Transverse Vibration of an Undamped Elastically Connected Double-Beam System with Arbitrary Boundary Conditions
Publication: Journal of Engineering Mechanics
Volume 142, Issue 2
Abstract
This paper presents a semianalytical method to analyze the natural frequencies and mode shapes of an undamped double-beam system, which is composed of two beams joined by a uniformly distributed connecting elastic layer, with arbitrary beam mass, beam flexural rigidity, and arbitrary boundary conditions. The classical modal expansion method is further applied to determine the forced vibration responses in the double-beam system based on the natural frequencies and mode shapes obtained from the free vibration analysis. A specific orthogonality condition for the double-beam system is derived, and then applied to decouple and simplify the motion differential equations. Numerical examples are presented and discussed in detail to verify and illustrate the efficiency of the proposed semianalytical method that can further help characterize the dynamic responses and design work for double-beam structures.
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Acknowledgments
This work is sponsored by the National Science Foundation (NSF) under Grant No. CMMI-0800417. The support of the NSF is gratefully acknowledged.
References
Aida, T., Toda, S., Ogawa, N., and Imada, Y. (1992). “Vibration control of beams by beam-type dynamic vibration absorbers.” J. Eng. Mech., 248–258.
Chen, Y. H., and Lin, C. Y. (1998). “Structural analysis and optimal design of a dynamic absorbing beam.” J. Sound Vib., 212(5), 759–769.
Chen, Y. H., and Sheu, J. T. (1993). “Axially-loaded damped Timoshenko beam on viscoelastic foundation.” Int. J. Numer. Meth. Eng., 36(6), 1013–1027.
Chen, Y. H., and Sheu, J. T. (1994). “Dynamic characteristics of layered beam with flexible core.” J. Vib. Acoust., 116(3), 350–356.
Chen, Y. H., and Sheu, J. T. (1995). “Beam on viscoelastic foundation and layered beam.” J. Eng. Mech., 340–344.
Chonan, S. (1976). “Dynamical behaviors of elastically connected double-beam systems subjected to an impulsive load.” Bull. JSME, 19(132), 595–603.
Cottle, E. T. (1990). “Damping of layered beams with mixed boundary conditions.” Air Force Institute of Technology, Wright-Patterson Air Force Base, OH.
Douglas, B. E., and Yang, J. C. S. (1978). “Transverse compressional damping in the vibratory response of elastic-viscoelastic-elastic beams.” AIAA J., 16(9), 925–930.
Dublin, M., and Friedrich, H. R. (1956). “Forced responses of two elastic beams interconnected by spring-damper systems.” J. Aeronaut. Sci., 23(9), 824–829.
Frostig, Y., and Baruch, M. (1993). “High-order buckling analysis of sandwich beams with transversely flexible core.” J. Eng. Mech., 476–495.
Frostig, Y., and Baruch, M. (1994). “Free vibrations of sandwich beams with a transversely flexible core: a high order approach.” J. Sound Vib., 176(2), 195–208.
Hamada, T. R., Nakayama, H., and Hayashi, K. (1983). “Free and forced vibrations of elastically connected double beam systems.” Bull. JSME, 26(221), 1936–1942.
Irie, T., Yamada, G., and Kobayashi, Y. (1982). “The steady-state response of an internally damped double-beam system interconnected by several springs.” J. Acoust. Soc. Am., 71(5), 1155–1162.
Kawazoe, K., Kono, I., Aida, T., Aso, T., and Ebisuda, K. (1998). “Beam-type dynamic vibration absorber comprised of free-free beam.” J. Eng. Mech., 476–479.
Kessel, P. G. (1966). “Resonances excited in an elastically connected double-beam system by a cyclic moving load.” J. Acoust. Soc. Am., 40(3), 684–687.
Kessel, P. G., and Raske, T. F. (1967). “Damped response of an elastically connected double-beam system due to a cyclic moving load.” J. Acoust. Soc. Am., 42(4), 873–881.
Kukla, S., and Skalmierski, B. (1994). “Free vibration of a system composed of two beams separated by an elastic layer.” J. Theor. Appl. Mech., 32(3), 581–590.
Li, J., and Hua, H. X. (2007). “Spectral finite element analysis of elastically connected double-beam systems.” Finite Elem. Anal. Des., 43(15), 1155–1168.
Lu, Y. P., and Douglas, B. E. (1974). “On the forced vibrations of three-layer damped sandwich beams.” J. Sound Vib., 32(4), 513–516.
Macé, M. (1994). “Damping of beam vibrations by means of a thin constrained viscoelastic layer: Evaluation of a new theory.” J. Sound Vib., 172(5), 577–591.
Oniszczuk, Z. (1999). “Transverse vibrations of the elastically connected rectangular double-membrane compound system.” J. Sound Vib., 221(2), 235–250.
Oniszczuk, Z. (2000a). “Free transverse vibrations of an elastically connected rectangular simply supported double-plate complex system.” J. Sound Vib., 236(4), 595–608.
Oniszczuk, Z. (2000b). “Free transverse vibrations of elastically connected simply supported double-beam complex system.” J. Sound Vib., 232(2), 387–403.
Oniszczuk, Z. (2000c). “Transverse vibrations of elastically connected double-string complex system.” J. Sound Vib., 232(2), 355–366.
Oniszczuk, Z. (2000d). “Transverse vibrations of elastically connected double-string complex system.” J. Sound Vib., 232(2), 367–386.
Oniszczuk, Z. (2002a). “Damped vibration analysis of a two-degree-of-freedom discrete system.” J. Sound Vib., 257(2), 391–403.
Oniszczuk, Z. (2002b). “Free transverse vibrations of an elastically connected complex beam-string system.” J. Sound Vib., 254(4), 703–715.
Oniszczuk, Z. (2003a). “Damped vibration analysis of an elastically connected complex double-string system.” J. Sound Vib., 264(2), 253–271.
Oniszczuk, Z. (2003b). “Forced transverse vibrations of an elastically connected complex simply supported double-beam system.” J. Sound Vib., 264(2), 273–286.
Oniszczuk, Z. (2003c). “Free transverse vibrations of an elastically connected rectangular plate-membrane complex system.” J. Sound Vib., 264(1), 37–47.
Oniszczuk, Z. (2004). “Forced transverse vibrations of an elastically connected complex rectangular simply supported double-plate system.” J. Sound Vib., 270(4–5), 997–1011.
Rao, S. S. (1974). “Natural vibrations of systems of elastically connected Timoshenko beams.” J. Acoust. Soc. Am., 55(6), 1232–1237.
Seelig, J. M., and Hoppmann, W. H. (1964a). “Impact on an elastically connected double-beam system.” J. Appl. Mech., 31(4), 621–626.
Seelig, J. M., and Hoppmann, W. H. (1964b). “Normal mode vibrations of systems of elastically connected parallel bars.” J. Acoust. Soc. Am., 36(1), 93–99.
Vu, H. V. (1987). “Distributed dynamic vibration absorber.” Ph.D. thesis, Univ. of Michigan, Ann Arbor, MI.
Vu, H. V., Ordóñez, A. M., and Karnopp, B. H. (2000). “Vibration of a double-beam system.” J. Sound Vib., 229(4), 807–822.
Xin, T., and Gao, L. (2011). “Reducing slab track vibration into bridge using elastic materials in high speed railway.” J. Sound Vib., 330(10), 2237–2248.
Yamaguchi, H. (1985). “Vibrations of a beam with an absorber consisting of a viscoelastic beam and a spring-viscous damper.” J. Sound Vib., 103(3), 417–425.
Yankelevsky, D. Z. (1991). “Analysis of a composite layered elastic foundation.” Int. J. Mech. Sci., 33(3), 169–177.
Zhang, Y. Q., Lu, Y., and Ma, G. W. (2008). “Effect of compressive axial load on forced transverse vibrations of a double-beam system.” Int. J. Mech. Sci., 50(2), 299–305.
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© 2015 American Society of Civil Engineers.
History
Received: Jan 27, 2015
Accepted: May 28, 2015
Published online: Jul 7, 2015
Discussion open until: Dec 7, 2015
Published in print: Feb 1, 2016
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