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Exact dynamic stiffness matrix for a thin-walled beam of doubly asymmetric cross-section filled with shear sensitive material. (English) Zbl 1194.74467

Summary: An exact dynamic stiffness matrix is developed for the flexural motion of a three-dimensional, bi-material beam of doubly asymmetric cross-section. The beam comprises a thin walled outer layer that encloses and works compositely with its shear sensitive core material. The outer layer may have the form of an open or closed section and provides flexural, warping and Saint-Venant rigidity, while the core material provides Saint-Venant and shear rigidity. 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, which enables the required natural frequencies to be converged upon to any required accuracy with the certain knowledge that none have been missed. Such a formulation enables the powerful modelling features associated with the finite element technique to be utilized when establishing structural models. Three examples are included to validate and illustrate the method. The work also holds considerable potential in its application to the approximate analysis of asymmetric, multi-storey, three-dimensional wall-frame structures.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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[1] , . Dynamic matrix analysis of framed structures. Proceedings of the Fourth U.S. National Congress on Applied Mechanics, vol. 1, 1962; 99–105.
[2] Cheng, Journal of Structural Engineering 96 pp 551– (1970)
[3] Wang, Journal of Sound and Vibration 14 pp 215– (1971)
[4] Howson, Journal of Sound and Vibration 26 pp 503– (1973)
[5] Howson, Advances in Engineering Software and Workstations 1 pp 181– (1979) · Zbl 0431.73075 · doi:10.1016/0141-1195(79)90016-0
[6] Howson, Advances in Engineering Software and Workstations 5 pp 137– (1983) · doi:10.1016/0141-1195(83)90108-0
[7] A teaching analysis and design program for the complete eigensolution of plane frames using microcomputers. International Conference on Education, Practice and Promotion of Computational Methods in Engineering using Small Computers (EPMESC). Macau, 1985.
[8] Williams, Earthquake Engineering and Structural Dynamics 15 pp 133– (1987)
[9] Issa, Journal of Sound and Vibration 127 pp 291– (1988)
[10] Capron, Journal of Sound and Vibration 124 pp 453– (1988)
[11] Banerjee, International Journal for Numerical Methods in Engineering 21 pp 2289– (1985)
[12] Gupta, Journal of Sound and Vibration 175 pp 145– (1994)
[13] Howson, Computers and Structures 55 pp 989– (1995)
[14] Howson, Journal of Engineering Mechanics 125 pp 19– (1999)
[15] Howson, Proceedings of the Institution of Mechanical Engineers Part C–Journal of Mechanical Engineering Science 213 pp 687– (1999)
[16] Gere, Journal of Applied Mechanics 25 pp 373– (1958) · Zbl 0083.40401
[17] Falco, Meccanica 8 pp 181– (1973)
[18] Dokumaci, Journal of Sound and Vibration 119 pp 443– (1987) · Zbl 1235.74275
[19] Hallauer, Journal of Sound and Vibration 85 pp 105– (1982) · Zbl 0493.73047
[20] Friberg, International Journal for Numerical Methods in Engineering 19 pp 479– (1983)
[21] Friberg, International Journal for Numerical Methods in Engineering 21 pp 1205– (1985)
[22] Banerjee, International Journal for Numerical Methods in Engineering 28 pp 1283– (1989)
[23] Banerjee, Computers and Structures 42 pp 301– (1992)
[24] Banerjee, Computers and Structures 59 pp 613– (1996)
[25] Tanaka, Computers and Structures 71 pp 1– (1999)
[26] Li, Mechanics Research Communications 31 pp 697– (2004)
[27] Li, International Journal of Mechanical Sciences 46 pp 299– (2004)
[28] Rafezy, Journal of Sound and Vibration 289 pp 938– (2006)
[29] . Natural frequencies of plane sway frames: an overview of two simple models. Proceedings of ICCES 2003: International Conference on Computational and Experimental Engineering and Sciences, Corfu, Greece, 2003; 1–6.
[30] Rafezy, International Journal of Solids and Structures (2006)
[31] The Behavior of Sandwich Structures of Isotropic and Composite Materials. Technomic Publishing Co.: Pennsylvania, U.S.A., 1999.
[32] The Handbook of Sandwich Construction. Engineering Materials Advisory Services Ltd.: West Midlands, U.K., 1997.
[33] Williams, International Journal of Mechanical Sciences 12 pp 781– (1970)
[34] Wittrick, Quarterly Journal of Mechanics and Applied Mathematics 24 pp 263– (1971)
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