پیوندهای مفید
آمار
| تعداد نشریات | 7 |
| تعداد شماره‌ها | 410 |
| تعداد مقالات | 5,457 |
| تعداد مشاهده مقاله | 5,871,595 |
| تعداد دریافت فایل اصل مقاله | 5,230,765 |
Exact Closed-Form Solution for Vibration Analysis of Beams Carrying Lumped Masses with Rotary Inertias | ||
| AUT Journal of Mechanical Engineering | ||
| مقاله 7، دوره 2، شماره 1، شهریور 2018، صفحه 73-90 اصل مقاله (1.36 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2017.12932.5475 | ||
| نویسندگان | ||
| H. Afshari1؛ K. Torabi* 2؛ F. Hajiaboutalebi2 | ||
| 1Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran | ||
| 2Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, 81746-73441 Isfahan, Iran | ||
| چکیده | ||
| In this paper, an exact closed-form solution is presented for free vibration analysis of Bernoulli–Euler beams carrying attached masses with rotary inertias. The proposed technique explicitly provides frequency equation and corresponding mode as functions with two integration constants which should be determined by external boundary conditions implementation and leads to the solution to a two by two eigenvalue problem. The concentrated masses and their rotary inertia are modeled using Dirac’s delta generalized functions without implementation of continuity conditions. The non-dimensional inhomogeneous differential equation of motion is solved by applying integration procedure. Using the fundamental solutions which are made of the appropriate linear composition of trigonometric and hyperbolic functions leads to making the implementation of boundary conditions much easier. The proposed technique is employed to study the effects of quantity, position and translational and rotational inertia of the concentrated masses on the dynamic behavior of the beam for all standard boundary conditions. Unlike many of the previous exact approaches, the presented solution has no limitation in a number of concentrated masses. | ||
| کلیدواژه‌ها | ||
| Vibration analysis؛ Concentrated mass؛ Rotary inertia؛ Dirac’s delta function | ||
| مراجع | ||
|
[1] Y. Chen, On the vibration of beams or rods carrying a concentrated mass, Journal of Applied Mechanics, 30(2) (1963) 310-311. [2] K. Low, A modified Dunkerley formula for eigenfrequencies of beams carrying concentrated masses, International Journal of Mechanical Sciences, 42(7) (2000) 1287-1305. [3] P. Laura, J. Pombo, E. Susemihl, A note on the vibrations of a clamped-free beam with a mass at the free end, Journal of Sound and Vibration, 37(2) (1974) 161-168. [4] E. Dowell, On some general properties of combined dynamical systems, American Society of Mechanical Engineers, (1978). [5] P. Laura, P.V. de Irassar, G. Ficcadenti, A note on transverse vibrations of continuous beams subject to an axial force and carrying concentrated masses, Journal of Sound and Vibration, 86(2) (1983) 279-284. [6] M. Gürgöze, A note on the vibrations of restrained beams and rods with point masses, Journal of Sound and Vibration, 96(4) (1984) 461-468. [7] M. Gürgöze, On the vibrations of restrained beams and rods with heavy masses, Journal of Sound and Vibration, 100(4) (1985) 588-589.
[8] W. Liu, J.-R. Wu, C.-C. Huang, Free vibration of beams with elastically restrained edges and intermediate concentrated masses, Journal of Sound and Vibration, 122(2) (1988) 193-207.
[9] K. Torabi, H. Afshari, M. Heidari-Rarani, Free vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses using DQEM, Engineering Solid Mechanics, 1(1) (2013) 9-20.
[10] K. Torabi, H. Afshari, M. Sadeghi, H. Toghian, Exact Closed-Form Solution for Vibration Analysis of Truncated Conical and Tapered Beams Carrying Multiple Concentrated Masses, Journal of Solid Mechanics, 9(4) (2017) 760-782.
[11] P. Laura, C. Filipich, V. Cortinez, Vibrations of beams and plates carrying concentrated masses, Journal of Sound Vibration, 117 (1987) 459-465.
[12] M. Hamdan, B. Jubran, Free and forced vibrations of a restrained uniform beam carrying an intermediate lumped mass and a rotary inertia, Journal of Sound and Vibration, 150(2) (1991) 203-216.
[13] C. Chang, Free vibration of a simply supported beam carrying a rigid mass at the middle, Academic Press (2000) 733-744.
[14] Y. Zhang, L.Y. Xie, X.J. Zhang, Transverse vibration analysis of euler-bernoulli beams carrying concentrated masses with rotatory inertia at both ends, Advanced Materials Research, Trans Tech Publ, (2010) 925-929.
[15] S. Maiz, D.V. Bambill, C.A. Rossit, P. Laura, Transverse vibration of Bernoulli–Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution, Journal of Sound and Vibration, 303(3-5) (2007) 895-908.
[16] J.-S. Wu, B.-H. Chang, Free vibration of axial-loaded multi-step Timoshenko beam carrying arbitrary concentrated elements using continuous-mass transfer matrix method, European Journal of Mechanics-A/Solids, 38 (2013) 20-37.
[17] K. Torabi, H. Afshari, H. Najafi, Vibration Analysis of Multi-Step Bernoulli-Euler and Timoshenko Beams Carrying Concentrated Masses, Journal of Solid Mechanics, 5(4) (2013) 336-349.
[18] K. Torabi, H. Afshari, H. Najafi, Whirling Analysis of Axial-Loaded Multi-Step Timoshenko Rotor Carrying Concentrated Masses, Journal of Solid Mechanics, 9(1) (2017) 138-156.
[19] L. Meirovitch, Elements of vibration analysis, McGraw-Hill, 1975.
[20] L. Meirovitch, Fundamentals of vibrations, Waveland Press, 2010.
[21] M.J. Lighthill, An introduction to Fourier analysis and generalised functions, Cambridge University Press, 1958.
[22] J.F. Colombeau, New generalized functions and multiplication of distributions, Elsevier, 2000.
[23] H. Bremermann, L. Durand III, On analytic continuation, multiplication, and Fourier transformations of Schwartz distributions, Journal of Mathematical Physics, 2(2) (1961) 240-258. | ||
|
آمار تعداد مشاهده مقاله: 1,050 تعداد دریافت فایل اصل مقاله: 734 |
||