پایان نامه تحلیل رفتار های غیرخطی یک تیر ترک‌ دار با سفتی غیرخطی

فهرست:

فهرست مطالب

فصل 1 - مقدمه و مرور کارهای انجام شده 16

1-1     مقدمه. 17

1-2     تاریخچه مطالعات و مرور کارهای انجام شده 17

1-3     انواع مدل سازی های ترک... 20

1-4     بیان مسئله مدل سازی ترک باز 20

1-5     اهداف و مسائل بررسی شده در پایان نامه. 21

فصل 2 - مدل سازی خطی  و غیر خطی ترک و بررسی معادلات حرکت... 22

2-1     مقدمه. 23

2-2     معادلات ارتعاش آزاد. 23

2-2-1           تئوری اویلر - برنولی.. 23

2-2-2           تئوری تیموشنکو. 32

2-2-3           بررسی تیر  شامل چند ترک... 41

2-2-4           ترک با شکل های هندسی مختلف: 45

2-3     مدل سازی ترک باز و بسته شونده 50

2-3-1           مدل سازی ترک ساختار منحنی.. 51

2-3-2           بررسی ترک v- شکل.. 61

2-3-3           حل مسئله با روش میانگین گیری.. 66

فصل 3 - نتایج مدل سازی.. 71

3-1     مقدمه. 72

3-2     نتایج ترک باز ساده 72

3-2-1           تیر با نسبت های مختلف عمق ترک... 72

3-2-2           تیر با نسبت های مختلف طول دهانه ترک... 75

3-2-3           بررسی اثر تغییر موقعیت ترک... 78

3-3     بررسی اثر تعداد ترک... 81

3-3-1           بررسی نتایج به ازای عمق و طول دهانه ثابت و موقعیت های متفاوت... 82

3-3-2           بررسی نتایج به ازای موقعیت و طول دهانه ثابت و عمق های متفاوت... 83

3-3-3           بررسی نتایج به ازای موقعیت و عمق ثابت و طول دهانه های متفاوت... 85

3-4     بررسی تیر با  شکل های هندسی  مختلف... 87

3-4-1           ترک بیضی شکل.. 87

3-4-2           ترک سهمی شکل.. 91

3-4-3           ترک مثلثی.. 92

3-5     ترک باز و بسته شونده 95

3-5-1           ترک منحنی با ساختار دایره ای شکل.. 96

3-6     شکل مود، شکل شیب، گشتاور خمشی و نیروی برشی.. 106

3-7     اعتبار سنجی نتایج مدل های پیشنهادی.. 111

3-7-1           ترک باز ساده 111

3-7-2           ترک مثلثی شکل.. 112

3-7-3           ترک باز و بسته شونده 115

فصل 4 - نتیجه گیری و پیشنهادات... 117

4-1     نتیجه گیری.. 118

منبع:

A.D. Dimarogonas, C. Papadopoulos, Vibrations of cracked shafts in bending, Journal of Sound and Vibration 91 (1983) 583-593.

S.W. Doebling, C.R. Farrar, M.B. Prime, D.W. Shevitz, Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review, Los Alamos National Laboratory, LA-
13070-MS, 1996.

T. G. Chondros, A.D. Dimarogonas, J. Yao, a continuous cracked beam vibration theory, journal of sound and vibration 215 (1998) 17-34.

B.O. Dirr, B.K. Schmalhorst, Crack depth analysis of a rotating shaft by vibration measurements, Journal of Vibration, Acoustics, Stress and Reliability in Design ASME 110 (1988) 158-164.

G. Gounaris, A. Dimarogonas, A Finite element of a cracked prismatic beam for structural analysis, Computers and Structures 28 (1988) 309-313.

R.Y. Liang, F.K. Choy, J. Hu, Detection of cracks in beam structures using measurements of natural frequencies, Journal of the Franklin Institute 328 (1991) 505-518.

S. Chinchalkar, Detection of the crack location in beams using natural frequencies, Journal of Sound and Vibration 247 (2001) 417-429.

P.N. Saavedra, L.A. Cuitino, Crack detection and vibration behavior of cracked beams, Computers and Structures 79 (2001) 1451-1459.

H. Nahvi, M. Jabbari, Crack detection in beams using experimental modal data and finite element model, International Journal of Mechanical Sciences 47 (2005) 1477- 1497.

P. Cawley, R.D. Adams, The locations of defects in structures from measurements of natural frequencies, Journal of Strain Analysis 14 (1979) 49-57.

R.D. Adams, P. Cawley, C.J. Pye, B.J. Stone, A vibration technique for non-destructively assessing the integrity of structures, Journal of Mechanical Engineering Science 20 (1978) 93-100.

B. S. Haistyamd W. T. Spronger, A general beam element for use in damage assessment of complex structures, Journal of Vibration, Acoustics, Stress and Reliability in Design, 1998, 110, 389-394.

G. Gounaris and A. D. Dimargonas, A finite element of a cracked prismatic beam for structural analysis, Computers and Structures, 1988, 28 (3), 309-313.

F. K. Ibrahim, An elasto-plastic cracked beam finite element for structural analysis, Computers and Structures, 1993, 49 (6), 981-988.

P. Gudmundson, The dynamic behavior of slender structures with cross sectional cracks, Journal of Mechanics and Physics of Solids 31 (1983) 329-345.

P. G. Kismser, The effect of discontinuities on the natural frequency of beams, In Proceedings of the American Society of Testing and Materials, 1994, 44, 897-904.

A. D. Dimarogonas, Vibration Engineering, West Publishers, 1976.

S. Christidesamd and A. D. S. Barr, One dimensional theory of cracked Bernoulli- Euler beams, International Journal of Mechanical Sciences, 1984, 26, 630-648.

M. H. H. Shen, and Y. C. Chu, Vibrations of beams with a fatigue crack, Computers and Structures, 1992, 45 (1), 79-93.

M. H. H. Shen and C. Pierre, Natural modes of Bernoulli- Euler beams with symmetric cracks, Journal of Sound and Vibration, 1990, 138 (1), 115-134.

M. H. H. Shen and C. Pierre, Free vibrations of beams with a single edge crack, Journal of Sound and Vibration, 1994, 170, 237-259.

T. G. Chondros, and A. D. Dimargonas, Vibration of a cracked cantilever beam, Transcation of ASME Journal of Vibration, Acoustics, 1998, 120.

T. G. Chondros, and A. D. Dimargonas, and J. YAO, A Continuous cracked beam vibration theory, Journal of Sound and Vibration, 1998, 215 (1), 17-34.

T. G. Chondros, and A. D. Dimargonas, and J. YAO, Longitudinal vibration of a bar with a breathing crack, Engineering Fracture Mechanics, 1998, 61, 503-518.

P. Cawley, and Adams, R. D., “The Location of Defects in Structures from Measurements of Natural Frequencies”, J. Strain Anal., Vol. 14(2), pp. 49–57, (1979).

R. Ruotolo, and C. Surace, “Damage Assessment of Multiple Cracked Beams: Numerical Results and Experimental Validation”, J. of Sound and Vibration, Vol. 206(4), pp. 567–588, (1997).

P. Gudmundson, Eigen frequency changes of structures due to cracks, notches or other geometrical changes, Journal of Mechanic Physics Solids, 1982, 30 (5), 339-353.

H. T. Banks, P. Emeric and L. Plancke, Modeling of non-symmetrical damage in plate-like structures, Technical Report CRSC-TR97-12, Center for Research in Scientific Computation, North California State University, 1997.

N. P. Plakhtinko, and S. A. Yasinskii, Resonance of second order in vibrations of a beam containing a transverse crack, Strength of Materials, 1995, 27 (3), 146-152.

I. Ballo, Nonlinear effects of vibration of a continuous transverse cracked slender shaft, Journal of Sound and Vibration, 1998, 217 (2), 321-333.

Z.A. Jassim, N.N. Ali, F. Mustapha and N.A. Abdul Jalil, A review on the vibration analysis for a damage occurrence of a cantilever beam, Engineering Failure Analysis 31 (2013) 442–461.

Mohammad A. AL-Shudeifat, On the finite element modeling of the asymmetric cracked rotor, Journal of Sound and Vibration 332 (2013) 2795–2807.

Herbert Martins Gomes and Frank Jonis Flores de Almeida, An analytical dynamic model for single-cracked beams including bending, axial stiffness, rotational inertia, shear deformation and coupling effects, Applied Mathematical Modeling (2013), http://dx.doi.org/10.1016/j.apm.2013.07.019

Salvatore Caddemi, Antonino Morassi, Multi-cracked Euler–Bernoulli beams: Mathematical modeling and exact solutions, International Journal of Solids and Structures 50 (2013) 944–956.

Sekhar, A. S., “Vibration Characteristics of a Cracked Rotor with Two Open Cracks”, J. of Sound and Vib., Vol. 223(4), pp. 497–512, )1999).

Ruotolo, R., and Surace, C., “Damage Assessment of Multiple Cracked Beams: Numerical Results and Experimental Validation”, J. of Sound and Vibration, Vol. 206(4), pp. 567–588, (1997).

Liang, R. Y., Hu, J., and Choy, F. K., “Quantitative NDE Technique for Assessing Damage in Beam Structures”, Journal of Engineering Mechanics, Vol. 118 (7), pp. 1468–1487, (1992).

Hu, J., and Liang, R. Y., “An Integrated Approach to Detection of Cracks using Vibration Characteristics”, J. Franklin Inst., Vol. 330(5), pp. 841–853, (1993).

Choy, F. K., Liang, R., and Xu, P., “Fault Identification in Beams on Elastic Foundation”, Comput. Geotech., Vol. 17(2), pp. 157–176, (1995).

Zheng, D. Y., and Fan, S. C., “Natural Frequencies of a Non-uniform Beam with Multiple Cracks via Modified Fourier Series”, J. of Sound and Vibration, Vol. 242(4), pp. 701–717, (2001).

Zheng, D. Y., and Fan, S. C., “Natural Frequency Changes of a Cracked Timoshenko Beam by Modified Fourier Series”, Journal of Sound and Vibration, Vol. 246(2), pp. 297–317, (2001).

Y. Narkis, Identification of crack location in vibrating simply supported beams, Journal of Sound and Vibration 172 (1994) 549-558.

H.P. Lee, T.Y. Ng, Natural frequencies and modes for the flexural vibration of a cracked beam, Applied Acoustic 43 (1994) 151-163.

J. Fernandez-Saez, L. Rubio, C. Navarro, Approximate calculation of the fundamental frequency for bending vibrations of cracked beams, Journal of Sound and Vibration 225 (1999) 345-352.

S. Chinchalkar, Detection of the crack location in beams using natural frequencies,
Journal of Sound and Vibration 247 (2001) 417-429.

S.P. Lele, S.K. Maiti, Modeling of transverse vibration of short beams for crack detection and measurement of crack extension, Journal of Sound and Vibration 257 (2002)559-583.

H. S. Zibdeh, Stochastic vibration of an elastic beam due to random moving loads and deterministic axial forces. Engineering structures 17 (1995) 530-535.

G. T. Michaltsos Dynamic behavior of a single-span beam subjected to loads moving with variable speeds. Journal of Sound and Vibration 258 (2002) 359-372.

M. Abu-Hilal, Dynamic response of a double Beroulli-Euler beam due to a moving constant load. Journal of Sounds and Vibration 297 (2006) 477-491.

M. Simsek, T. Kocaturk, Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load. Journal of Composite structures, (2009) Article in press.

J. Yang, Y. Chen, Y. Xiang, X.L. Jia, Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load, Journal of Sound and Vibration 312 (2008) 166-181.

M.H. Richardson, M.A. Mannan, Remote detection and location of structural faults using modal parameters, Proceedings of the 10th International Modal Analysis Conference IMACX, San Diego, CA, 1992, pp. 502-507.

J.E.T. Penny, D.A.L. Wilson, M.I. Friswell, Damage location in structures using vibration data, Proceedings of the 11th International Modal Analysis Conference IMAC XI, 1993, pp. 861-867.

M.I. Friswell, J.E.T. Penny, D.A.L. Wilson, Using vibration data and statistical measures to locate damage in structures, Modal Analysis 9 (1994) 239-254.

B.P. Nandwana, S.K. Maiti, Detection of the location and size of a crack in stepped cantilever beams based on measurements of natural frequencies, Journal of Sound and Vibration 203 (1997) 435-446.

O.S. Salawu, Detection of structural damage through changes in frequencies: a review, Engineering Structures 19 (1997) 718-723.

M. Behzad, A. Meghdari, A. Ebrahimi, A new approach for vibration analysis of a cracked beam, International Journal of Engineering B 18 (2005) 319-330.

T.W. Lim, Structural damage detection using modal test data, American Institute of Aeronautics and Astronautics Journal 29 (1991) 2271-2274.

O.S. Salawu, Detection of structural damage through changes in frequencies: a review, Engineering Structures 19 (1997) 718-723.

M. Behzad, A. Meghdari, A. Ebrahimi, A new approach for vibration analysis of a cracked beam, International Journal of Engineering B 18 (2005) 319-330.

T.W. Lim, Structural damage detection using modal test data, American Institute of
Aeronautics and Astronautics Journal 29 (1991) 2271-2274.

A.K. Pandey, M. Biswas, Damage detection in structures using change in flexibility, Journal of Sound and Vibration 169 (1994) 3-17.

S.W. Doebling, L.D. Peterson, K.F. Alvin, Estimation of reciprocal residual flexibility from experimental modal data, American Institute of Aeronautics and Astronautics Journal 34 (1996), 1678-1685.

J.K. Sinha, M.I. Friswell, S. Edwards, Simplified models for the location of cracks in beam structure using measured vibration data, Journal of Sound and Vibration 251 (2002) 13-38.

T. Wolff, M. Richardson, Fault detection in structures from changes in their modal parameters, Proceedings of the 7th International Modal Analysis Conference IMAC VII, 1989, pp. 87-94.

A.K. Pandey, M. Biswas, M.M. Samman, Damage detection from change in curvature mode shapes, Journal of Sound and Vibration 145 (1991) 321-332.

N. Khaji, M. Shafiei, M. Jalalpour International Journal of Mechanical Sciences 51 (2009) 667–681. Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions.

H.-P. Lin, Direct and inverse methods on free vibration analysis of simply supported beams with a crack, Engineering Structures 26(2004) 427-436.

T.G.Chondros, A.D.Dimarogonas and j.yao. vibration of a beam with a breathing crack. Journal of Sound and Vibration, 2001, 239(1), 57-67.