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Journal articles on the topic 'Curvature mode shape'

Author: Grafiati

Published: 30 June 2021

Last updated: 3 February 2022

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1

Gorgin, Rahim, and Ziping Wang. "Structural Damage Identification Based on Principal Curvatures of Mode Shape." International Journal of Acoustics and Vibration 25, no. 4 (December 30, 2020): 566–76. http://dx.doi.org/10.20855/ijav.2020.25.41714.

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This paper presents a procedure for damage identification and characterization on plates, based on the principal curvatures of their first mode shape. Each mode shape represents the displacement of the structure at its corresponding natural frequency. Since, variations in the geometry due to cracks or material property degradation, make changes in the mode shapes of the structure, such changes can be used for damage identification methods. The presented procedure only requires the first mode shape of the intact and damaged structure. It is shown that the principal curvatures of the surface defined by the first mode shape of the structure, are sensitive to damage and the maximum principal curvature can be used to highlight damages on the structure. The performance of the developed method is firstly evaluated using finite element analysis. To this aim, the procedure is applied to highlight both single and multi-damages in different locations of the plate with different boundary conditions. It is shown that the location of the maximum curvature variation coincides well with the location of damages and the amount of the maximum curvature change can be used as a parameter to describe damage severity. The accuracy of the proposed method is also experimentally verified by test on an aluminum plate and it is demonstrated that the proposed method remains effective even in experimental condition when only a limited number of measurements are available.

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2

Guo, Jin Quan, Fen Lan Ou, Jian Feng Zhong, Shun Cong Zhong, Xiao Xiang Yang, and Li Gang Yao. "Damage Detection of Cantilever Beams Based on Derivatives of Mode Shapes." Applied Mechanics and Materials 488-489 (January 2014): 817–20. http://dx.doi.org/10.4028/www.scientific.net/amm.488-489.817.

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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.

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Rucevskis, S., and M. Wesolowski. "Identification of Damage in a Beam Structure by Using Mode Shape Curvature Squares." Shock and Vibration 17, no. 4-5 (2010): 601–10. http://dx.doi.org/10.1155/2010/729627.

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During the last decades a great variety of methods have been proposed for damage detection by using the dynamic structure characteristics, however, most of them require modal data of the structure for the healthy state as a reference. In this paper the applicability of the mode shape curvature squares determined from only the damaged state of the structure for damage detection in a beam structure is studied. To establish the method, two aluminium beams containing different-size mill-cut damage at different locations are tested by using the experimentally measured modal data. The experimental modal frequencies and the corresponding mode shapes are obtained by using a scanning laser vibrometer with a PZT actuator. From the mode shapes, mode shape curvatures are obtained by using a central difference approximation. With the example of the beams with free-free and clamped boundary conditions, it is shown that the mode shape curvature squares can be used to detect damage in the structures. Further, the extent of a mill-cut damage is identified via modal frequencies by using a mixed numerical-experimental technique. The method is based on the minimization of the discrepancy between the numerically calculated and experimentally measured frequencies.

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4

Ručevskis, Sandris, and Andris Chate. "DAMAGE IDENTIFICATION IN A PLATE-LIKE STRUCTURE USING MODAL DATA." Aviation 17, no. 2 (July 1, 2013): 45–51. http://dx.doi.org/10.3846/16487788.2013.805863.

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In this paper, an on-going research effort aimed at detecting and localising damage in plate-like structures by using mode shape curvature–based damage detection algorithms is described. Two alternative damage indexes are examined. The first one uses exclusively mode shape curvature data from the damaged structure. This method was originally developed for beam-like structures. In this paper, the method is generalised to plate-like structures that are characterised by two-dimensional mode shape curvature. To examine limitations of the method, several sets of simulated data are applied and damage detection results are compared to the damage identification method that requires mode shape information from both the undamaged and the damaged states of the structure. The modal frequencies and the corresponding mode shapes for the first 15 modes of a plate are obtained via finite element models. Simulated test cases include damage of various levels of severity. In order to ascertain the sensitivity of the proposed method to noisy experimental data, numerical mode shapes are corrupted with different levels of random noise.

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5

Rucevskis, Sandris, Pavel Akishin, and Andris Chate. "Numerical and Experimental Study on the Application of Mode Shape Curvature for Damage Detection in Plate-Like Structures." Solid State Phenomena 220-221 (January 2015): 264–70. http://dx.doi.org/10.4028/www.scientific.net/ssp.220-221.264.

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The paper describes on-going research effort at detecting and localizing damage in plate-like structures using mode shape curvature based damage detection algorithm. The proposed damage index uses data on exclusively mode shape curvature from the damaged structure. This method was originally developed for beam-like structures. The article generalizes the method of plate-like structures characterized by two-dimensional mode shape curvature. To examine limitations of the method, several sets of simulated data are applied and the obtained results of the numerical detection of damage are validated by comparing them with the findings of the case of the experimental test. The simulated test cases include the damage of various levels of severity. In order to ascertain the sensitivity of the proposed method for noisy experimental data, numerical mode shapes are corrupted with different levels of random noise. Modal frequencies and corresponding mode shapes of an aluminium plate containing mill-cut damage are obtained via finite element models for numerical simulations and by using a scanning laser vibrometer (SLV) for the experimental study.

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6

Yan, Guirong, Xuelin Peng, and Hong Hao. "Localization of free-spanning damage using mode shape curvature." Journal of Physics: Conference Series 305 (July 19, 2011): 012017. http://dx.doi.org/10.1088/1742-6596/305/1/012017.

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7

Roy, Koushik. "Structural Damage Identification Using Mode Shape Slope and Curvature." Journal of Engineering Mechanics 143, no. 9 (September 2017): 04017110. http://dx.doi.org/10.1061/(asce)em.1943-7889.0001305.

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8

Pavlova, Anastasia V., Judith R. Meakin, Kay Cooper, Rebecca J. Barr, and Richard M. Aspden. "Variation in lifting kinematics related to individual intrinsic lumbar curvature: an investigation in healthy adults." BMJ Open Sport & Exercise Medicine 4, no. 1 (July 2018): e000374. http://dx.doi.org/10.1136/bmjsem-2018-000374.

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ObjectiveLifting postures are frequently implicated in back pain. We previously related responses to a static load with intrinsic spine shape, and here we investigate the role of lumbar spine shape in lifting kinematics.MethodsThirty healthy adults (18–65 years) performedfreestyle,stoopandsquatlifts with a weighted box (6–15 kg, self-selected) while being recorded by Vicon motion capture. Internal spine shape was characterised using statistical shape modelling (SSM) from standing mid-sagittal MRIs. Associations were investigated between spine shapes quantified by SSM and peak flexion angles.ResultsTwo SSM modes described variations in overall lumbar curvature (mode 1 (M1), 55% variance) and the evenness of curvature distribution (mode 2 (M2), 12% variance). M1 was associated with greater peak pelvis (r=0.38, p=0.04) and smaller knee flexion (r=–0.40, p=0.03) angles; individuals with greater curviness preferred to lift with a stooped lifting posture. This was confirmed by analysis of those individuals with very curvy or very straight spines (|M1|>1 SD). There were no associations between peak flexion angles and mode scores instooporsquattrials (p>0.05). Peak flexion angles were positively correlated betweenfreestyleandsquattrials but not betweenfreestyleandstooporsquatandstoop, indicating that individuals adjusted knee flexion while maintaining their preferred range of lumbar flexion and that ‘squatters’ adapted better to different techniques than ‘stoopers’.ConclusionSpinal curvature affects preferred lifting styles, and individuals with curvier spines adapt more easily to different lifting techniques. Lifting tasks may need to be tailored to an individual’s lumbar spine shape.

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9

Qiao, Pizhong, Kan Lu, Wahyu Lestari, and Jialai Wang. "Curvature mode shape-based damage detection in composite laminated plates." Composite Structures 80, no. 3 (October 2007): 409–28. http://dx.doi.org/10.1016/j.compstruct.2006.05.026.

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10

Fan, R., S. K. Singh, and C. D. Rahn. "Modal Analysis of Ballooning Strings With Small Curvature." Journal of Applied Mechanics 68, no. 2 (August 29, 2000): 332–38. http://dx.doi.org/10.1115/1.1355776.

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During the manufacture and transport of textile products, yarns are rotated at high speed. The surface of revolution generated by the rotating yarn is called a balloon. The dynamic response of the balloon to varying rotation speed, boundary excitation, and aerodynamic disturbances affects the quality of the associated textile product. Resonance, in particular, can cause large tension variations that reduce product quality and may cause yarn breakage. In this paper, the natural frequencies and mode shapes of a single loop balloon are calculated to predict resonance. The three-dimensional nonlinear equations of motion are simplified under assumptions of small displacement and quasi-static axial motion. After linearization, Galerkin’s method is used to calculate the mode shapes and natural frequencies. Experimental measurements of the steady-state balloon shape and the first two natural frequencies and mode shapes are compared with theoretical predictions.

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11

Ručevskis, Sandris, Miroslaw Wesolowski, and Andris Chate. "VIBRATION-BASED DAMAGE DETECTION IN A BEAM STRUCTURE WITH MULTIPLE DAMAGE LOCATIONS." Aviation 13, no. 3 (September 30, 2009): 61–71. http://dx.doi.org/10.3846/1648-7788.2009.13.61-71.

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During the last two decades structural damage identification using dynamic parameters of the structure has become an important research area for civil, mechanical, and aerospace engineering communities. The basic idea of the vibration‐based damage detection methods is that a damage as a combination of different failure modes in the form of loss of local stiffness in the structure alters its dynamic characteristics, i.e., the modal frequencies, mode shapes, and modal damping values. A great variety of methods have been proposed for damage detection by using dynamic structure parameters; however, most of them require modal data of the healthy state of structure as a reference. In this paper a vibration‐based damage detection method, which uses the mode shape information determined from only the damaged state of the structure is proposed. To establish the method, two aluminium beams containing different sizes of mill‐cut damage at a single location as well as two aluminium beams containing different sizes of mill‐cut damage at multiple locations are examined. The experimental modal frequencies and the corresponding mode shapes for the first 15 flexural modes are obtained by using a scanning laser vibrometer with a PZT actuator. From the mode shapes, mode shape curvatures are obtained by using a central difference approximation. In order to exclude the influence of measurement noise on the modal data and misleading damage indices, it is proposed to use the sum of mode shape curvature squares for each mode. With the example of the beams with free‐free and clamped boundary conditions, it is shown that the mode shape curvature squares can be used to detect damage in the structures. The extent of mill‐cut damage is identified via the modal frequencies by using mixed numerical‐experimental technique. The method is based on the minimization of the discrepancy between the numerically calculated and the experimentally measured frequencies. The numerical frequencies are calculated by employing a finite‐element model for beam with introduced damage. Further, by using the response surface approach, a relationship (second‐order polynomial function) between the modal frequencies and the damage extent is constructed. The damage extent is obtained by solving the minimization problem. Santrauka Tyrimo metu buvo ieškomos sijines konstrukcijos pažeidimo frezuojant vietos, apimtis ir pažeidimo dydis pagal atlikto vibraciju eksperimento dinamines charakteristikas. Pažeidimo padetis ir apimtis buvo nustatomi pagal išlinkio formos virpesiu kvadrato dydi. Pažeidimo dydis buvo nustatomas skaitiniu‐eksperimentiniu metodu, taikant modalinius dažnius. Šio metodo efektyvumas ir patikimumas parodytas tiriant dvi aliuminio sijas, kurios buvo pažeistos frezos vienoje vietoje ir kurios buvo pažeistos skirtingose vietose.

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12

Wu, D., and S. S. Law. "Sensitivity of Uniform Load Surface Curvature for Damage Identification in Plate Structures." Journal of Vibration and Acoustics 127, no. 1 (February 1, 2005): 84–92. http://dx.doi.org/10.1115/1.1857918.

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In this paper a new sensitivity-based method of using measured modal parameters to locate and quantify damage is developed for plate-like structures. With the measured incomplete modal data for only the few lower modes in both the intact and damaged states, the two-dimensional distributed curvatures of uniform load surface (ULS) over the plate are approximated using the Chebyshev polynomials. Instead of directly comparing the curvatures before and after damage, like many existing damage localization methods using curvature techniques, e.g., mode shape curvature and flexibility curvature, the proposed method analytically studies the sensitivity of the ULS curvature with respect to the element-by-element stiffness parameters. The changes in the elemental stiffness parameters due to damage give the location and magnitude of the damaged plate elements. Based on the first-order Taylor series approximation, the inverse problem is modeled as a linear equation system and solved iteratively using truncated SVD technique. Numerical simulations are performed to verify the effectiveness of the proposed method with different support conditions, measurement noise, and sensor sparsity.

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13

Yang, Chong, Yu Fu, Jianmin Yuan, Min Guo, Keyu Yan, Huan Liu, Hong Miao, and Changchun Zhu. "Damage Identification by Using a Self-Synchronizing Multipoint Laser Doppler Vibrometer." Shock and Vibration 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/476054.

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The vibration-based damage identification method extracts the damage location and severity information from the change of modal properties, such as natural frequency and mode shape. Its performance and accuracy depends on the measurement precision. Laser Doppler vibrometer (LDV) provides a noncontact vibration measurement of high quality, but usually it can only do sampling on a single point. Scanning LDV is normally used to obtain the mode shape with a longer scanning time. In this paper, a damage detection technique is proposed using a self-synchronizing multipoint LDV. Multiple laser beams with various frequency shifts are projected on different points of the object, reflected and interfered with a common reference beam. The interference signal containing synchronized temporal vibration information of multiple spatial points is captured by a single photodetector and can be retrieved in a very short period. Experiments are conducted to measure the natural frequencies and mode shapes of pre- and postcrack cantilever beams. Mode shape curvature is calculated by numerical interpolation and windowed Fourier analysis. The results show that the artificial crack can be identified precisely from the change of natural frequencies and the difference of mode shape curvature squares.

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14

Béda, Michael G. "A Curvature-Based Interpretation of the Steinberg Criterion for Fatigue Life of Electronic Components." International Symposium on Microelectronics 2015, no. 1 (October 1, 2015): 000707–12. http://dx.doi.org/10.4071/isom-2015-tha63.

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The “Steinberg Criterion” is a well-known method for determining the fatigue life of Printed Circuit Board (PCB) components based on the deflection of the PCB. It has been adopted as a de facto industry standard for the fatigue analysis of electronic components, and has been successfully used on many programs. However it has some limitations. Steinberg derived this equation to describe the behavior of rectangular PCBs simply supported on all sides. In this configuration the deformed shape of the first mode of a PCB under vibratory loads is assumed by Steinberg to be described by two perpendicular half sine waves. Unfortunately many PCBs have distorted mode shapes as a result of clamped or asymmetric edge constraints, stiffeners, or irregular PCB outline. Finite Element Models (FEMs) can be used to predict mode shapes for these PCBs, but there has been no clear way to use Steinberg's equation to determine the fatigue margin for components on such boards. The traditional method (when the discrepancy is addressed) is to use a value for PCB length in the equation based on an approximation of the length of an equivalent half sine wave superimposed on the predicted mode shape. This approach, while better than ignoring the problem, can lead to inconsistency in results or the overlooking of localized effects, and in the case of extremely odd mode shapes can be nearly impossible. This paper presents a method of using FEM data for curvature as well as deflection at a single location to eliminate the shape and location variables from the Steinberg criterion, allowing it to be applied confidently to PCBs and Printed Wiring Assemblies (PWAs) with any shape and boundary conditions. Test cases are described that show equivalence between this method and the existing Steinberg criterion. Lastly the methodology used to extract phase-consistent curvature and deflection results from FEM analysis is briefly discussed.

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15

Janeliukstis, R., S. Rucevskis, M. Wesolowski, and A. Chate. "Damage Identification Dependence on Number of Vibration Modes Using Mode Shape Curvature Squares." Journal of Physics: Conference Series 744 (September 2016): 012054. http://dx.doi.org/10.1088/1742-6596/744/1/012054.

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16

Lestari, Wahyu, Pizhong Qiao, and Sathya Hanagud. "Curvature Mode Shape-based Damage Assessment of Carbon/Epoxy Composite Beams." Journal of Intelligent Material Systems and Structures 18, no. 3 (October 10, 2006): 189–208. http://dx.doi.org/10.1177/1045389x06064355.

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17

Nanda, Bharadwaj, Damodar Maity, and Dipak Kumar Maiti. "Damage assessment from curvature mode shape using unified particle swarm optimization." Structural Engineering and Mechanics 52, no. 2 (October 25, 2014): 307–22. http://dx.doi.org/10.12989/sem.2014.52.2.307.

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18

Jia, Hong Yu, Peng Fei Yue, and Zhi Hua Fang. "Space Rigid Frame Damage Identification Based on Finite Element Method and Experiment." Applied Mechanics and Materials 405-408 (September 2013): 929–32. http://dx.doi.org/10.4028/www.scientific.net/amm.405-408.929.

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The finite element model of space rigid frame with no damage and damage were established by ANSYS and the physical model experiment was carried out. The damage identification methods include that variety rate of three-dimensional vibration mode, curvature mode, strain energy of element mode and axial mode shape difference. Consider identify result and measurement cost that the axial mode shape difference is a good label amount for three-dimension damage identification by vibration method and the single damage and combination damage could identified, which it was proved by the experiment result.

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19

Morlier, Joseph, F. Bos, and P. Castera. "Benchmark of Damage Localisation Algorithms Using Mode Shape Data." Key Engineering Materials 293-294 (September 2005): 305–12. http://dx.doi.org/10.4028/www.scientific.net/kem.293-294.305.

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This paper presents a comparative study of three enhanced signal processing methods to locate damage on mode shape data. The first method called curvature mode shape is used as a reference. The second tool uses wavelet transform and singularity detection theory to locate damage. Finally we introduce the windowed fractal dimension of a signal as a tool to easily measure the local complexity of a signal. Our benchmark aims at comparing the crack detection using optimal spatial sampling under different severity, beam boundary conditions (BCs) and added noise measurements.

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20

Knill, D. C. "From Contour to Texture: Static Texture Flow is a Strong Cue to Surface Shape." Perception 26, no. 1_suppl (August 1997): 205. http://dx.doi.org/10.1068/v970082.

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Contours projected from geodesic boundaries of developable surfaces (as are formed by folding and twisting flat surfaces) are particularly salient cues to 3-D surface shape. Textures which are strongly anisotropic (highly oriented) provide a similar source of information. The natural definition of homogeneity for such textures leads to the constraint that the oriented ‘flow’ of texture on a surface follows geodesics of the surface (on average). In the current work, it is shown that the shapes of contours projected from geodesics of developable surfaces, and analogously of oriented texture flow, reliably determine the shapes of the surfaces. On the basis of this analysis, it is suggested that human perception of surface shape from texture has two modes of operation: an isotropic mode, in which the visual system infers surface shape from local texture compression information, and a texture flow mode, in which the curvature of local texture flow determines local surface curvature, based on a geodesic constraint. In order to test the theory, planar texture patterns have been isometrically mapped with varying degrees of global orientation (ranging from isotropic to purely oriented) onto developable surfaces. The theory predicts that subjects' ability to make judgements about surface shape will be good for the isotropic textures and for highly oriented textures, but not for anisotropic textures that are only weakly oriented. As predicted, images of the surfaces with isotropic texture patterns induce strong percepts of shape, as do those of highly oriented textures. Images of anisotropic, weakly oriented patterns, however, elicit only weak percepts of shape.

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21

Rucevskis, Sandris, Mezhlum A. Sumbatyan, Pavel Akishin, and Andris Chate. "Tikhonov's regularization approach in mode shape curvature analysis applied to damage detection." Mechanics Research Communications 65 (April 2015): 9–16. http://dx.doi.org/10.1016/j.mechrescom.2015.01.006.

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22

He, Rong, Yafei Zhu, Wei He, and Huai Chen. "Structural Damage Recognition Based on Perturbations of Curvature Mode Shape and Frequency." Acta Mechanica Solida Sinica 31, no. 6 (September 21, 2018): 794–803. http://dx.doi.org/10.1007/s10338-018-0058-y.

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23

Zhong, Hai, and Mijia Yang. "Damage detection for plate-like structures using generalized curvature mode shape method." Journal of Civil Structural Health Monitoring 6, no. 1 (December 11, 2015): 141–52. http://dx.doi.org/10.1007/s13349-015-0148-1.

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24

Karpouzian, G., G. Spedding, and H. K. Cheng. "Lunate-tail swimming propulsion. Part 2. Performance analysis." Journal of Fluid Mechanics 210 (January 1990): 329–51. http://dx.doi.org/10.1017/s0022112090001318.

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The theory of an oscillating, high-aspect-ratio, lifting surface with a curved centreline (Cheng & Murillo 1984) is applied to a performance analysis of lunate-tail swimming propulsion. Thrust, power and propulsive efficiency are calculated for model lunate tails with various combinations of mode shapes and morphological features to ascertain the viability of the proportional-feathering concept, and to determine the influence of sweep and centreline curvature. One of the principal conclusions concerns the interchangeability of the heaving amplitude of the peduncle (identified with the major pitching axis) with the centreline sweep, and its effect on the propulsive efficiency, while maintaining the same thrust. Hydrodynamic reasons are also offered for the apparent preference for the crescent-moon fin shape over the V-shape at moderate sweep angles, and for the large sweep angles often found in V-shaped fins.

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25

Narita, Daisuke, and Yoshihiro Narita. "Analysis for Vibration of Laminated Shallow Shells with Non-Uniform Curvature." Key Engineering Materials 334-335 (March 2007): 85–88. http://dx.doi.org/10.4028/www.scientific.net/kem.334-335.85.

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Despite a large number of technical papers on vibration of composite shallow shells, all the previous papers have dealt with shallow shells with uniform curvature to avoid difficulty in the analysis. Recent composite products, however, require various surface designs of thin panels from the viewpoint of industrial design, for example, in the fender and door panel designs of commercial vehicles. The present study proposes an analytical method to deal with vibration of shallow shells with non-uniform curvature. An interpolating function is introduced to represent the required surface shape and the corresponding curvature is derived as a function of the position (x,y). The obtained curvature is substituted into the total potential energy of the shell, and the procedure is shown to derive a frequency equation in the Ritz method. Numerical examples clarifies the effects of non- uniform curvature on the natural frequencies and mode shapes.

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26

Dixit, A., and S. Hanagud. "Comments on: ‘Curvature Mode Shape-based Damage Assessment of Carbon/Epoxy Composite Beams’." Journal of Intelligent Material Systems and Structures 21, no. 6 (March 2010): 659–63. http://dx.doi.org/10.1177/1045389x10363506.

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27

Hasrizam, C. M., and Noor Fawazi. "Effect of inclusion lagrange interpolation method in mode shape curvature based damage detection." IOP Conference Series: Materials Science and Engineering 469 (January 16, 2019): 012025. http://dx.doi.org/10.1088/1757-899x/469/1/012025.

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28

Janeliukstis, Rims, Sandris Ručevskis, and Sakdirat Kaewunruen. "Mode shape curvature squares method for crack detection in railway prestressed concrete sleepers." Engineering Failure Analysis 105 (November 2019): 386–401. http://dx.doi.org/10.1016/j.engfailanal.2019.07.020.

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29

Man, M. H. C., M. A. Amiruddin, and N. Fawazi. "Evaluation of Improved Mode Shape Curvature-Based Damage Detection using Robust Regression Method." IOP Conference Series: Materials Science and Engineering 1092, no. 1 (March 1, 2021): 012036. http://dx.doi.org/10.1088/1757-899x/1092/1/012036.

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30

Mytiai, I. S., O. V. Shatkovska, and M. Ghazali. "Size and shape of eggs of Neognathae: effects of developmental mode and phylogeny." Canadian Journal of Zoology 95, no. 5 (May 2017): 359–66. http://dx.doi.org/10.1139/cjz-2016-0142.

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We evaluated the variation in absolute size and shape of birds’ eggs and the effects of developmental mode and phylogenetic relatedness on these traits. Eggs were characterized by length, diameter, and three indices of egg shape. Indices of egg shape were calculated as the ratio of radii that described the curvature of pointed end (cloacal zone), blunt end (infundibular zone), and lateral zone to egg diameter. We found that eggs shape was less variable than the absolute size of eggs. Index of the cloacal zone was the most changeable and index of the infundibular zone was very conservative. Size and shape of eggs could be better explained with phylogenetic relatedness than developmental mode.

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Adlerman, Edwin J., and Kelvin K. Droegemeier. "The Dependence of Numerically Simulated Cyclic Mesocyclogenesis upon Environmental Vertical Wind Shear." Monthly Weather Review 133, no. 12 (December 1, 2005): 3595–623. http://dx.doi.org/10.1175/mwr3039.1.

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Abstract Building upon the authors’ previous work that examined the dynamics of numerically simulated cyclic mesocyclogenesis and its dependence upon model physical and computational parameters, this study likewise uses idealized numerical simulations to investigate associated dependencies upon ambient vertical wind shear. Specifically, the authors examine variations in hodograph shape, shear magnitude, and shear distribution, leading to storms with behavior ranging from steady state to varying degrees of aperiodic occluding cyclic mesocyclogenesis. However, the authors also demonstrate that a different mode of nonoccluding cyclic mesocyclogenesis may occur in certain environments. Straight hodographs (unidirectional shear) produce only nonoccluding cyclic mesocyclogenesis. Introducing some curvature by adding a quarter circle of turning at low levels results in steady, nonoccluding, and occluding modes. When a higher degree of curvature is introduced—for example, turning through half and three-quarter circles—the tendency for nonoccluding behavior is diminished. None of the full-circle hodographs exhibited cycling during 4 h of simulation. Overall, within a given storm, the preferred mode of cycling is related principally to hodograph shape and magnitude of the ambient vertical shear.

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He, Jia-Hao, Ding-Peng Liu, Cheng-Hsien Chung, and Hsin-Haou Huang. "Infrared Thermography Measurement for Vibration-Based Structural Health Monitoring in Low-Visibility Harsh Environments." Sensors 20, no. 24 (December 10, 2020): 7067. http://dx.doi.org/10.3390/s20247067.

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In this study, infrared thermography is used for vibration-based structural health monitoring (SHM). Heat sources are employed as sensors. An acrylic frame structure was experimentally investigated using the heat sources as structural marker points to record the vibration response. The effectiveness of the infrared thermography measurement system was verified by comparing the results obtained using an infrared thermal imager with those obtained using accelerometers. The average error in natural frequency was between only 0.64% and 3.84%. To guarantee the applicability of the system, this study employed the mode shape curvature method to locate damage on a structure under harsh environments, for instance, in dark, hindered, and hazy conditions. Moreover, we propose the mode shape recombination method (MSRM) to realize large-scale structural measurement. The partial mode shapes of the 3D frame structure are combined using the MSRM to obtain the entire mode shape with a satisfactory model assurance criterion. Experimental results confirmed the feasibility of using heat sources as sensors and indicated that the proposed methods are suitable for overcoming the numerous inherent limitations associated with SHM in harsh or remote environments as well as the limitations associated with the SHM of large-scale structures.

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Fan, Jin Sheng, Ying Yuan, and Xiu Ling Cao. "Study on Structural Damage Detection Using RBF Network." Applied Mechanics and Materials 578-579 (July 2014): 1125–28. http://dx.doi.org/10.4028/www.scientific.net/amm.578-579.1125.

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Based on mode shape, a new parameter was put forward—mode shape curvature ratio, for detecting structure damages. And it was also the input vector of the RBF neural network. Then through finite element analysis and calculating, the training and forecasting samples were got for the network. The trained neural network can identify the damage location and degree of the frame structure. It proved that this method is simple and valid.

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He, Wen-Yu, Jian He, and Wei-Xin Ren. "The Use of Mode Shape Estimated from a Passing Vehicle for Structural Damage Localization and Quantification." International Journal of Structural Stability and Dynamics 19, no. 10 (October 2019): 1950124. http://dx.doi.org/10.1142/s0219455419501244.

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Mode shapes estimated from the vehicle responses are normally used to detect bridge damage efficiently for their high spatial resolution. However, an updated baseline finite element model (FEM) is normally required to quantify damages for such an approach. A two-stage damage detection procedure is presented for bridges by utilizing the mode shape estimated from a moving vehicle. Damage locations are first determined through a damage localization index (DLI) defined by regional mode shape curvature (RMSC). Then the relationship between the damage extents and the RMSC changes is investigated by FEM simulation. Finally, an equation set to quantify the single and multiple damages is deduced by combining the RMSCs and the relationship between the damage extents and the RMSC changes established by an un-updated FEM. Numerical and experimental examples are carried out to verify the validity and efficiency of the two-stage method. The results revealed that it can localize and quantify damages with satisfactory precision by using the response measured from one sensor only.

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RIBE, N. M. "A general theory for the dynamics of thin viscous sheets." Journal of Fluid Mechanics 457 (April 9, 2002): 255–83. http://dx.doi.org/10.1017/s0022112001007649.

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A model for the deformation of thin viscous sheets of arbitrary shape subject to arbitrary loading is presented. The starting point is a scaling analysis based on an analytical solution of the Stokes equations for the flow in a shallow (nearly planar) sheet with constant thickness T0 and principal curvatures k1 and k2, loaded by an harmonic normal stress with wavenumbers q1 and q2 in the directions of principal curvature. Two distinct types of deformation can occur: an ‘inextensional’ (bending) mode when [mid ]L3(k1q22 + k2q21)[mid ] [Lt ] ε, and a ‘membrane’ (stretching) mode when [mid ]L3(k1q22 + k2q21)[mid ] [Gt ] ε, where L ≡ (q21 + q22)−1/2 and ε = T0/L [Lt ] 1. The scales revealed by the shallow-sheet solution together with asympotic expansions in powers of ε are used to reduce the three-dimensional equations for the flow in the sheet to a set of equivalent two-dimensional equations, valid in both the inextensional and membrane limits, for the velocity U of the sheet midsurface. Finally, kinematic evolution equations for the sheet shape (metric and curvature tensors) and thickness are derived. Illustrative numerical solutions of the equations are presented for a variety of buoyancy-driven deformations that exhibit buckling instabilities. A collapsing hemispherical dome with radius L deforms initially in a compressional membrane mode, except in bending boundary layers of width ∼ (εL)1/2 near a clamped equatorial edge, and is unstable to a buckling mode which propagates into the dome from that edge. Buckling instabilities are suppressed by the extensional flow in a sagging inverted dome (pendant drop), which consequently evolves entirely in the membrane mode. A two-dimensional viscous jet falling onto a rigid plate exhibits steady periodic folding, the frequency of which varies with the jet height and extrusion rate in a way similar to that observed experimentally.

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Radzieński, Maciej, Marek Krawczuk, and Wiesław M. Ostachowicz. "Experimental Verification and Comparison of Mode Shape-Based Damage Detection Methods." Key Engineering Materials 413-414 (June 2009): 699–706. http://dx.doi.org/10.4028/www.scientific.net/kem.413-414.699.

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This paper presents experimental verification and comparison of damage detection methods based on changes in mode shapes such as: mode shape curvature (MSC), modal assurance criterion (MAC), strain energy (SE), modified Laplacian operator (MLO), generalized fractal dimension (GFD) and Wavelets Transform (WT). The object of the investigation is to determine benefits and drawbacks of the aforementioned methods and to develop data preprocessing algorithms for increasing damage assessment effectiveness by using signal processing techniques such as interpolation and extrapolation measured points. Noise reduction algorithms based on moving average, median filter and wavelet decomposition are also tested. The experiments were performed on a 1m long steal cantilever beam. Damage was introduced in form of 10% and 20% deep saw cut, placed in 10%, 30%, 50%, 70% and 90% beam length. Measurements were made using non-contact Scanning Laser Doppler Vibrometer at 125 points equally spaced along beam length.

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Xiang, Chang-Sheng, Ling-Yun Li, Yu Zhou, and Zi Yuan. "Damage Identification Method of Beam Structure Based on Modal Curvature Utility Information Entropy." Advances in Civil Engineering 2020 (September 19, 2020): 1–20. http://dx.doi.org/10.1155/2020/8892686.

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Generally, the damage of the structure will lead to the discontinuity of the local mode shape, which can be well reflected by the modal curvature of the structure, and the local information entropy of the beam structure will also change with the discontinuity of the mode. In this paper, based on the information entropy theory and combining the advantages of modal curvature index in damage identification of beam structure, the modal curvature utility information entropy index is proposed. The modal curvature curves of nondestructive structures were obtained by fitting the modal curvature curves of damage structures with the gapped smoothing technique to avoid dependence on the baseline data of nondestructive structures. The index comprehensively reflects the damage state of the structure by calculating mutual weight change matrix and the weight-probability coefficient. The performance of the new index was verified by the finite element simulation and model test of simply supported beam, respectively. The results show that the modal curvature utility information entropy index takes advantage of the modal curvature index which is sensitive to damage and can overcome its shortcomings effectively. The index proposed can identify the damage location and damage degree accurately and has certain noise immunity, which provides an effective damage identification indicator for beam structures.

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38

Dahak, Mustapha, Noureddine Touat, and Mounir Kharoubi. "Damage detection in beam through change in measured frequency and undamaged curvature mode shape." Inverse Problems in Science and Engineering 27, no. 1 (February 28, 2018): 89–114. http://dx.doi.org/10.1080/17415977.2018.1442834.

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Xiang, Jiawei, Toshiro Matsumoto, Yanxue Wang, and Zhansi Jiang. "Detect damages in conical shells using curvature mode shape and wavelet finite element method." International Journal of Mechanical Sciences 66 (January 2013): 83–93. http://dx.doi.org/10.1016/j.ijmecsci.2012.10.010.

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Feng, Dongming, and Maria Q. Feng. "Output-only damage detection using vehicle-induced displacement response and mode shape curvature index." Structural Control and Health Monitoring 23, no. 8 (January 6, 2016): 1088–107. http://dx.doi.org/10.1002/stc.1829.

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41

Hasrizam, C. M., and Noor Fawazi. "Damage Identification Based on Curvature Mode Shape using Cubic Polynomial Regression and Chebyshev Filters." IOP Conference Series: Materials Science and Engineering 271 (November 2017): 012091. http://dx.doi.org/10.1088/1757-899x/271/1/012091.

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Randiligama, S. M. Chathurangi M., David P. Thambiratnam, Tommy H. T. Chan, and Sabrina Fawzia. "Damage assessment in hyperbolic cooling towers using mode shape curvature and artificial neural networks." Engineering Failure Analysis 129 (November 2021): 105728. http://dx.doi.org/10.1016/j.engfailanal.2021.105728.

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43

Liew, K. M., and C. W. Lim. "A Higher-Order Theory for Vibration Analysis of Curvilinear Thick Shallow Shells with Constrained Boundaries." Journal of Vibration and Control 1, no. 1 (January 1995): 15–39. http://dx.doi.org/10.1177/107754639500100103.

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This article presents the vibration analysis of thick doubly curved shallow shells having curvilinear planform. The Gaussian curvature of shell varies from positive (such as spherical) to negative (such as hyperbolic paraboloidal). The boundaries are constrained with either soft-simply supported or fully clamped edges. A higher-order shear deformation theory, which includes transverse shear strain and rotary inertia, is developed to model the vibration characteristics of the shell. The inclusion of Lamé parameters in the present formulation accounts for the presence of shell curvature and yields cubic transverse shear strain distribution in contrast with the existing quadratic expressions. A set of versatile, globally continuous shape functions is adopted in the Ritz numerical procedure to approximate the displacement and rotation fields. A set of new results for a wide range of shell configurations is presented with some selected contour and three-dimensional displacement mode shapes.

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Gillich, Gilbert Rainer, and Zeno Iosif Praisach. "Detection and Quantitative Assessment of Damages in Beam Structures Using Frequency and Stiffness Changes." Key Engineering Materials 569-570 (July 2013): 1013–20. http://dx.doi.org/10.4028/www.scientific.net/kem.569-570.1013.

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This paper is concerned with vibration based non-destructive evaluation of structures, with a focus on quantitative assessment of damage. In previous works, a reliable method to locate open cracks in beams has been proposed and tested using both data from numerical simulations and laboratory experiments. It bases on the fact the natural frequency of a bending vibrations mode attend different changes, depending on the loss of stored energy for the slice on which the damage is located. As bigger the mode shape curvature value on that location, so bigger the loss of stored energy and consequently the natural frequency decrease in that mode. Analyzing the natural frequency changes for a larger series of vibration modes, it’s possible to precisely locate damages. The authors succeed to find a single mathematical relation describing the frequency changes for all bending vibration modes, involving one term defining damage’s location and one defining its depth. While the first term changes for different modes, being defined by the mode shape curvature, the second maintain its value for all modes, being affected just by damage depth. This finding permits decoupling the location issue with that of quantitative assessment of damage. Latest researches, presented in this paper, succeed by finding the relation between the second term of the relation and some mechanical characteristics of the beam, i.e. extending the proposed method by including evaluation of damage severity. The approach is illustrated on a cantilever beam, modeled with 3D elements.

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Saleh, Fadillawaty. "Determination of Damage Location in Reinforced Concrete Beams Using Mode Shape Curvature Square (MSCS) Method." Applied Mechanics and Materials 845 (July 2016): 140–47. http://dx.doi.org/10.4028/www.scientific.net/amm.845.140.

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This paper presents a numerical algorithm technique to detect cracks propagated in concrete beams based on the frequency response curve of the beam determined from vibration testing. Impact tests on simply supported reinforced concrete beams were conducted to measure vibration on the beam. The ICATS software was carried out to capture the Frequency Response Functions (FRFs) data at each load step. Utilizing the FRFs data, a numerical algorithm based on finite different methods was performed to compute the different FRFs between undamage and damage beams based on the mode shape curvature square (MSCS) method. The numerical damage location was defined by subtracting the MSCS undamage to damage of beams. Therefore, the accurate damage location was identified by comparing the numerical and observed experimental results.

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Tomaszewska, A. "Influence of statistical errors on damage detection based on structural flexibility and mode shape curvature." Computers & Structures 88, no. 3-4 (February 2010): 154–64. http://dx.doi.org/10.1016/j.compstruc.2009.08.017.

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Jannesari, Reyhaneh, Thomas Grille, Cristina Consani, Gerald Stocker, Andreas Tortschanoff, and Bernhard Jakoby. "Design of a Curved Shape Photonic Crystal Taper for Highly Efficient Mode Coupling." Sensors 21, no. 2 (January 15, 2021): 585. http://dx.doi.org/10.3390/s21020585.

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The design and modeling of a curved shape photonic crystal taper consisting of Si rods integrated with a photonic crystal waveguide are presented. The waveguide is composed of a hexagonal lattice of Si rods and optimized for CO2 sensing based on absorption spectroscopy. We investigated two different approaches to design a taper for a photonic crystal waveguide in a hexagonal lattice of silicon rods. For the first approach (type 1), the taper consists of a square lattice taper followed by a lattice composed of a smooth transition from a square to a hexagonal lattice. In the second approach (type 2), the taper consists of a distorted hexagonal lattice. Different shapes, such as convex, concave, and linear, for the curvature of the taper were considered and investigated. The structure of the taper was improved to enhance the coupling efficiency up to 96% at a short taper length of 25 lattice periods. The finite-difference time-domain (FDTD) technique was used to study the transmission spectrum and the group index. The study proves the improvement of coupling using a curved shape taper. Controlling the group index along the taper could be further improved to enhance the coupling efficiency in a wider spectral range.

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Lahoz, R., L. Gracia-Villa, and J. A. Pue´rtolas. "Training of the Two-Way Shape Memory Effect by Bending in NiTi Alloys." Journal of Engineering Materials and Technology 124, no. 4 (September 30, 2002): 397–401. http://dx.doi.org/10.1115/1.1495001.

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The two-way shape memory effect (TWSME), has been studied in a near-equiatomic NiTi commercial alloy. Two bending training methods have been applied on NiTi wires. One is based on the martensite deformation and the other on thermal cycling under constant bending curvature. The efficiency of each method has been evaluated with better results of TWSME in the martensite deformation method. Finite element simulation has been performed on wires, in the pure bending mode, in order to calculate the maximum tensile strain in the transversal section of the wire. These simulations have allowed us to compare our results with the TWSME data obtained in prior studies under the tensile mode.

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Bundy, Mark, James Newill, Vince Marcopoli, Michael Ng, and Charles Wells. "A Methodology for Characterizing Gun Barrel Flexure due to Vehicle Motion." Shock and Vibration 8, no. 3-4 (2001): 223–28. http://dx.doi.org/10.1155/2001/746901.

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Barrel centerline curvature is known to influence the location of projectile shot impacts. Superimposed on the unique manufactured barrel centerline is the flexed barrel shape that can occur prior to firing while the vehicle is on the move. In order to understand and quantify the effects of barrel flexure on gun accuracy, it is necessary to determine what combination of fundamental mode shapes is most likely to occur. A method to accomplish this task is described in this paper. The method is demonstrated by enumerating the 10 most likely flexed barrel shapes that were found to occur in a tank-mounted gun barrel while it traversed a bump course.

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Liu, Fan, Xiaomin Ji, Gang Hu, and Jing Gao. "A Novel Shape-Adjustable Surface and Its Applications in Car Design." Applied Sciences 9, no. 11 (June 6, 2019): 2339. http://dx.doi.org/10.3390/app9112339.

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In this paper, a new parameterized surface, termed SQ-Coons surface, is proposed according to the build mode of Coons patch. The surface is always interpolated to the boundary curves, and its shape details could be controlled by the shape parameters in CE-Bézier basis functions, which makes it suitable for styling design in computer aided design (CAD). In order to exert its geometric advantages in car design, a simplified body CAD template based on characteristic lines is built according to common vehicle features. The template is built entirely from SQ-Coons surfaces, so that the overall style and detail shapes could all be modified by the control points and shape parameters of each surface. By analyzing the curvature of fifty commercial car types generated through the template and various parameters, a set of methods for constraining the range of shape parameters is proposed. On this basis, as an example, the four shape parameters of the hood surface in one model are used as variables to optimize the body shape to achieve the lowest possible aerodynamic drag coefficient in computational fluid dynamics (CFD). The results show that the design method, combining the new surface and the model template, could reflect the modeling characteristics of different cars, and improve the design and scheme adjustment efficiency in the conceptual design stage.

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