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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 (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 def

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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, sec

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3

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 m

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Ručevskis, Sandris, and Andris Chate. "DAMAGE IDENTIFICATION IN A PLATE-LIKE STRUCTURE USING MODAL DATA." Aviation 17, no. 2 (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 damag

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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

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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 (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 (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.Re

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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 (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 (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 nonlin

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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 (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

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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 (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 p

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13

Yang, Chong, Yu Fu, Jianmin Yuan, et al. "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

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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 (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 perpendicu

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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 (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 (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 (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

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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 (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 (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 majo

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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 t

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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 (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 (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 (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. Siz

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31

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 (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

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32

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 (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

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33

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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34

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 (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

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35

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(k1

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36

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. N

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37

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

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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 (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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40

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 (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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42

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 (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 yiel

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44

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

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45

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

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46

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

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47

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 (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 (typ

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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 (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 com

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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-

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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 (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 styl

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