Abstract
The present paper considers the dynamic behavior of beams with open thin-walled cross-sections along their length with bracings (connecting beams and truss). The effect of the constrained torsion warping, rotary inertia, and flexural-torsion coupling due to nonsymmetric cross-sections is included. In the case of simply supported beams, closed-form solutions for determining coupled natural frequencies and corresponding mode shapes are newly derived. The frequency equation, given in a determinantal form, is expanded in an explicit analytical form and then solved using the Mathcad 2001 Professional symbolic computing package. Some illustrative examples on the application of the present theory are given for coupled bending-torsion vibrations of braced thin-walled beams. As compared with FEM, numerical results demonstrate the accuracy and effectiveness of the proposed method
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. O. Friberg, “Coupled vibrations of beams—an exact dynamic element stiffness matrix,” Int. J. Numer. Meth. Eng., 19, 479–493 (1983).
E. Dokumaci, “An exact solution for coupled bending and torsion vibrations of uniform beams having single cross-sectional symmetry,” J. Sound Vibr., 119(3), 443–449 (1997).
J. R. Banerjee, “Coupled bending-torsional dynamic stiffness matrix for beam elements,” Int. J. Numer. Meth. Eng., 28, 1283–1298 (1989).
M. Y. Kim, S. P. Chang, and S. B. Kim, “Spatial stability and free vibration of shear flexible thin-walled elastic beams. I: Analytical approach,” Int. J. Numer. Meth. Eng., 37, 4097–4115 (1994).
M. Tanaka and A. N. Bercin, “Free vibration for uniform beams of nonsymmetrical cross-section using Mathematica,” Comput. Struct., 71, 1–8 (1977).
J. R. Banerjee, “Explicit frequency equation and mode shapes of a cantilever beam coupled in bending and torsion,” J. Sound Vibr., 224, 267–281 (1999).
L. P. Kollár, “Flexural-torsional vibration of open section composite beams with shear deformation,” Int. J. Solids Struct., 38, 7543–7558 (2001).
A. Arpaci and E. Bozdag, “On free analysis of thin-walled beams with nonsymmetrical open cross-sections,” Comput. Struct., 80, 691–695 (2002).
A. Arpaci, S. E. Bozdag, and E. Sunbuloglu, “Triply coupled vibrations of thin-walled open cross-section beams including rotary inertia effects,” J. Sound Vibr., 260, 889–900 (2003).
A. Prokić, “On fivefold coupled vibrations of Thimoshenko thin-walled beams,” Eng. Struct., 28, 54–62 (2006).
A. Prokić, “On triply coupled vibrations of thin-walled beams with arbitrary cross-section,” J. Sound Vibr., 279, 723–737 (2005).
B. S. Smith and B. S. Taranath, “The analysis of tall core-supported structures subject to torsion,” in: Proc. Inst. Civil Engs., 53, Part 2, 173–188 (1972).
A. C. Heidebrecht and B. S. Smith, “Approximate analysis of open-section shear walls subject to torsional loading,” J. Struct. Div., 99, 2355–2373 (1973).
A. W. Irwin and C. J. Bolton, “Torsion of tall building cores,” 63, Part 2, 579–591 (1977).
T. C. Liauw, “Torsion of multi-storey spatial core walls,” in: Proc. Inst. Civil Engs., 65, Part 2, 601–609 (1978).
T. C. Liauw and W. K. Luk, “Torsion of core walls of nonuniform section,” J. Struct. Div., 106, 1921–1931 (1980).
A. Rutenberg, M. Shtarkman, and M. Eisenberger, “Torsional analysis methods for perforated cores,” J. Struct. Eng., 112(6), 1207–1227 (1986).
P. Mendis, “Warping analysis of concrete cores,” The Structural Design of Tall Buildings, 10, 43–52 (2001).
A. Prokic, “Computer program for determination of geometrical properties of thin-walled beams with open-closed section,” Comput. Struct., 74, 705–715 (2000).
Tower 5, Professional Integrated Software—Finite Element Analysis and Design of Structures, Radimpex, Beograd.
Author information
Authors and Affiliations
Additional information
Published in Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 129–143, November 2007.
Rights and permissions
About this article
Cite this article
Prokić, A., Lukić, D. Dynamic behavior of braced thin-walled beams. Int Appl Mech 43, 1290–1303 (2007). https://doi.org/10.1007/s10778-007-0134-3
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-007-0134-3