Influence of shear deformation and rotary inertia on nonlinear free vibration of a beam with pinned ends

Computers and Structures

Volumn 71, Issue 6, 1999, Pages 663-670

  Foda, Mosaad A ^a  

^a KING SAUD UNIVERSITY   (Saudi Arabia)

Author keywords

[No Author keywords available]

Indexed keywords

BEAMS AND GIRDERS; PERTURBATION TECHNIQUES; SHEAR DEFORMATION; VIBRATIONS (MECHANICAL);

NONLINEAR FREE VIBRATIONS; ROTARY INERTIA;

STRUCTURAL ANALYSIS;

EID: 0032668472     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(98)00299-5     Document Type: Article

References (27)

1. Ray J.D., Bert C.W. Nonlinear vibrations of beam with pinned ends. J Engng Ind. 91B:1969;997-1004.
2. Bennet J.A., Eisley J.G. A multiple degree of freedom approach to nonlinear beam vibrations. Am Inst Aeron Astron J. 8:1970;734-739.
3. Testng W.Y., Dujundji J. Nonlinear vibrations of a beam under harmonic excitation. J Appl Mech. 37:1970;292-299.
4. Bert C.W., Fisher C.A. Stability analysis of a pinned-end beam undergoing nonlinear free vibration. J Sound Vibr. 22:1972;129-131.
5. Raju I.S., Rao G.V., Raju K.K. Effect of longitudinal or inplane deformation and inertia on the large amplitude flexural vibrations of slender beams and thin plates. J Sound Vibr. 49:1976;415-422.
6. Sarma B.S., Varadn T.K., Parathap G. On various formulations of large amplitude free vibrations of beams. Comput Struct. 29:1988;959-966.
7. Singh G., Sharma A.K., Rao G.V. Large-amplitude free vibrations of beams - a discussion on various formulations and assumptions. J Sound Vibr. 142:1990;77-85.
8. Singh G., Rao G.V., Iyengar N.G.R. Re-investigation of large-amplitude free vibrations of beams using finite elements. J Sound Vibr. 143:1990;351-355.
9. Dumir P.C., Bhaskar A. Some erroneous finite element formulations of non-linear vibrations of beams and plates. J Sound Vibr. 123:1988;517-527.
10. Rao B. Large-amplitude vibrations of simply supported beams with immovable ends. J Sound Vibr. 155:1992;523-527.
11. Foda M.A. On nonlinear vibrations of a beam with pinned ends. King Saud Univ J Engng Sci. 7:(1):1995;93-107.
12. Foda MA. Analysis of large amplitude free vibrations of beams using the KBM method, J Engng Appl Sci Fac Engng Cairo Univ 1995;125-138.
13. Abramovich H. Natural frequencies of Timoshenko beams under compressive axial loads. J Sound Vibr. 157:1992;183-189.
14. Rao G.V., Raju I.S., Kanaka K. Nonlinear vibrations of beams considering shear deformation and rotary inertia. Am Inst Aeron Astron J. 14:1976;685-687.
15. Chuh M. Nonlinear vibrations of beams by matrix displacement method. Am Inst Aeron Astron J. 10:1972;355-357.
16. Shastry B.P., Rao G.V. Dynamic stability of bars considering shear deformation and rotary inertia. Comput Struct. 16:1984;823-827.
17. Lord Rayleigh. Theory of sound. 2nd ed :1945;Dover, New York.
18. Timoshenko S.P. On the correction for shear of the differential equation for transverse vibrations of prismatic bar. Phil Mag. 41:1921;744-746.
19. Cowper G.R. The shear coefficient in Timoshenko's beam theory. J Appl Mech. 33:1966;335-340.
20. Sato K. On the governing equations for free vibration and stability of a Timoshenko beam: Hamilton's principle. J Sound Vibr. 145:1991;338-340.
21. Kolousek V. Calcul des Efforts Dynamiques dans les Ossatures Rigides. 1959;86-89 Dunod, Paris.
22. Kounadis A.N. On the derivation of equation of motion for a vibrating Timoshenko column. J Sound Vibr. 73:1980;174-184.
23. Nayfeh A.H. Perturbation methods. 1973;Wiley Interscience, New York.
24. Nayfeh A.H. Introduction to perturbation techniques. 1981;Wiley Interscience, New York.
25. Nayfeh A.H., Mook D.T. Nonlinear oscillations. 1979;Wiley Interscience, New York.
26. Abramovich H., Elishakoff I. Application of the Krein's method for determination of natural frequencies of periodically supported beam based on simplified Bresse-Timoshenko equations. Acta Mech. 66:1987;39-59.
27. Golpalakrishinan S., Martin M., Doyle J.F. A matrix methodology for spectral analysis of wave propagation in multiple connected Timoshenko beams. J Sound Vibr. 158:1992;11-24.