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Exact vibration of Timoshenko beam combined with multiple mass spring sub-systems
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 Title & Authors
Exact vibration of Timoshenko beam combined with multiple mass spring sub-systems
El-Sayed, Tamer A.; Farghaly, Said H.;
 Abstract
This paper deals with the analysis of the natural frequencies, mode shapes of an axially loaded beam system carrying ends consisting of non-concentrated tip masses and three spring-two mass sub-systems. The influence of system design and sub-system parameters on the combined system characteristics is the major part of this investigation. The effect of material properties, rotary inertia and shear deformation of the beam system is included. The end masses are elastically supported against rotation and translation at an offset point from the point of attachment. Sub-systems are attached to center of gravity eccentric points out of the beam span. The boundary conditions of the ordinary differential equation governing the lateral deflections and slope due to bending of the beam system including developed shear force frequency dependent terms, due to the sub.system suspension, have been formulated. Exact formulae for the modal frequencies and the modal shapes have been derived. Based on these formulae, detailed parametric studies are carried out. The geometrical and mechanical parameters of the system under study have been presented in non-dimensional analysis. The applied mathematical model is presented to cover wide range of mechanical, naval and structural engineering applications.
 Keywords
vibration frequencies;exact solution;Timoshenko beam;eccentric mass;sub-system;combined system;
 Language
English
 Cited by
 References
1.
Ari-Gur, J. and Elishakoff, I. (1990), "On the effect of shear deformation on buckling of columns with overhang", J. Sound Vib., 139(1), 165-169. crossref(new window)

2.
Bergman, L. and Nicholson, J. (1985), "Forced vibration of a damped combined linear system", J. Vib. Acoust., 107(3), 275-281. crossref(new window)

3.
Bokaian, A. (1990), "Natural frequencies of beams under tensile axial loads", J. Sound Vib., 142(3), 481-498. crossref(new window)

4.
Chang, T.P. (1993), "Forced vibration of a mass-loaded beam with a heavy tip body", J. Sound Vib., 164(3), 471-484. crossref(new window)

5.
Chen, Y., McFarland, D.M., Spencer, B.F. and Bergman, L.A. (2015), "Exact solution of free vibration of a uniform tensioned beam combined with both lateral and rotational linear sub-systems", J. Sound Vib., 341, 206-221. crossref(new window)

6.
Cowper, G. (1966), "The shear coefficient in Timoshenko's beam theory", J. Appl. Mech., 33(2), 335-340. crossref(new window)

7.
Farghaly, S.H. and Shebl, M. (1995), "Exact frequency and mode shape formulae for studying vibration and stability of Timoshenko beam system", J. Sound Vib., 180(2), 205-227. crossref(new window)

8.
Farghaly, S.H. (1992), "Bending vibrations of an axially loaded cantilever beam with an elastically mounted end mass of finite length", J. Sound Vib., 156(2), 373-380. crossref(new window)

9.
Farghaly, S.H. (1993), "Comments on "The general equation of frequencies for vibrating uniform one-span beams under compressive axial loads", J. Sound Vib., 161(1), 181-183. crossref(new window)

10.
Grossi, R.O. and Laura, P.A.A. (1982), "Further results on a vibrating beam with a mass and spring at the end subjected to an axial force", J. Sound Vib., 84(4), 593-594. crossref(new window)

11.
Gurgoze, M. (1996), "On the eigenfrequencies of a cantilever beam with attached tip mass and a springmass system", J. Sound Vib., 190(2), 149-162. crossref(new window)

12.
Gurgoze, M. and Batan, H. (1996), "On the effect of an attached spring-mass system on the frequency spectrum of a cantilevered beam", J. Sound Vib., 195(1), 163-168. crossref(new window)

13.
Huang, T. (1961), "The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions", J. Appl. Mech., 28(4), 579-584. crossref(new window)

14.
Kounadis, A.N. (1980), "On the derivation of equations of motion for a vibrating Timoshenko column", J. Sound Vib., 73(2), 177-184. crossref(new window)

15.
Naguleswaran, S. (2004), "Transverse vibration of an uniform Euler-Bernoulli beam under linearly varying axial force", J. Sound Vib., 275(1), 47-57. crossref(new window)

16.
Rossi, R.E., Laura, P.A.A., Avalos, D.R. and Larrondo, H. (1993), "Free vibrations of Timoshenko beams carrying elastically mounted, concentrated masses", J. Sound Vib., 165(2), 209-223. crossref(new window)

17.
Saito, H. and Otomi, K. (1979), "Vibration and stability of elastically supported beams carrying an attached mass under axial and tangential loads", J. Sound Vib., 62(2), 257-266. crossref(new window)

18.
Sato, K. (1991), "On the governing equations for vibration and stability of a Timoshenko beam: Hamilton's principle", J. Sound Vib., 145(2), 338-340. crossref(new window)

19.
Snowdon, J. (1966), "Vibration of cantilever beams to which dynamic absorbers are attached", J. Acoust. Soc. Am., 39(5A), 878-886. crossref(new window)

20.
Takahashi, K. (1980), "Eigenvalue problem of a beam with a mass and spring at the end subjected to an axial force", J. Sound Vib., 71(3), 453-457. crossref(new window)

21.
Timoshenko, S.P. (1922), "On the transverse vibrations of bars of uniform cross-section", London, Edinburgh, and Dublin Philos. Mag. J. Sci., 43(253), 125-131. crossref(new window)

22.
To, C.W.S. (1982), "Vibration of a cantilever beam with a base excitation and tip mass", J. Sound Vib., 83(4), 445-460. crossref(new window)