EFFECT OF FREE VIBRATION ANALYSIS ON EULER-BERNOULLI BEAM WITH DIFFERENT BOUNDARY CONDITIONS

Authors

Keywords:

Beam, Fixed-Fixed Beam, Free-Free Beam, Simply Supported Beam, Deflection

Abstract

This paper presents an analysis of the effect of free vibrations of a free-free beam, fixed-fixed beam and simply supported beam using the series solution. It was found that the mode shape for each of the modes has effects on the displacement or deflection of such beam so that the deflection increases as the increase of the mode. Also, a Simply-Supported beam has a lower displacement compared to the free-free beam and fixed-fixed beam which almost have the same displacement. At mode one, it is seen that a Simply Supported beam has a higher amplitude, followed by a free-free beam and then a fixed-fixed beam.

Dimensions

Ariaei, A., Ziaei-Rad, S. and Ghayour, M. (2009). Vibration analysis of beams with open and breathing cracks subjected to moving masses. Journal of Sound and Vibration, 326: 709-724.

Catal H. H. (2002). Free vibration of partially supported piles with the effects of bending moment, axial and shear force, Engineering Structures, 24(12):1615–1622.

Catal S. (2008). The solution of free vibration equations of the beam on elastic soil by using differential transform method. Applied Mathematical Modelling, 32(9):1744–1757.

Chen C.K. and Ho S.H. (1996). Application of differential transformation to eigenvalue problems. Applied Mathematics and Computation, 79(2-3):173–188.

Chen C. K. and Ho S. H. (1999). Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform. International Journal of Mechanical Sciences 41(11):1339–1356.

Civalek O. and Ozturk B. (2010). Free vibration analysis of tapered beam-column with pinned ends embedded in the Winkler-Pasternak elastic foundation. Geomechanics and Engineering, 2(1):45–56.

Coskun S. B., Atay M. T. and Ozturk B.(2011). Transverse vibration analysis of Euler-Bernoulli beams using analytical approximate techniques. Advances in Vibration Analysis Research, chapter 1, pp. 1–22, In-Tech, Vienna, Austria.

Douka, E. and Hadjileontiadis, J.L. (2005). Time-frequency analysis of the free vibration response of a beam with a breathing crack. NDT&E International, 38: 3-10.

Doyle P. F. and Pavlovic M. N.(1982). The vibration of beams on partial elastic foundations. Earthquake Engineering and Structural Dynamics, 10(5):663–674.

Firouz-Abadi R. D., Haddadpour H., and Novinzadeh A. B. (2007). An asymptotic solution to transverse free vibrations of variable-section beams. Journal of Sound and Vibration, 304(3-5): 530–540.

Huang Y. and Li X.F. (2010). A new approach for free vibration of axially functionally graded beams with non-uniform cross-section. Journal of Sound and Vibration, 329(11):2291–2303, 2010.

Kozien M. S. (2013). Analytical solution of exciting vibrations of a beam with the application of distribution. Acta Physica Polonica A, 126(6):1029-1033.

Ozdemir O. and Kaya M. O. (2006). Flaps bending vibration analysis of a rotating tapered cantilever Bernoulli-Euler beam by differential transform method. Journal of Sound and Vibration, 289(1-2):413–420.

Ozturk B. (2009). Free vibration analysis of beam on an elastic foundation by the variational iteration method. International Journal of Nonlinear Sciences and Numerical Simulation, 10(10):1255–1262.

Papadimitrou C., Haralampidis Y., and Sobczyk K. (2005). Optimal experimental design in stochastic structural dynamics. Probabilistic Engineering Mechanics, 20:67-78.

Sioma A. (2013). The rope wear analysis with the use of 3D vision system, Control Engineering, 60(5):48-49

Snamina J.and Sapin´s ski B., Romaszko M. (2012a). Vibration parameter analysis of a sandwich cantilever beams with multiple MR fluid segments. Engineering Modeling, 43:247-254

Snamina J. and Sapin´ski B., Wszol Ek W., Romaszko M. (2012b). Investigation on vibrations of a cantilever beam with magnetorheological fluid by using the acoustic signal. Acta Physica Polonica A, 121:1-8

Sriram P. and Hanagud S., Craig J.I. (1992). Mode shape measurement using a scanning laser Doppler vibrometer. The International Journal of Analytical and Experimental Modal Analysis, 7(3):169-178

Trucco E. and Verri A. (1998). Introductory Techniques for 3D Computer Vision, Prentice-Hall

Tuma J. and Cheng F. (1983). Theory and Problems of Dynamic Structural Analysis, Schaum’s Outline Series, McGraw-Hill, New York, NY, USA.

Usman M,A. (2003). Dynamic response of a Bernoulli beam on the Winkler foundation under the action of moving partially distributed moving load. Nigeria Journal of Mathematics and Application, 16:128-147

Usman M.A., Hammed F.A., Olayiwola M. O, Okusaga S. T. and Daniel D. O. (2018). Free Vibrational Analysis of Beam with Different Support Conditions. Transaction of the Nigerian Association of Mathematical Physics, 7:27-32.

Van der Auweraer H., Steinbichler H., Haberstok C., Freymann R. and Storer D. (2002). Integration of pulsed laser ESPI with spatial domain modal analysis. Shock and Vibration, 9(1/2):29-42

West H. H. and Mafi M.(1984). Eigenvalues for beam-columns on elastic supports. Journal of Structural Engineering, 110(6):1305–1320.

Published

12-04-2023

How to Cite

EFFECT OF FREE VIBRATION ANALYSIS ON EULER-BERNOULLI BEAM WITH DIFFERENT BOUNDARY CONDITIONS. (2023). FUDMA JOURNAL OF SCIENCES, 3(4), 501-510. https://fjs.fudutsinma.edu.ng/index.php/fjs/article/view/1679

Issue

Vol. 3 No. 4 (2019): FUDMA Journal of Sciences - Vol. 3 No. 4

Section

Research Articles
Copyright & Licensing

FUDMA Journal of Sciences

How to Cite

EFFECT OF FREE VIBRATION ANALYSIS ON EULER-BERNOULLI BEAM WITH DIFFERENT BOUNDARY CONDITIONS. (2023). FUDMA JOURNAL OF SCIENCES, 3(4), 501-510. https://fjs.fudutsinma.edu.ng/index.php/fjs/article/view/1679

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