Abstract
An exact dynamic stiffness method is presented in this paper to determine the natural frequencies and mode shapes of the axially loaded double-beam systems, which consist of two homogeneous and prismatic beams with a distributed spring in parallel between them. The effects of the axial force, shear deformation and rotary inertia are considered, as shown in the theoretical formulation. The dynamic stiffness influence coefficients are formulated from the governing differential equations of the axially loaded double-beam system in free vibration by using the Laplace transform method. An example is given to demonstrate the effectiveness of this method, in which ten boundary conditions are investigated and the effect of the axial force on the natural frequencies and mode shapes of the double-beam system are further discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abu-Hilal M 2006 Dynamic response of a double Euler-Bernoulli beam due to a moving constant load. J. Sound Vib. 297: 477–491
Aida T, Toda S, Ogawa N and Imada Y 1992 Vibration control of beams by beam-type dynamic vibration absorbers. J. Eng. Mech. 118: 248–258
Balkaya M, Kaya M O and Saglamer A 2010 Free transverse vibrations of an elastically connected simply supported twin pipe system. Struct. Eng. Mech. 34: 549–561
Char B W, Geddes K O, Gonnet G H, Monagan M B and Watt S M 1988 Maple reference manual (Canada: Watcom Publications)
Chen Y H and Sheu J T 1994 Dynamic characteristics of layered beam with flexible core. J. Vib. Acoust. 116: 350–356
Chen Y H, Lin C Y 1998 Structural analysis and optimal design of a dynamic absorbing beam. J. Sound Vib. 212: 759–769
Chonan S 1976 Dynamical behaviours of elastically connected double-beam systems subjected to an impulsive load. T. JSME 19: 595–603
Hamada T R, Nakayama H and Hayashi K 1983 Free and forced vibrations of elastically connected double-beam systems. T. JSME 26: 1936–1942
Kessel P G 1966 Resonances excited in an elastically connected double-beam system by a cyclic moving load. J. Acoust. Soc. Am. 40: 684–687
Oniszczuk Z 2000 Free transverse vibrations of elastically connected simply supported double-beam complex system. J. Sound Vib. 232: 387–403
Oniszczuk Z 2003 Forced transverse vibrations of an elastically connected complex simply supported double-beam system. J. Sound Vib. 264: 273–286
Palmeri A and Adhikari S 2011 A Galerkin-type state-space approach for transverse vibrations of slender double-beam systems with viscoelastic inner layer. J. Sound Vib. 330: 6372–6386
Rao S S 1974 Natural vibrations of systems of elastically connected Timoshenko beams. J. Acoust. Soc. Am. 55: 1232–1237
Seelig J M and Hoppmann II W H 1964 Normal mode vibrations of systems of elastically connected parallel bars. J. Acoust. Soc. Am. 36: 93–99
Vu H V, Ordonez A M and Karnopp B H 2000 Vibration of a double-beam system. J. Sound Vib. 229: 807–822
Wittrick W H and Williams F W 1971 A general algorithm for computing natural frequencies of elastic structures. Q. J. Mech. Appl. Math 24: 263–284
Zhang Y Q, Lu Y and Wang S L, Liu X 2008 Vibration and buckling of a double-beam system under compressive axial loading. J. Sound Vib. 318: 341–352
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
XIAOBIN, L., SHUANGXI, X., WEIGUO, W. et al. An exact dynamic stiffness matrix for axially loaded double-beam systems. Sadhana 39, 607–623 (2014). https://doi.org/10.1007/s12046-013-0214-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12046-013-0214-5