Curvature Mode Research Articles

Nondestructive Damage Assessment of Composite Structures Based on Wavelet Analysis of Modal Curvatures: State-of-the-Art Review and Description of Wavelet-Based Damage Assessment Benchmark

The application of composite structures as elements of machines and vehicles working under various operational conditions causes degradation and occurrence of damage. Considering that composites are often used for responsible elements, for example, parts of aircrafts and other vehicles, it is extremely important to maintain them properly and detect, localize, and identify the damage occurring during their operation in possible early stage of its development. From a great variety of nondestructive testing methods developed to date, the vibration-based methods seem to be ones of the least expensive and simultaneously effective with appropriate processing of measurement data. Over the last decades a great popularity of vibration-based structural testing has been gained by wavelet analysis due to its high sensitivity to a damage. This paper presents an overview of results of numerous researchers working in the area of vibration-based damage assessment supported by the wavelet analysis and the detailed description of the Wavelet-based Structural Damage Assessment (WavStructDamAs) Benchmark, which summarizes the author’s 5-year research in this area. The benchmark covers example problems of damage identification in various composite structures with various damage types using numerous wavelet transforms and supporting tools. The benchmark is openly available and allows performing the analysis on the example problems as well as on its own problems using available analysis tools.

The use of modal curvatures for damage localization in beam-type structures

The localization of stiffness variation in damaged beams through modal curvatures, i.e., second derivative of mode shapes, is studied by exploiting a perturbative solution of the Euler–Bernoulli equation. It is shown that for low order modes the difference between undamaged and damaged modal curvatures has only one distinct peak if the damage is localized in a narrow region. This phenomenon is independent of the presence of experimental noise and of the technique used to reconstruct the curvature mode shapes from the displacement mode shapes. Broader damages cause the modal curvature difference to have several peaks outside the damage region that could result in a false damage localization. The same effect is present at higher modes for both narrow and broad damages. As a result, modal curvatures can be effectively used to localize structural damages only once they have been properly filtered. Here the perturbative solution is used to introduce an effective damage measure able to localize correctly narrow and broad damages and also single and multiple damages cases.

Vibration analysis of laminated composite plates with damage using the perturbation method

The present work focuses on vibration characteristics of damaged laminated composite plates. Damage is considered as a local reduction of anisotropic plate stiffness, and three damage factors (representing the damage severity, damage anisotropy, and damage location/area, respectively) are defined to describe damage status in the laminated composite plates. The analytical solutions are obtained by the perturbation method. A numerical analysis is conducted on the vibration of damaged laminated composited plates, and the effect of damage factors on the vibration characteristics is discussed. Results indicate that three damage factors have different influences on the vibration characteristics. Also, the modal curvatures and strain energy show higher damage sensitivity than the natural frequencies and displacement mode shapes. The perturbation-based vibration analysis developed in this study can be used to effectively evaluate the effect of damage on the vibration behavior of anisotropic plates and potentially identify the damage in the laminated plates.

Basin constrained κ-dimer method for saddle point finding.

Within the harmonic approximation to transition state theory, the rate of escape from a reactant is calculated from local information at saddle points on the boundary of the state. The dimer minimum-mode following method can be used to find such saddle points. But as we show, dimer searches that are initiated from a reactant state of interest can converge to saddles that are not on the boundary of the reactant state. These disconnected saddles are not directly useful for calculating the escape rate. Additionally, the ratio of disconnected saddles can be large, especially when the dimer searches are initiated far from the reactant minimum. The reason that the method finds disconnected saddles is a result of the fact that the dimer method tracks local ridges, defined as the set of points where the force is perpendicular to the negative curvature mode, and not the true ridge, defined as the boundary of the set of points which minimize to the reactant. The local ridges tend to deviate from the true ridge away from saddle points. Furthermore, the local ridge can be discontinuous and have holes which allow the dimer to cross the true ridge and escape the initial state. To solve this problem, we employ an alternative definition of a local ridge based upon the minimum directional curvature of the isopotential hyperplane, κ, which provides additional local information to tune the dimer dynamics. We find that hyperplanes of κ = 0 pass through all saddle points but rarely intersect with the true ridge elsewhere. By restraining the dimer within the κ < 0 region, the probability of converging to disconnected saddles is significantly reduced and the efficiency of finding connected saddles is increased.

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.

Three-step damage identification method based on dynamic characteristics

A three-step damage identification method based on dynamic characteristics is proposed to improve the structure reliability and security and avoid serious accident. In the proposed method, the frequency and difference of modal curvature (DMC) are used as damage indexes. Firstly, the detection of the occurrence of damage is addressed by the frequency or the square of frequency change. Then the damage location inside the structure is measured by the DMC. Finally, with the stiffness reduction rate as a damage factor, the amount of damage is estimated by the optimization algorithm. The three-step damage identification method has been validated by conducting the simulation on a cantilever beam and the shaking table test on a submerged bridge. The results show that the method proposed in this paper can effectively solve the damage identification problem in theory and engineering practice.

The neutral curve for stationary disturbances in rotating disk flow for power-law fluids

This paper is concerned with the convective instabilities associated with the boundary-layer flow due to a rotating disk. Shear-thinning fluids that adhere to the power-law relationship are considered. The neutral curves are computed using a sixth-order system of linear stability equations which include the effects of streamline curvature, Coriolis force and the non-Newtonian viscosity model. Akin to previous Newtonian studies it is found that the neutral curves have two critical values, these are associated with the type I upper-branch (cross-flow) and type II lower-branch (streamline curvature) modes. Our results indicate that an increase in shear-thinning has a stabilising effect on both the type I and II modes, in terms of the critical Reynolds number and growth rate. Favourable agreement is obtained between existing asymptotic predictions and the numerical results presented here.

Damage Identification of Continuous Rigid Frame Concrete Bridge

During a bridge service life, many factors can cause damage accumulation such as overloaded traffic, fatigue effect, and so on. Hence, the identification of potential damages has been received wide attention to prevent such sudden fatal accident. An experiment of a continuous rigid frame concrete bridge, which had 3 spans and a total length of 18 meters, was presented in this paper. Two load stages and ten different load steps were simulated to test various scenario of long-term loading and different levels of overload. Curvature mode method was adopted to detect the damage during the exercises. The changes of curvature modes were used to detect damage after the ten load steps. This method performed excellent to identify the damage position of the bridge. So, it is concluded that the curvature modes can be used to detect damage in actual structures. In addition, the Finite-Element Analysis (FEA) was utilized, and the experimental recurring was verified positively through FEA model.

Preface: A SPECIAL ISSUE ON PROGRESS IN CIVIL ENGINEERING

The Open Civil Engineering Journal, which is one of the most relevant international journals in civil engineering area, wishes to promote the latest researches in engineering structures. This special issue contains 8 invited outstanding articles covering a wide range of topics. We have assembled recent studies in the field of several typical structures, attempting to provide a glimpse into the wide range of engineering problems. It is expected that the special issue will benefit researchers and engineers who are interested in the design of protective structures and stimulate the research interests in this important an d promising area of civil engineering. A brief overview of each article published in this special issue is provided here. In “Experimental Study on Assembled Monolithic Concrete Shear Walls Built with Precast Two-way Hollow Slabs” , Zhijuan Sun et al. present a quasi-static experiment on one reinforced concrete shear wall and two shear walls built with precast two-way hollow slab. Test result shows that the new type of shear walls experienced the loading process from the whole wall to the portioned wall due to the internal and vertical joints of the wall body, which can be applied in practical construction. In “Study on Metering Scheme of Seismic Experiment for Shear Wall Built with Precast Hollow Slab” , Zhijuan Sun et al. present the measuring scheme of shear wall deformation and steel strain. The special mechanical characteristic of the shear wall built with precast two-way hollow slab is the relative deformation of the concrete on both sides of vertical joint. The study shows that the measuring methods of shear wall deformation and relative deformation are reasonable and feasible. In “Experimental Study on Precast Concrete Shear Walls with Different Hollow Slabs” , Qinyan Zhao et al. present a test on two shear walls built with precast two-way hollow slab with different details. The study shows that brittle shear failure can be avoided and the failure behaviors tend to evolve from integral wall to the combination of wall and columns. Also, compressive capacity of walls can be affected by the dimension of transverse holes. In “Test Study on Strength and Permeability Properties of Lime -Fly Ash Loess Under Freeze-Thaw Cycles”, Zhiquan Zhang and Yufen Zhang present a study on the engineering behaviors of lime-fly ash loess using uniaxial compressive test, fast direct shearing test and permeability test. Test data show that uniaxial compressive strength of lime-fly ash loess has good water stability and freeze-thaw stability, and can be applied in permafrost subgrade. In “Unloading Phenomena Characteristics in Brittle Rock Masses by A Large-scale Excavation in Dam Foundation”, Changgen Yan et al. investigate a large-scale excavation around the foundation of the dam. The characteristics of unloading rock masses were described with the acoustic wave velocity monitoring method. The unloading deformation has a direct temporal dependence, and increases quickly during the first 90 days, then with a slower rate from 90 to 180 days, and after that the unloading deformation will be small enough to be neglected In “A Review on Progressive Collapse of Building Structures” , Hao Wang et al. assess the recent studies on the progressive collapse of building structures from experimental study, numerical simulation and theoretical analysis. The design methods to prevent progressive collapse for building structures are also discussed. In “Damage Identification of Continuous Rigid Frame Concrete Bridge”, Shengnan Huang et al. present a large-scale experimental study on safety monitoring methodology for continuous rigid frame concrete bridge. Two load stages and ten different load steps were simulated to test various scenario of long-term loading and different levels of overload. Curva ture mode method was adopted to detect the damage during the exercises. In addition, the Finite-Element Analysis (FEA) was utilized, and the experimental recurring was verified positively through FEA model. In “Corrosion Monitoring Using Embedded Piezoelectric Sensors”, Lei Qin et al. develop a new type of corrosion detection technique for reinforced concrete. The technique used piezoelectric sensors to detect the ultrasonic signals during corrosion. The state of bonding layer of concrete and steel bar could be monitored. It can also detect the initial of corrosion and cracking of bonding layer. I am grateful to all the authors and reviewers for the contribution and support during the course of editing this special issue. Their prompt responses have made it possible for us to publish this special issue on time.

Damage localization in bridges via the FRF interpolation method

Vibration based methods are powerful tools to assess the structural behavior of a bridge. In this paper, the Interpolation Damage Detection Method is used to give an interpretation of frequency response function (FRF) measurements performed on a reinforced concrete single span bridge subject to increasing levels of concentrated damage. The sensitivity of the method is documented and discussed with respect to the amount of experimental data available and the severity of the damage. The results are encouraging. They show the ability of the method to correctly detect the damage location in the majority of the scenarios considered and to give quantitative indication of the relative severity of the damage. A comparison with the results obtained by the Modal Curvature Method is also presented.

Damage detection by modal curvatures: numerical issues

This work is concerned with modal curvature-based damage detection in slender beam-like structures, whereby the modal curvatures are computed by numerical differentiation of noisy mode shapes sampled at a finite number of measurement points. Within this framework, most common techniques greatly amplify the measurement errors and their application leads to unreliable outcomes, especially when a large set of measurement points is considered. Preliminary signal processing, even if beneficial for reducing the noise level, does not solve the problem in that neither the detection of damaged zones nor the reduction of false alarms exhibit significant improvements. In a comparative fashion, we herein demonstrate that a modified Savitzky–Golay filter and the cubic smoothing spline method can provide a more affordable way for detecting damages when using numerically obtained modal curvatures. In doing so, the robustness against the measurement errors and the role of the adopted formulation for the modal curvature-based damage index are considered. A simple statistical procedure that can further improve the detection of damaged regions together with the identification of possible false positives is also presented.

Calculation and experiment for dynamic response of bridge in deep water under seismic excitation

The fluid-structure interaction under seismic excitation is very complicated, and thus the damage identification of the bridge in deep water is the key technique to ensure the safe service. Based on nonlinear Morison equation considering the added mass effect and the fluid-structure interaction effect, the effect of hydrodynamic pressure on the structure is analyzed. A series of underwater shaking table tests are conducted in the air and in water. The dynamic characteristics affected by hydrodynamic pressure are discussed and the distribution of hydrodynamic pressure is also analyzed. In addition, the damage of structure is distinguished through the natural frequency and the difference of modal curvature, and is then compared with the test results. The numerical simulation and test of this study indicate that the effect of hydrodynamic pressure on the structure should not be neglected. It is also found that the presence of the damage, the location of the damage and the degree of the severity can be judged through the variation of structure frequency and the difference of modal curvature.

Damage identification techniques via modal curvature analysis: Overview and comparison

This paper aims to compare several damage identification methods based on the analysis of modal curvature and related quantities (natural frequencies and modal strain energy) by evaluating their performances on the same test case, a damaged Euler–Bernoulli beam. Damage is modelled as a localized and uniform reduction of stiffness so that closed-form expressions of the mode-shape curvatures can be analytically computed and data accuracy, which affects final results, can be controlled. The selected techniques belong to two categories: one includes several methods that need reference data for detecting structural modifications due to damage, the second group, including the modified Laplacian operator and the fractal dimension, avoids the knowledge of the undamaged behavior for issuing a damage diagnosis. To explain better the different performances of the methods, the mathematical formulation has been revised in some cases so as to fit into a common framework where the underlying hypotheses are clearly stated. Because the various damage indexes are calculated on ‘exact’ data, a sensitivity analysis has been carried out with respect to the number of points where curvature information is available, to the position of damage between adjacent points, to the modes involved in the index computation. In this way, this analysis intends to point out comparatively the capability of locating and estimating damage of each method along with some critical issues already present with noiseless data.

A Two Step Damage Prognosis Method for Beam-Like Truss Structures

In this study, a two step damage prognosis method is proposed for beam-like truss structures via combining modal curvature change (MCC) with modal strain energy change ratio (MSECR). Changes in the modal curvature and the elemental strain energy are selected as the indicator of damage prognosis. Different damage elements with different damage degrees are simulated. In the first step, the finite element method is used to model a beam-like truss structure and the displacement modes are got. The damage region is estimated by the MCC of top and bottom chords of a beam-like truss structure. In the second step, the elemental MSECR in the damage region is calculated and the maximum MSECR element is deemed as the damage element. The simulation results show that this method can accurately locate the damage in the beam-like truss structure.

Study on Damage Identification of Simple Beam Bridge Based on the First-Order Curvature Mode Ratio

Starting with damage identification index method on the basis of the curvature mode, the first-order curvature mode ratio is proposed, and then it is made a numerical simulation analysis for a single span simple beam bridge with ANSYS. The identification of structure damage degree under the damage on the single position is studied. The fitted polynomial based on the derivation of the first-order curvature mode ratio can estimate the damage degree; it has a good reference value for the damage detection of structures in practical engineering.

Research on Structure Damage Identification Method Based on Multi-Modal Parameters

The multi-modal parameters which are composed of the curvature mode and the flexibility curvature are used to identify the damage on the base of finite element method model based on continuous beam. It has been proved that multi-mode parameters are considered as the networks inputting parameters, and the location of the structure damage can be accurately determined and the damage degree can be obtained by the neural networks. It has indicated that this neural network has a excellent identification ability with good fault tolerance and robustness.

Secondary CMB anisotropies from bulk motions in the presence of stochastic magnetic fields

Bulk motions of electrons along the line of sight induce secondary temperature fluctuations in the post-decoupling, reionized universe. In the presence of a magnetic field not only the scalar mode but also the vector mode act as a source for the bulk motion. The resulting angular power spectrum of temperature anisotropies of the cosmic microwave background is calculated assuming a simple model of reionization.Contributions from the standard adiabatic, curvature mode and a non helical magnetic field are included. The contribution due to magnetic fields with field strengths of order nG and negative magnetic spectral indices becomes important for multipoles larger than $\ell \sim 10^4$.

A point-by-point impact vibration method for damage detection in beam-type structures

This paper develops the point-by-point impact vibration method, a damage diagnosis method for beam structures. The theoretical development and experimental verification were carried out on aluminum beams with single and double cracks in the vertical direction and on pre-stressed concrete beams with local breaks. The processing signals were the time histories of the acceleration responses of the beams and the impact force. The point-by-point impact vibration method is combined with the Dynamic Reciprocal Theorem, the Frequency Domain Decomposition method, and the Damage Index idea, all of which cover the modal curvature change (MCC) and the change of strain energy, as well as other measures. One of the advantages of this method is the ability to use fewer sensors to obtain higher order eigenmodes, which can be applied in the damage index. Experimental results indicate that higher order vibration modes exhibit great potential for damage identification.

Hair curvature: a natural dialectic and review

Although hair forms (straight, curly, wavy, etc.) are present in apparently infinite variations, each fibre can be reduced to a finite sequence of tandem segments of just three types: straight, bent/curly, or twisted. Hair forms can thus be regarded as resulting from genetic pathways that induce, reverse or modulate these basic curvature modes. However, physical interconversions between twists and curls demonstrate that strict one-to-one correspondences between them and their genetic causes do not exist. Current hair-curvature theories do not distinguish between bending and twisting mechanisms. We here introduce a multiple papillary centres (MPC) model which is particularly suitable to explain twisting. The model combines previously known features of hair cross-sectional morphology with partially/completely separated dermal papillae within single follicles, and requires such papillae to induce differential growth rates of hair cortical material in their immediate neighbourhoods. The MPC model can further help to explain other, poorly understood, aspects of hair growth and morphology. Separate bending and twisting mechanisms would be preferentially affected at the major or minor ellipsoidal sides of fibres, respectively, and together they exhaust the possibilities for influencing hair-form phenotypes. As such they suggest dialectic for hair-curvature development. We define a natural-dialectic (ND) which could take advantage of speculative aspects of dialectic, but would verify its input data and results by experimental methods. We use this as a top-down approach to first define routes by which hair bending or twisting may be brought about and then review evidence in support of such routes. In particular we consider the wingless (Wnt) and mammalian target of rapamycin (mTOR) pathways as paradigm pathways for molecular hair bending and twisting mechanisms, respectively. In addition to the Wnt canonical pathway, the Wnt/Ca(2+) and planar cell polarity (PCP) pathways, and others, can explain many alternatives and specific variations of hair bending phenotypes. Mechanisms for hair papilla budding or its division by bisection or fission can explain MPC formation. Epithelial-to-mesenchymal (EMT) and mesenchymal-to-epithelial (MET) transitions, acting in collaboration with epithelial-mesenchymal communications are also considered as mechanisms affecting hair growth and its bending and twisting. These may be treated as sub-mechanisms of an overall development from neural-crest stem cell (NCSC) lineages to differentiated hair follicle (HF) cell types, thus providing a unified framework for hair growth and development.

Primordial magnetic field limits from the CMB trispectrum: Scalar modes and Planck constraints

Cosmic magnetic fields are observed to be coherent on large scales and could have a primordial origin. Non-Gaussian signals in the cosmic microwave background (CMB) are generated by primordial magnetic fields as the magnetic stresses and temperature anisotropy they induce depend quadratically on the magnetic field. We compute the CMB scalar trispectrum on large angular scales, for nearly scale-invariant magnetic fields, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately ${10}^{\ensuremath{-}29}$ and ${10}^{\ensuremath{-}19}$, respectively. The scalar anisotropic stress trispectrum is also calculated in the flat-sky approximation and yields a similar result. Observational limits on CMB non-Gaussianity from the Planck mission data allow us to set upper limits of ${B}_{0}\ensuremath{\lesssim}0.6\text{ }\text{ }\mathrm{nG}$ on the present value of the primordial cosmic magnetic field. Considering the inflationary magnetic curvature mode in the trispectrum can further tighten the magnetic field upper limit to ${B}_{0}\ensuremath{\lesssim}0.05\text{ }\text{ }\mathrm{nG}$. These sub-nanoGauss constraints from the magnetic trispectrum are the most stringent limits so far on the strength of primordial magnetic fields, on megaparsec scales, significantly better than the limits obtained from the CMB bispectrum and the CMB power spectrum.