Browse > Article
http://dx.doi.org/10.5050/KSNVE.2011.21.1.066

Free Vibrations of Tapered Beams with Constant Surface Area  

Lee, Byoung-Koo (원광대학교 토목환경공학과)
Oh, Sang-Jin (전남도립대학 토목환경과)
Park, Chang-Eun (원광대학교 대학원 토목환경공학과)
Lee, Tae-Eun (원광대학교 토목환경공학과)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.21, no.1, 2011 , pp. 66-73 More about this Journal
Abstract
This paper deals with free vibrations of the tapered beams with the constant surface area. The surface area of the objective beams are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear and parabolic ones. Ordinary differential equations governing free vibrations of such beams are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various beam parameters such as section ratio, surface area ratio, end constraint and taper type are reported in tables and figures. Especially, section ratios of the strongest beam are calculated, under which the maximum frequencies are achieved.
Keywords
Free Vibration; Constant Surface Area; Tapered Beam; Natural Frequency; Mode Shape;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Hikami, Y., 1982, Wind Tunnel Test Methods and Facilities for Bridge Aerodynamic Stability Investigation, IHI Report, Vol. 6, pp. 47-52.
2 Haftka, R. T., Grudal, Z. and Kamat, M. P., 1990, Elements of Structural Optimization, Kluwer Academic Publisher, Netherlands.
3 Lee, B. K., Lee, T. E. and Kim, Y. I., 2009, Stronget Simple Beams with Constant Volume, Transactions of the Korea Society for Civil Engineering, Vol. 29, No. 2A, pp. 155-162.
4 Wilson, J. F., Holloway, D. M. and Biggers, S. B., 1971, Stability Experiments on the Strongest Columns and Circular Arches, Experimental Mechanics, Vol. 11, pp. 303-308.   DOI
5 Cox, S. J. and Overton, M. I., 1992, On the Optimal Design of Columns Against Buckling, SIAM Journal on Mathematical Analysis, Vol. 23, pp. 287-325.   DOI
6 Atanackovic, T. M. and Simic, S. S., 1999, On the Optimal Shape of a Pfluger Column, European Journal of Mechanics A-Solid, Vol. 18, pp. 903-913.   DOI
7 Lee, B. K. and Oh, S. J., 2000, "Elastica and Buckling Loads of Simple Tapered Columns with Constant Volume, International Journal of Solids and Structures, Vol. 37, Issue 18, pp. 2507-2518.   DOI
8 Lee, B. K., Carr, A. J., Lee, T. E. and Kim, I. J., 2006, Buckling Loads of Columns with Constant Volume, Journal of Sound and Vibrations. Vol. 294, Issues. 1-2, pp. 381-387.   DOI
9 Lee, B. K., Lee, T. E., Yoon, H. M. and Choi, J. M., 2010, Free Vibrations of Tapered Cicular Arches with Constant Volume, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 20, No. 2, pp. 144-152.   DOI
10 Timoshenko, S. P. and Gere, J. M., 1963, Theory of Elastic Stability, McGraw-Hill Book Company, USA.
11 Timoshenko, S. P., Young, D. H. and Weaver, W., 1974, Vibration Problems in Engineering, Wiley, USA.
12 Al-Khafaji, A. W. and Tooley, J. R., 1986, Numerical Methods in Engineering Practice, Holt, Rinehart and Winston, Inc.