پیوندهای مفید
آمار
| تعداد نشریات | 8 |
| تعداد شماره‌ها | 414 |
| تعداد مقالات | 5,478 |
| تعداد مشاهده مقاله | 6,010,584 |
| تعداد دریافت فایل اصل مقاله | 5,299,928 |
پاسخ تحلیلی ارتعاشات آزاد میرای تیر ترکدار با معادلات حرکت چند مودی کوپل | ||
| نشریه مهندسی مکانیک امیرکبیر | ||
| مقاله 11، دوره 52، شماره 1، فروردین 1399، صفحه 155-172 اصل مقاله (2.28 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2018.13957.5762 | ||
| نویسندگان | ||
| موسی رضائی* 1؛ وحید شاطریان القلندیس2 | ||
| 1دانشگاه تبریز | ||
| 2گروه مهندسی مکانیک، دانشکده مهندسی مکانیک، دانشگاه تبریز | ||
| چکیده | ||
| در این مقاله، ارتعاشات چند مودی آزاد تیر با ترک خستگی تحت شرایط اولیه دلخواه مطالعه شده است. اعمال شرایط اولیه دلخواه باعث تحریک همزمان چند مود ارتعاشی تیر می شود. برای تحلیل مسأله، با در نظر گرفتن گشتاور خمشی تیر در محل ترک، رابطه ای برای تعیین میزان باز شدگی آنی ترک به صورت تابعی چندهارمونیک از زمان ارائه می شود. تابع توصیف کننده وضعیت آنی ترک در مجموعه معادالت مودال توصیف کننده ارتعاشات تیر ترکدار ظاهر شده و سبب کوپل شدن معادالت می شود. این معادالت با استفاده از روش اغتشاشات حل و پاسخ تحلیلی ارتعاش چند مودی تیر ترکدار به تحریک اولیه دلخواه به دست می آید. سپس پاسخ ارتعاشی تیر در سه حالت: تحریک مود اول، تحریک همزمان مودهای اول و دوم و تحریک همزمان مودهای اول تا سوم به دست آمد. نتایج نشان می ً دهد که با تحریک صرفا در مود اول، مؤلفههای هارمونیک پاسخ ارتعاشی اطالعات بسیار محدودی در مورد ترک ارائه می دهد در حالی که با تحریک همزمان مودهای باالتر، مؤلفه های هارمونیک متعددی به علت وجود ترک در پاسخ ارتعاشی ایجاد میشوند که حساسیت زیادی به ترک دارند و از تحلیل آنها اطالعات دقیقی در مورد موقعیت و عمق ترک حاصل می شود. | ||
| کلیدواژه‌ها | ||
| تیر با ترک خستگی؛ ارتعاش چند مودی آزاد میرا؛ روش اغتشاشات؛ تحلیل فرکانسی | ||
| عنوان مقاله [English] | ||
| An Analytical Method for Damped Free Vibration Analysis of a Cracked Beam Considering the Coupled Multimode Equations | ||
| نویسندگان [English] | ||
| mousa rezaee1؛ vahid shaterian alghalandis2 | ||
| 2mechanical engineering department, university of tabriz | ||
| چکیده [English] | ||
| The multimodal free vibration of a beam with a breathing crack excited by arbitrary initial conditions is investigated. Taking the initial conditions to be arbitrary makes more than one mode of the beam to be excited simultaneously. By considering the bending moment at the crack position, a multi-harmonic function describing the instantaneous opening and closing of the crack is extracted. Since the modal stiffnesses of the beam are dependent on the crack parameters, the extracted crack breathing function will appear in the equations of motion and makes them to be coupled. These equations are solved using the perturbation method. Then, the free response of the beam is extracted under three cases of initial conditions: excitation of the first mode, simultaneous excitation of the first and second modes, and simultaneous excitation of the first three modes. The results show that by exciting the first mode solely, the harmonic components of the response offer very limited information about the crack. However, by exciting the first several modes simultaneously, many other harmonic components appears at the frequency response curves which are more sensitive to the crack and contain more comprehensive information about the crack parameters. | ||
| کلیدواژه‌ها [English] | ||
| Beam with a fatigue crack, Multimode free damped vibration, Perturbation method, Frequency analysis | ||
| مراجع | ||
|
[1] Y.C. Chu, M.H.H. Shen, Analysis of forced bilinear oscillators and the application of cracked beam dynamics, AIAA Journal, 30(10) (1992) 2512-2519. [2] A. Rivola, P.R. White, Bispectral analysis of the bilinear oscillator with application to the detection of fatigue cracks, Journal of Sound and Vibration, 216(5) (1998) 889-910. [3] L. Gelman, S. Gorpinich, C. Thompson, Adaptive diagnosis of the bilinear mechanical systems, Mechanical Systems and Signal proccessing, 23(5) (2009) 1548-1553. [4] A.P. Bovsunovskii, Numerical study of vibrations of a non-linear mechanical system simulating a cracked body, Strength of Materials, 31(6) (1999) 571-581. [5] A.P. Bovsunovskii, Vibrations of a non-linear mechanical system simulating a cracked body, Strength of Materials, 33(4) (2001) 370-379. [6] P. Crespo, R. Ruotolo, C. Surace, Non-linear modeling of a cracked beam, in: Proceedings of the 14th International Modal Analysis Conference, Dearborn, Michigan, Usa, 1996. [7] A. Chatterjee, Identification and parameter estimation of abilinear oscillatorusing Volterra series with harmonic probing, International Journal of Nonlinear Mechanics, 45 (2010) 12-20. [8] C. Surace, R. Ruotolo, D. Storer, Detecting non-linear behavior using the Volterra series to assess damage in beam-like structures, Journal of Theoretical and Applied Mechanics, 49(3) (2011) 905-926. [9] S.L. Lau, W.S. Zhang, Non-linear vibrations of piecewise-linear systems by incremental harmonic balance method, Journal of Applied Mechanics, 59 (1992) 153-160. [10] D. Broda, L. Pieczonka, V. Hiwarkar, W.J. Staszewski, V.V. Silberschmidt, Generation of higher harmonics in longitudinal vibration of beams with breathing cracks, Journal of Sound and Vibration, 381 (2016) 206-219. [11] F.E. Dotti, V.H. Cortínez, F. Reguera, Non-linear dynamic response to simple harmonic excitation of a thin-walled beam with a breathing crack, Applied Mathematical Modelling, 40(1) (2016) 451-467. [12] S. Smith, G. Wang, D. Wu, Bayesian approach to breathing crack detection in beam structures, Engineering Structures, 148 (2017) 829–838. [13] D.M. Joglekar, M. Mitra, Nonlinear analysis of flexural wave propagation through 1D waveguides with a breathing crack, Journal of Sound and Vibration, 344 (2015) 242–257. [14] D.M. Joglekar, M. Mitra, Analysis of flexural wave propagation through beams with a breathing crack using wavelet spectral finite element method, Mechanical Systems and Signal Processing, 76–77 (2016) 576-591. [15] J. Prawin, A.R.M. Rao, Development of Polynomial Model for Cantilever Beam with Breathing Crack, Procedia Engineering, 144 (2016) 1419-1425. [16] J. Prawin, A.R.M. Rao, Nonlinear identification of MDOF systems using Volterra series approximation, Mechanical Systems and Signal Processing, 84 (2017) 58–77. [17] S.M. Chengh, X.J. Wu, W. Wallace, Vibrational Response of a Beam With a Breathing Crack, Journal of Sound and Vibration, 225(1) (1999) 201-208. [18] M. Rezaee, R. Hassannejad, A new approach to free vibration analysis of a beam with a breathing crack based on mechanical energy balance method, Acta Mechanica Solida Sinica, 24(2) (2011) 185-194. [19] M. Rezaee, R. Hassannejad, Free Vibration Analysis Of Simply Supported Beam With Breathing Crack Using Perturbation Method, Acta Mechanica Solida Sinica, 23(5) (2010) 459-470. [20] J.J. Sinou, On the use of non-linear vibrations and the anti-resonances of higher-order frequency response functions for crack detection in pipeline beam, Mechanics Research Communications, 43 (2012) 87-95. [21] E. Douka, L.J. Hadjileontiadis, Time–frequency analysis of the free vibration response of a beam with a breathing crack, NDT & E International, 38 (2005) 3-10. [22] S. Loutridis, E. Douka, L.J. Hadjileontiadis, Forced vibration behavior and crack detection of cracked beams using instantaneous frequency, NDT & E International, 38 (2005) 411-419. [23] K. Vigneshwaran, R.K. Behera, Vibration Analysis of a Simply Supported Beam with Multiple Breathing Cracks, Procedia Engineering, 86 (2014) 835- 842. [24] R. Ruotolo, C. Surace, P. Crespo, D. Storer, Harmonic analysis of the vibrations of a cantilevered beam with a closing crack, Computers & Structures, 61 (1996) 1057-1074. [25] N.P. Plakhtienko, S.A. Yasinskii, Resonance of second order in vibrations of a beam containing a transverse crack, Strength of Materials, 27(3) (1995) 146-152. [26] S. Caddemi, I. Calio, M. Marletta, The non-linear dynamic response of the Euler–Bernoulli beam with an arbitrary number of switching cracks, International Journal of Nonlinear Mechanics, 45 (2010) 714-726. [27] A.P. Bovsunovsky, C. Surace, Considerations regarding superharmonic vibrations of a cracked beam and the variation in damping caused by the presence of the crack, Journal of Sound and Vibration, 288(4-5) (2005) 865-886. [28] P.N. Saavedra, L.A. Cuitino, Crack detection and vibration behavior of cracked beams, Computers & Structures, 79 (2001) 1451-1459. [29] N. Pugno, C. Surace, R. Ruotolo, Evaluation of the non-linear dynamic response to harmonic excitation of a beam with several breathing cracks, Journal of Sound and Vibration, 235(5) (2000) 749-762. [30] A.P. Bovsunovsky, C. Surace, O.A. Bovsunovsky, The effect of damping and force application point on the non-linear dynamic behavior of a cracked beam at sub and super Resonance Vibrations, Strength of Materials, 38(5) (2006) 492-497. [31] U. Andreaus, P. Casini, F. Vestroni, Non-Linear Dynamics Of A Cracked Cantilever Beam Under Harmonic Excitation, International Journal of Nonlinear Mechanics, 42(3) (2007) 566-575. [32] L. Meirovitch, Analytical methods in vibrations, Macmillan, London, 1967. [33] H.P. Lin, S.C. Chang, J.D. Wu, Beam Vibrations with an Arbitrary Number of Cracks, Journal of Sound and Vibration, 258(5) (2002) 987-999. [34] U. Andreaus, P. Baragatti, Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response, Journal of Sound and Vibration, 330 (2011) 721-742. | ||
|
آمار تعداد مشاهده مقاله: 670 تعداد دریافت فایل اصل مقاله: 1,523 |
||