaluation using Stockwell Transform under seismic excitation

The key parameters for damage detection and localization are eigenfrequencies, related equivalent viscous damping factors and mode shapes. The classical approach is based on the evaluation of these structural parameters before and after a seismic event, but by using a modern approach based on time-frequency transformations it is possible to quantify these parameters throughout the ground shaking phase. In particular with the use of the S-Transform, it is possible to follow the temporal evolution of the structural dynamics parameters before, during and after an earthquake. In this paper, a methodology for damage localization on framed structures subjected to strong motion earthquakes is proposed based on monitoring the modal curvature variation in the natural frequency of a structure. Two examples of application are described to illustrate the technique: Computer simulation of the nonlinear response of a model, and several laboratory (shaking table) tests performed at the University of Basilicata (Italy). Damage detected using the proposed approach and damage revealed via visual inspections in the tests are compared.

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.

A combined modal strain energy and particle swarm optimization for health monitoring of structures

Main complexities of classical health-monitoring techniques, such as modal strain energy (MSE) and modal curvature (MCR), are noise sensitivity and false alarming. On the other hand, the modern techniques, such as model updating, become very complex for a large number of variables and large search space. In this present study, a new health-monitoring technique based on the combination of MSE and model updating is presented for fast and accurate identification of structural damage. In this technique, the probable locations of an unknown damage are determined using MSE-based damage index (MSEDI). The effect of noise is reduced by passing the vibration data through Morlet wavelet filter. In this context, the peaks of the MSEDI in the wavelet domain are considered as the suspicious locations of damages. The exact location and the severity of the damage are then determined by applying model updating technique. To achieve this, reduction of stiffnesses at the probable locations is considered as the updating variable. The objective function is developed using MCR in wavelet domain and minimized by particle swarm optimization technique. The final updated values of the stiffnesses at those locations represent the actual locations and severity of the damage. The technique is applied on a simulated single-storied plane steel frame structure and a similar experimental model with welded joints for single and multiple damage scenarios. The damage was introduced either near to or away from the joints by making saw-cut grooves representing loss of stiffness. The results depict the effectiveness of the technique for potential application in real-life structures.

Two-dimensional curvature mode shape method based on wavelets and Teager energy for damage detection in plates

Vibration-based damage detection in plates has been investigated by various methods relying on mode shapes, among which the 2D curvature mode shape is a damage feature attracting much attention of researchers. Unlike the sound understanding of the use of the 1D curvature mode shape for detecting damage in beams, however, use of the 2D curvature mode shape to detect damage in plates is not yet well elucidated, major unresolved issues including lack of clarity about the mechanism of characterizing damage, susceptibility to noise, and insensitivity to sight damage. These deficiencies severely hamper use of the 2D curvature mode shape to portray damage in plates. To deal with these deficiencies, the mechanism of using 2D curvature mode shape to depict damage is analytically clarified in light of thin plate theory. On the basis of this clarification, a synergy between wavelet transform and a Teager energy operator is proposed to tackle the other deficiencies of susceptibility to noise and insensitivity to sight damage, leading an enhanced 2D curvature mode shape. The efficacy of the enhanced 2D curvature mode shape is numerically demonstrated using finite element simulations and experimentally validated through noncontact measurement by a scanning laser vibrometer, whereby its advances of clear mechanism of characterizing damage, robustness against noise, and sensitivity to slight damage are sufficiently corroborated.

Development of temperature-robust damage factor based on sensor fusion for a wind turbine structure

Wind power systems have gained much attention due to the relatively high reliability, maturity in technology and cost competitiveness compared to other renewable alternatives. Advances have been made to increase the power efficiency of the wind turbines while less attention has been focused on structural integrity assessment of the structural systems. Vibration-based damage detection has widely been researched to identify damages on a structure based on change in dynamic characteristics. Widely spread methods are natural frequency-based, mode shape-based, and curvature mode shape-based methods. The natural frequency-based methods are convenient but vulnerable to environmental temperature variation which degrades damage detection capability; mode shapes are less influenced by temperature variation and able to locate damage but requires extensive sensor instrumentation which is costly and vulnerable to signal noises. This study proposes novelty of damage factor based on sensor fusion to exclude effect of temperature variation. The combined use of an accelerometer and an inclinometer was considered and damage factor was defined as a change in relationship between those two measurements. The advantages of the proposed method are: 1) requirement of small number of sensor, 2) robustness to change in temperature and signal noise and 3) ability to roughly locate damage. Validation of the proposed method is carried out through numerical simulation on a simplified 5 MW wind turbine model.

Damage Identification of Bridge Based on Chebyshev Polynomial Fitting and Fuzzy Logic without Considering Baseline Model Parameters

The paper presents an effective approach for damage identification of bridge based on Chebyshev polynomial fitting and fuzzy logic systems without considering baseline model data. The modal curvature of damaged bridge can be obtained through central difference approximation based on displacement modal shape. Depending on the modal curvature of damaged structure, Chebyshev polynomial fitting is applied to acquire the curvature of undamaged one without considering baseline parameters. Therefore, modal curvature difference can be derived and used for damage localizing. Subsequently, the normalized modal curvature difference is treated as input variable of fuzzy logic systems for damage condition assessment. Numerical simulation on a simply supported bridge was carried out to demonstrate the feasibility of the proposed method.