Abstract
Free transverse vibration and buckling of a double-beam continuously joined by a Winkler elastic layer under compressive axial loading with the influence of rotary inertia and shear are considered in this paper. The motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli–Fourier method. The boundary value and initial value problems are solved. The natural frequencies and associated amplitude ratios of an elastically connected double-beam complex system and the analytical solution of the critical buckling load are determined. The presented theoretical analysis is illustrated by a numerical example, in which the effect of physical parameters characterizing the vibrating system on the natural frequency, the associated amplitude ratios and the critical buckling load are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Matsunaga H.: Buckling instabilities of thick elastic beams subjected to axial stresses. Comput. Struct. 59, 859–868 (1996)
Matsunaga H.: Free vibration and stability of thin elastic beams subjected to axial forces. J. Sound Vib. 191, 917–933 (1996)
Matsunaga H.: Vibration and buckling of deep beam-columns on two-parameter elastic foundations. J. Sound Vib. 228, 359–376 (1999)
Levinson M.: A new rectangular beam theory. J. Sound Vib. 74, 81–87 (1981)
Levinson M.: Further results of a new beam theory. J. Sound Vib. 77, 440–444 (1981)
Wang W.T., Stephens E.J.: Natural frequencies of Timoshenko beams on Pasternak foundations. J. Sound Vib. 51, 149–155 (1977)
De Rosa M.A.: Free vibrations of Timoshenko beams on two-parameter elastic foundation. Comput. Struct. 57, 151–156 (1995)
Ariaei, A., Ziaei-Rad, S., Ghaypur, M.: Transverse vibration of a multiple-Timoshenko beam system with intermediate elastic connections due to a moving load. Arch. Appl. Mech. doi:10.1007/s00419-010-0410-2 (2010)
Oniszczuk Z.: Free transverse vibrations of elastically connected simply supported double-beam complex system. J. Sound Vib. 232, 387–403 (2000)
Zhang Q.Y., Lu Y., Wang L.S., Liu X.: Vibration and buckling of a double-beam system under compressive axial loading. J. Sound Vib. 318, 341–352 (2010)
Mei M., Karpenko Y., Moody S., Allen D.: Analytical approach to free and forced vibrations of axially loaded cracked Timoshenko beams. J. Sound Vib. 291, 1041–1060 (2006)
Li J., Hua H.: Spectral finite element analysis of elastically connected double-beam systems. Finite Elements Anal. Des. 43, 1155–1168 (2007)
Timoshenko S.P., Gere M.J.: Theory of Elastic Stability. McGraw-Hill Book Company, Inc., New York (1961)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Stojanović, V., Kozić, P., Pavlović, R. et al. Effect of rotary inertia and shear on vibration and buckling of a double beam system under compressive axial loading. Arch Appl Mech 81, 1993–2005 (2011). https://doi.org/10.1007/s00419-011-0532-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-011-0532-1