On triply coupled vibration of eccentrically loaded thin-walled beam using dynamic stiffness matrix method

다국어 초록 (Multilingual Abstract)

The effect of central axial load on natural frequencies of various thin-walled beams, are investigated by some researchers using different methods such as finite element, transfer matrix and dynamic stiffness matrix methods. However, there are situations that the load will be off centre. This type of loading is called eccentric load. The effect of the eccentricity of axial load on the natural frequencies of asymmetric thin-walled beams is a subject that has not been investigated so far. In this paper, the mentioned effect is studied using exact dynamic stiffness matrix method. Flexure and torsion of the aforesaid thin-walled beam is based on the Bernoulli-Euler and Vlasov theories, respectively. Therefore, the intended thin-walled beam has flexural rigidity, saint-venant torsional rigidity and warping rigidity. In this paper, the Hamilton’s principle is used for deriving governing partial differential equations of motion and force boundary conditions. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using ABAQUS software.

참고문헌 (Reference)

1 Sheikh, A. H., "Vibration of thin-walled laminated composite beams having open and closed sections" 134 : 209-215, 2015

2 Chang Hong Chen, "The finite element model research of the pre-twisted thin-walled beam" 국제구조공학회 57 (57): 389-402, 2016

3 김남일, "Series solutions for spatially coupled buckling anlaysis of thin-walled Timoshenko curved beam on elastic foundation" 국제구조공학회 33 (33): 447-484, 2009

4 Jun, L., "Response of monosymmetric thin-walled Timoshenko beams to random excitations" 41 : 6023-6040, 2004

5 Eslimy-Isfahany, S. H. R., "Response of a bending-torsion coupled beam to deterministic and random loads" 195 : 267-283, 1996

6 Ghandi, E., "On the biplanar motion of a Timoshenko beam with shear resistant infill" 57 (57): 1-8, 2012

7 Howson, W. P., "Natural frequencies of frames with axially loaded Timoshenko members" 26 (26): 503-515, 1973

8 Tanaka, M., "Free vibration solution for uniform beams of nonsymmetrical cross section using Mathematica" 71 (71): 1-8, 1999

9 Eken, S., "Flexural-torsional coupled vibration of anisotropic thin-walled beams with biconvex crosssection" 94 : 372-383, 2015

10 Banerjee, J. R., "Exact dynamic stiffness matrix of a bending-torsion coupled beam including warping" 59 (59): 613-621, 1996

11 A. Shirmohammadzade, "Exact dynamic stiffness matrix for a thin-walled beam-column of doubly asymmetric cross-section" 국제구조공학회 38 (38): 195-210, 2011

12 Rafezy, B., "Exact dynamic stiffness matrix for a thin-walled beam of doubly asymmetric crosssection filled with shear sensitive material" 69 (69): 2758-2779, 2007

13 Banerjee, J. R., "Dynamic stiffness formulation for structural elements : A general approach" 63 (63): 101-103, 1997

14 Eslimy-Isfahany, SH. R., "Dynamic response of an axially loaded bending-torsion coupled beam" 33 (33): 601-607, 1996

15 Ghandi, E., "Coupled flexural-torsional dynamic stiffness matrix of an elastically supported axially loaded beam with shear resistant in‐fill" 24 (24): 537-554, 2015

16 Banerjee, J. R., "Coupled bendingtorsional dynamic stiffness matrix for an axially loaded Timoshenko beam element" 31 (31): 749-762, 1994

17 Banerjee, J. R., "Coupled bendingtorsional dynamic stiffness matrix for Timoshenko beam elements" 42 (42): 301-310, 1992

18 Banerjee, J. R., "Coupled bending-torsional dynamic stiffness matrix for axially loaded beam elements" 33 (33): 739-751, 1992

19 Banerjee, J. R., "Coupled bending torsional dynamic stiffness matrix for beam elements" 28 (28): 1283-1298, 1989

20 Chen, H. H., "Coupled axial-torsional vibration of thin-walled Z-section beam induced by boundary conditions" 45 (45): 573-583, 2007

21 Wittrick, W. H., "A general algorithm for computing natural frequencies of elastic structures" 24 (24): 263-284, 1971

22 Banerjee, J. R., "A Fortran routine for computation of coupled bending-torsional dynamic stiffness matrix of beam elements" 13 (13): 17-24, 1991