ORIGINAL_ARTICLE
Sensitivity Analysis of Frequency Response of Atomic Force Microscopy in Liquid Environment on Cantilever's Geometrical Parameters
In this paper, the non-linear dynamic response of rectangular atomic force microscopy in tapping mode is considered. The effect of cantilever’s geometrical parameters (e.g., cantilever length, width, thickness, tip length and the angle between the cantilever and the sample's surface in liquid environment has been studied by taking into account the interaction forces. Results indicate that the resonant frequency, amplitude and phase are very sensitive to changes of geometrical parameters. In order to improve and optimize the system's behavior, the sensitive analysis (SA) of geometrical parameters on the first resonant frequency and amplitude of cantilever's vertical displacement has been conducted using Sobol's method. Results show that the influence of each geometrical variable on frequency response of the system can play a crucial role in designing the optimum cantilever in liquid medium for soft and sensitive biological samples. Also, one way to speed up the imaging process is to use short cantilevers. For short beams, the Timoshenko model seems to be more accurate compared to other models such as the Euler-Bernoulli. By using the Timoshenko beam model, the effects of rotational inertia and shear deformation are taken into consideration. In this paper, this model has been used to obtain more accurate results
http://jsme.iaukhsh.ac.ir/article_521423_287aac7faab2b1147534102ee3245f29.pdf
2016-02-20
221
237
Sensitive analysis
Geometrical parameters
Timoshenko beam
Liquid Environment
Sobol method
M.
Damircheli
m.damircheli@qodsiau.ac.ir
1
Assistant professor, Department of Mechanical Engineering, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran
LEAD_AUTHOR
[Giessibl, #7][1] Giessibl F.J., Forces and frequency shifts in atomic-resolution dynamic-force microscopy, Physical Review B, vol. 56, No. 24, 1997, pp. 16010.
1
[2] San Paulo A., García R., Tip-surface forces, amplitude, and energy dissipation in amplitude-modulation (tapping mode) force microscopy, Physical Review B, vol. 64, No. 19, 2001, pp. 193411.
2
[3] Rabe U., Janser K., Arnold W., Vibrations of free and surface‐coupled atomic force microscope cantilevers: theory and experiment, Review of Scientific Instruments, vol. 67, No. 9, 1996, pp. 3281-3293.
3
[4] Turner J.A., Hirsekorn S., Rabe U., Arnold W., High-frequency response of atomic-force microscope cantilevers, Journal of Applied Physics, vol. 82, No. 3, 1997, pp. 966-979.
4
[5] Stark R.W., Schitter G., Stark M., Guckenberger R., Stemmer A., State-space model of freely vibrating and surface-coupled cantilever dynamics in atomic force microscopy, Physical Review B, vol. 69, No. 8, 2004, pp. 085412.
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[6] Butt H.J., Jaschke M., Calculation of thermal noise in atomic force microscopy, Nanotechnology, vol. 6, No. 1, 1995, pp. 1.
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[7] Rabe U., Turner J., Arnold W., Analysis of the high-frequency response of atomic force microscope cantilevers, Applied Physics A: Materials Science & Processing, vol. 66, 1998, pp. S277-S282.
7
[8] Lee S., Howell S., Raman A., Reifenberger R., Nonlinear dynamics of microcantilevers in tapping mode atomic force microscopy: A comparison between theory and experiment, Physical Review B, vol. 66, No. 11, 2002, pp. 115409.
8
[9] Arinero R., Lévêque G., Vibration of the cantilever in force modulation microscopy analysis by a finite element model, Review of scientific instruments, vol. 74, No. 1, 2003, pp. 104-111.
9
[10] Sadeghi A., Zohoor H., Nonlinear vibration of rectangular atomic force microscope cantilevers by considering the Hertzian contact theory, Canadian Journal of Physics, vol. 88, No. 5, 2010, pp. 333-348.
10
[11] Hansma P., Cleveland J., Radmacher M., Walters D., Hillner P., Bezanilla M., Fritz M., Vie D., Hansma H., Prater C., Tapping mode atomic force microscopy in liquids, Applied Physics Letters, vol. 64, No. 13, 1994, pp. 1738-1740.
11
[12] Putman C. A., Van der Werf K.O., De-Grooth B.G., N. F. Van Hulst, J. Greve, Tapping mode atomic force microscopy in liquid, Applied Physics Letters, vol. 64, No. 18, 1994, pp. 2454-2456.
12
[13] Chen G., Warmack R., Huang A., Thundat T., Harmonic response of near‐contact scanning force microscopy, Journal of applied physics, vol. 78, No. 3, 1995, pp. 1465-1469.
13
[14] Chen G., Warmack R., Oden P., Thundat T., Transient response of tapping scanning force microscopy in liquids, Journal of Vacuum Science & Technology B, vol. 14, No. 2, 1996, pp. 1313-1317.
14
[15] Burnham N., Behrend O., Oulevey F., Gremaud G., Gallo P., Gourdon D., Dupas E., Kulik A., Pollock H., Briggs G., How does a tip tap?, Nanotechnology, vol. 8, No. 2, 1997, pp. 67.
15
[16] Sader J.E., Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope, Journal of applied physics, Vol. 84, No. 1, 1998, pp. 64-76.
16
[17] Y. Song, B. Bhushan, Finite-element vibration analysis of tapping-mode atomic force microscopy in liquid, Ultramicroscopy, vol. 107, No. 10, 2007, pp. 1095-1104.
17
[18] Korayem M., Ebrahimi N., Nonlinear dynamics of tapping-mode atomic force microscopy in liquid, Journal of Applied Physics, vol. 109, No. 8, 2011, pp. 084301.
18
[19] Lee H.L., Chang W.J., Sensitivity of V-shaped atomic force microscope cantilevers based on a modified couple stress theory, Microelectronic Engineering, vol. 88, No. 11, 2011, pp. 3214-3218.
19
[20] Moosapour M., Hajabasi M.A., Ehteshami H., Frequency and sensitivity analysis of atomic force microscope (afm) cantilever considering coupled flexural-torsional vibrations, Digest Journal of Nanomaterials and Biostructures, vol. 7, No. 3, 2012, pp. 1103-1115.
20
[21] Timoshenko S., Goodier, Theory of Elasticity, McGraw3 1aill, New York, vol. 1, No. 95, 1951, pp. 1.
21
[22] Hosaka H., Itao K., Kuroda S., Damping characteristics of beam-shaped micro-oscillators, Sensors and Actuators A: Physical, vol. 49, No. 1, 1995, pp. 87-95.
22
[23] Hsu J.C., Lee H.L., Chang W.J., Flexural vibration frequency of atomic force microscope cantilevers using the Timoshenko beam model, Nanotechnology, vol. 18, No. 28, 2007, pp. 285503.
23
[24] Derjaguin B.V., Muller V.M., Toporov Y.P., Effect of contact deformations on the adhesion of particles, Journal of Colloid and interface science, vol. 53, No. 2, 1975, pp. 314-326.
24
[25] Saltelli A., Chan K., Scott EM: Sensitivity analysis, Wiley, vol. 79, 2000, pp. 80.
25
[26] Korayem M., Damircheli M., The effect of fluid properties and geometrical parameters of cantilever on the frequency response of atomic force microscopy, Precision Engineering, vol. 38, No. 2, 2014, pp. 321-329.
26
ORIGINAL_ARTICLE
Dynamic Stability of Nano FGM Beam Using Timoshenko Theory
Based on the nonlocal Timoshenko beam theory, the dynamic stability of functionally gradded (FG) nanoeams under axial load is studied in thermal environment, with considering surface effect. It is used power law distribution for FGM and the surface stress effects are considered based on Gurtin-Murdoch continuum theory. Using Von Karman geometric nonlinearity, governing equations are derived based on Hamilton’s principle. The developed nonlocal models have the capability to interpret small scale effects. Winkler and Pasternak types elastic foundation are employed to represent the interaction of the nano FG beam and the surrounding elastic medium. A parametric study is conducted to investigate the influences of the static load factor, temperature change, nonlocal elastic parameter, slenderness ratio, surface effect and springs constant of the elastic medium on the dynamic stability characteristics of the FG beam, with simply-supported boundary conditions. It is found that the difference between instability regions predicted by local and nonlocal beam theories is significant for nanobeams with lower aspect ratios. Moreover, it is observed that in contrast to high temperature environments, at low temperatures, increasing the temperature change moves the origins of the instability regions to higher excitation frequencies and leads to further stability of the system at lower excitation frequencies, considering surface stress effect shifts the FG beam to higher frequency zone
http://jsme.iaukhsh.ac.ir/article_521424_2b37e8e3ea932fa8565117a9124978b5.pdf
2016-02-20
239
250
Dynamic stability
Surface stress effects
Nanobeams
Functionally Graded Materials
S.
saffari
1
MSc Student, Department of Mechanical Engineering, Islamic Azad University, Khomeinishar Branch, Esfahan, Iran
AUTHOR
M.
Hashemian
mohamad.hashemian@gmail.com
2
Assistant Prof., Department of Mechanical Engineering, Islamic Azad University, Khomeinishar Branch, Esfahan, Iran
LEAD_AUTHOR
[1] Peddieson, J., G.R. Buchanan, and R.P. McNitt, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, vol. 41, No. 3–5, 2003, pp. 305-312.
1
[2] قربانپورآرانی ع.، شریف زارعی م.، محمدی مهر م.، تأثیرحرارت بر کمانش پیچشی نانو لوله کربنی دو جداره تحت بستر الاستیک نوع پاسترناک، فصل نامه علمی پژوهشی مکانیک جامدات، سال 4، شماره 1، 2011، صفحات 11 تا 16.
2
[3] الهامی م.، زینلی م.، تحلیل پایداری دینامیکی یک تیر دو سر آزاد تحت نیروی تعقیبکننده ناپایستار، مجله مکانیک هوا فضا، سال 7، شماره 1، 2011، صفحات 15 تا 26.
3
[4] Ansari R., Gholami R., Sahmani S., On the dynamic stability of embedded single-walled carbon nanotubes including thermal environment effects, Scientia Iranica, vol. 19, No. 3, 2012, pp. 919-925.
4
[5] Hosseini-Hashemi S. Nazemnezhad R., An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects, Composites Part B: Engineering, vol. 52, 2013, pp. 199-206.
5
[6] Eltaher M.A., et al., Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position, Applied Mathematics and Computation, vol. 235, 2014, pp. 512-529.
6
[7] Malekzadeh P. Shojaee M., Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams, Composites Part B: Engineering, vol. 52, 2013, pp. 84-92.
7
[8] Ansari, R., et al., Nonlinear vibration analysis of Timoshenko nanobeams based on surface stress elasticity theory, European Journal of Mechanics - A/Solids, vol. 45, 2014. pp. 143-152.
8
[9] Ghorbanpour Arani A., Kolahchi R., Hashemian M., Nonlocal surface piezoelasticity theory for dynamic stability of double-welled boron nitride nanotube conveying viscose fluid based on different theories, Mechanical Engineering Science, 2014, pp. 23.
9
[10] Goldberg J.E., The dynamic stability of elastic systems: by V. V. Bolotin. Russian trans. by V. I. Weingaxten et al. 451 pages, diagrams, 7 × 10 in. San Francisco, Calif., Holden-Day, Inc., 1964. Price, $12.95, Journal of the Franklin Institute, vol. 279, No. 6, 1965, pp. 478-479.
10
ORIGINAL_ARTICLE
Static and Dynamic Analyze of the an Aluminum Pad used as Portable Roadway
Due to geographic and climatic conditions in mountainous northwest area, Roads in these areas are often covered with snow, ice and mud. Hence Transportation of equipment and soldiers encounter hardship and difficulties in rural area and specially outposts. To solve these problems, it is needed to fabricate portable roadway or traction mats. These high strength mats cover surface of roads and are compatible with mentioned conditions. In this Research an Aluminum alloy profile used as a portable pad and loads was analyzed and simulated for a Toyota Hilux with 3 ton weight. In order to selection optimal geometry, relation between stress and geometric parameters such as dimension, profile channel length and forming angle of pad was investigated.Results showed that the optimal profile angel, thickness and channel length is 90°, 4 mm and 3 mm respectively
http://jsme.iaukhsh.ac.ir/article_521425_427f779c65ea100e83972ed6785dbbf3.pdf
2016-02-20
251
260
Portable roadway
Aluminum profile
Profile channel
Pad angel
M.
Rezaye
mm_rezayi@mut.ac.ir
1
MSc, North West Institute of the Defense Science and Technology, Malek Ashtar University, Urmia, Iran
LEAD_AUTHOR
A.
Mahmoudi
2
MSc, North West Institute of the Defense Science and Technology, Malek Ashtar University, Urmia, Iran
AUTHOR
A.
Ehsaghi oskoei
3
Phd student, Department of Mechanical Engineering, Tehran University, Tehran, Iran
AUTHOR
R.
Husseini Sane
4
MSc, North West Institute of the Defense Science and Technology, Malek Ashtar University, Urmia, Iran
AUTHOR
Due to geographic and climatic conditions in mountainous northwest area, Roads in these areas are often covered with snow, ice and mud. Hence Transportation of equipment and soldiers encounter hardship and difficulties in rural area and specially outposts. To solve these problems, it is needed to fabricate portable roadway or traction mats. These high strength mats cover surface of roads and are compatible with mentioned conditions. In this Research an Aluminum alloy profile used as a portable pad and loads was analyzed and simulated for a Toyota Hilux with 3 ton weight. In order to selection optimal geometry, relation between stress and geometric parameters such as dimension, profile channel length and forming angle of pad was investigated.Results showed that the optimal profile angel, thickness and channel length is 90°, 4 mm and 3 mm respectively
1
ORIGINAL_ARTICLE
Implementing a Practical Light Transmission System in order to Lighting an Office with Zero Energy Consumption
One of the recently considered applications of fiber optic, in their usage in building lighting systems. In this research, in order to reduce energy consumption, by transmission of sun light from the roof to the desired place (i.e. an office), the required standard luminance is produced. The main aims of this research are : 1. Reduction of energy consumption. 2. Making the place compatible with the human favorable mental conditions and environment. 3. Preparing the basics of mass production of the system and economical benefits for the university In this research besides concentrating the sun light to magnify its density, some investigations are made for light transmission by fiber optics, because, no mathematical model was found for this per pose, practical tests are made in addition to statistical analysis. Using different lenses and fiber optics and a position control system (which specially designed for this research), many experiences were made and iluminances were measured by a lux meter. After that by SPSS V.17 software, the results were analyzed. Finally the best Lenz and fiber were selected and a straight forward method was presented for designing a typical office in such manner
http://jsme.iaukhsh.ac.ir/article_521426_3b821f5a4990f5e417bd3eddf048be43.pdf
2016-02-20
261
274
J.
Ashkboos Esfahani
ashkboos@iaukhsh..ac.ir
1
Lecturer, Engineering Department, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran.
LEAD_AUTHOR
S.
Shojaeian
shojaeian@iaukhsh.ac.ir
2
Assisstant Prof., Engineering Department, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran
AUTHOR
[1] معاونت انرژی وزارت نیرو، مدیریت انرژی و تجارت مفید در روشنایی، مجموعه کتابچه های راهنمای فنی مدیریت انرژی، 1381.
1
[2] www.isna.ir
2
[3] بعنونی س.، روش نوین در روشنایی ساختمان ها، سومین همایش بهینه سازی مصرف سوخت در ساختمان، تهران، 1382.
3
[4] رضایی م.، بعنونی س.، به کارگیری لوله های خورشیدی جهت روشنایی ساختمان ها، اولین کنفرانس سراسری اصلاح الگوی مصرف انرژی الکتریکی، اهواز، اسفند 1388.
4
[5] Bailey D., Wright E., Practical Fiber Optics, Elsevier, 2003.
5
[6] Driggers R. G., Encyclopedia of Optical Engineering, Marcel Dekker, New York, 2003.
6
[7] جعفری نائینی ع.، ابوعلی ابنهیثم، دائره المعارف بزرگ اسلامی، 1367.
7
[8] Grondzik W.T.,Kwok A.G., Mechanical and Electrical Equipment for Buildings, Wiley, 2014.
8
[9] Golnabi H., Azimi P., Design and operation of a double-fiber displacement sensor, Optics Communications, vol. 281, No. 4, 2008, pp. 614-662.
9
[10] Golnabi H., Azimi P., Design and performance of a plastic optical fiber leakage sensor, Optics & Lasers Technology, vol. 39, No. 7, 2007, pp. 1346-1350.
10
[11] Xiaochun Q., Xuefeng Z., Shuai Q., Hao H., Design of Solar Optical Fiber lighting System for Enhanced Lighting in Highway Tunnel Threshold Zone: A Case Study of Huashuyan Tunnel in China, Hindawi, 2015, pp. 1-10.
11
[12] Ullah I., Allen J., Woei W., Development of Optical Fiber-Based Daylighting System and Its Comparison, energies, vol. 8, 2015, pp. 7185-7201.
12
ORIGINAL_ARTICLE
Modeling & Comparison of Mechanical Behavior of Foam Filled & Hollow Aluminum Tubes by LS-DYNA & Introducing a Neural Network Model
Energy absorption capability of thin-walled structures with various cross sections has been considered by researchers up to now. These structures as energy absorbers are used widely in different industries such as automotive and aerospace and protect passengers and goods against impact. In this paper, mechanical behavior of thin-walled aluminum tubes with and without polyurethane foam filler subjected to axial impact has been investigated. The tubes are very thin so that (D/t) ≈ 550 governs for cylindrical specimen. Structure behavior was analyzed through finite element analysis by LS-DYNA. Circular, hexagonal, and square cross sections with the same length, thickness, and circumference of sections were studied. The results show that circular cross section has the highest energy absorption while experiences the lowest change in length compared to hexagonal and square cross sections. Besides, the effects of stress concentration in hexagonal and square sections can be observed on the corners of walls. Also under the dynamic loading circular structure was crushed more symmetric, while hexagonal and square structures tended to the buckling. Also an Artificial Neural Network is introduced to predict load & energy Absorption behavior. The Neural Network's data obtained from LS-DYNA. The introduced model could present acceptable results in comparison with analysis of LS-DYNA
http://jsme.iaukhsh.ac.ir/article_521427_bf47dc31275689225676459a23b6b7b7.pdf
2016-02-20
275
293
Thin Walled Structures
Polyurethane Foam
energy absorption
Mechanical Behavior
Neural network
LS-DYNA
M.
Rostami
meysam.rostami66@yahoo.com
1
Lecturer, Mechanical Engineering, Payame Noor University of Qazvin, Qazvin, Iran.
AUTHOR
M.
Hasanlou
hasanlou@aol.com
2
M.Sc., Mechanical Engineering, University of Guilan, Rasht, Iran
LEAD_AUTHOR
M.
Siavashi
msiavashi67@gmail.com
3
M.Sc., Mechanical Engineering, University of Guilan, Rasht, Iran
AUTHOR
[1] Hanssen A.G., Lorenzi L., Berger K.K., Hopperstad, O.S., Langseth, M. A demonstrator bumper system based on aluminium foam filled crash boxes, International Journal of Crashworthiness, vol. 5, No. 4, 2000, pp. 381–392.
1
[2] Wang Z., Tian H., Lu Z., Zhou W., “High-Speed Axial Impact of Aluminum Honeycomb – Experiments and Simulations, Composites Part B: Engineering, vol. 56, 2014, pp. 1–8.
2
[3] Algalib D., Limam A., Experimental and Numerical Investigation of Static and Dynamic Axial Crushing of Circular Aluminum Tubes, Thin-Walled Structures, vol. 42, 2004, pp. 1103–1137.
3
[4] Seitzberger M., Rammerstorfer F.G., Degischer, H.P., Gradinger, R., Crushing of Axially Compressed Steel Tubes Filled with Aluminium Foam, Acta Mechanica, vol. 125, No. (1–4), 1997, pp. 93–105.
4
[5] Nariman-Zadeh N., Darvizeh A., Jamali A., Pareto Optimization of Energy Absorption of Square Aluminium Columns Using Multi-Objective Genetic Algorithms, Proc. IME BJ Engineering Manufacturing, vol. 220, Issue 2, 2006, pp. 213–224.
5
[6] Zarei H.R., Kroger M., Optimization of the Foam-Filled Aluminum Tubes for Crush Box Application, Thin-Walled Structures, vol. 46, No. 2, 2008, pp. 214–221.
6
[7] Zarei H.R., Kroger M., Crashworthiness Optimization of Empty and Filled Aluminum Crash Boxes, International Journal of Crashworthiness, vol. 12, No. 3, 2007, pp. 255–264.
7
[8] Zarei H.R., Ghamarian A., Experimental and Numerical Crashworthiness Investigation of Empty and Foam-Filled Thin-Walled Tubes with Shallow Spherical Caps, Experimental Mechanics, vol. 54, 2014, pp. 115–126.
8
[9] Ghamarian A., Zarei H.R., Abadi M.T., Experimental and Numerical Crashworthiness Investigation of Empty and Foam-Filled End-Capped Conical Tubes, Thin-Walled Structures, vol. 49, 2011, pp. 1312–1319.
9
[10] Gupta N.K., Velmurugan R., Axial Compression of Empty and Foam Filled Composite Conical Shells, Journal of Composite Material, vol. 33, No. 6, 1999, pp. 567–591.
10
[11] Fan Z., Lu G., Liu K., Quasi-Static Axial Compression of Thin-Walled Tubes with Different Cross-Sectional Shapes, Engineering Structures, vol. 55, 2013, pp. 80–89.
11
[12] Reddy T.Y., Wall R.J., Axial Compression of Foam-Filled Thin-Walled Circular Tubes, International Journal of Impact Engineering, Vol. 7, No. 2, 1988, pp. 151–166.
12
[13] Reid S.R., Reddy T.Y., Gray M.D., Static and Dynamic Axial Crushing of Foam-Filled Sheet Metal Tubes, International Journal of Mechanical Sciences, vol. 28, 1986, pp. 295–322.
13
[14] Gameiro C.P., Cirne J., Dynamic Axial Crushing of Short to Long Circular Aluminium Tubes with Agglomerate Cork Filler, International Journal of Mechanical Sciences, vol. 49, 2007, pp. 1029–1037.
14
[15] Yamashita M., Gotoh M., Sawairi Y., Axial Crush of Hollow Cylindrical Structures with Various Polygonal Cross-Sections Numerical Simulation and Experiment, Journal of Materials Processing Technology, vol. 140, 2003, pp. 59–64.
15
[16]. LS-DYNA 971 Keyword User’s Manual.
16
[17] Pugsley A., Macaulay M.A., The large scale crumpling of thin cylindrical columns, Quarterly Journal of Mechanics & Applied Mathematics, vol. 13, 1960, pp. 1-9.
17
ORIGINAL_ARTICLE
Modeling of the Beam Discontinuity with Two Analyses in Strong and Weak Forms using a Torsional Spring Model
In this paper, a discontinuity in beams whose intensity is adjusted by the spring stiffness factor is modeled using a torsional spring. Adapting two analyses in strong and weak forms for discontinuous beams, the improved governing differential equations and the modified stiffness matrix are derived respectively. In the strong form, two different solution methods have been presented to make an analogy between the formulation of the Euler-Bernoulli and Timoshenko theories that indicates the influence of the shear deformation in discontinuous beams. The flexural stiffness of discontinuous beams is corrected by using the Dirac’s delta function. In the weak form, the reduced stiffness matrix is derived from the strain energy equation established by the continuity, kinematics and constitutive equations. The linearity assumption of the geometry and material is considered to construct the kinematics and constitutive equations respectively. The continuity conditions mathematically connect two divided parts of the Euler-Bernoulli beam for which an improved Hermitian shape function is employed to interpolate displacement field. An application shows the comparison and validation of the results of the strong and weak forms, and also the static behavior of discontinuous beams
http://jsme.iaukhsh.ac.ir/article_521428_b15f429512e65302c2bc5b7419a3ada3.pdf
2016-02-20
295
309
Discontinuity
Beam
Strong and Weak Forms
Euler-Bernoulli
Timoshenko Theories
M.
Mastan Abadi
m.mastanabadi@gmail.com
1
MSc Student, Department of Mechanical Engineering, Takestan Branch, Islamic Azad University, Takestan, Iran
AUTHOR
A.
Alijani
alijani@iaubanz.ac.ir
2
Assistant Prof., Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran
LEAD_AUTHOR
A.
Darvizeh
3
Professor, Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran
AUTHOR
F.
Mottaghian
ellnaz.mottaghian@gmail.com
4
MSc Student, Department of Mechanical Engineering, University of Guilan, Rasht, Iran
AUTHOR
[1] G. R. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate, Journal of Applied Mechanics, vol. 1, No. 24, 1957, pp. 361–364.
1
[2] A. D. Dimarogonas, C. A. Papadopulus, Vibration of cracked shafts in bending, Journal of Sound and Vibration, vol. 91, No. 4, 1983, pp. 583–593.
2
[3] H. Okamura, H. W. Liu, C. Chorng-Shin, A cracked column under compression, Engineering Fracture Mechanics, vol. 1, pp. 547–564, 1969.
3
[4] W. M. Ostachowicz, M. Krawczuk, Vibrational analysis of cracked beam, Composite Structures, vol. 36–22, 1990, pp. 245–250.
4
[5] M. Krawczuk, W. M. Ostachowicz, Influence of a crack on the dynamic stability of a column,Journal of Sound and Vibration, vol. 167, No. 3, 1993, pp. 541–555.
5
[6] M. Skrinar, T. Pliberšek, New linear spring stiffness definition for displacement analysis of cracked beam elements, Proceedings in Applied Mathematics and Mechanics, vol. 4, 2004, pp. 654–655.
6
[7] A. J. Dentsoras, A. D. Dimarogonas, Resonance controlled fatigue crack propagation in a beam under longitudinal vibrations, International Journal of Fracture, vol. 1, No. 23, 1983, pp. 15–22.
7
[8] T. G. Chondros, A. D. Dimarogonas, Identification of cracks in welded joints of complex structures, Journal of Sound and Vibration, vol. 4, No. 64, 1980, pp. 531–538.
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[9] P. F. Rizos, N. Aspragathos, A. D. Dimarogonas, Identification of crack location and magnitude in a cantilever beam from the vibration modes, Journal of Sound and Vibration, vol. 3, No. 138, 1990, pp. 381–388.
9
[10] F. Bagarello, Multiplication of distribution in one dimension: possible approaches and applications to d-function and its derivatives, Journal of Mathematical Analysis and Applications, vol. 196, 1995, pp. 885–901.
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[11] F. Bagarello, Multiplication of distribution in one dimension and a first application to quantum field theory, Journal of Mathematical Analysis and Applications, vol. 266, 2002, pp. 298–320.
11
[12] B. Biondi, S. Caddemi, Closed form solutions of Euler–Bernoulli beam with singularities, International Journal of Solids and Structures, vol. 42, 2005, pp. 3027–3044.
12
[13] B. Biondi, S. Caddemi, Euler–Bernoulli beams with multiple singularities in the flexural stiffness, European Journal of Mechanics A/Solids, vol. 26, 2007, pp. 789–809.
13
[14] A. Palmeri, A. Cicirello, Physically-based Dirac‘s delta functions in the static analysis of multi-cracked Euler–Bernoulli and Timoshenko beams, International Journal of Solids and Structures, vol. 48, 2011, pp.2184–2195.
14
[15] A. Cicirello, A. Palmeri, Static analysis of Euler-Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads, International Journal of Solids and Structures, vol. 51, 2014, pp. 1020-1029.
15
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