Revised dynamic characteristics of uniform beams with free - hinged and free - free end conditions
-
2017-05-17 https://doi.org/10.14419/ijet.v6i2.7465
-
Eigenvalues, Modes of Vibrations, Nodal Points, Stiffness. -
Abstract
The uniform beams with free-hinged ends and with free-free ends have very slack bonds and, therefore, in accordance with Rayleigh’s theorem, their lowermost eigenvalue must be lesser compared to the lower most eigenvalue of beams with clamped-free and clamped-hinged ends. In spite of the physical evidence, the magnitudes of lowermost eigenvalue of beams with slack bonds, available in all publications, are larger. This contradiction signifies that there are the missing modes of vibration with the lowermost eigenvalue for beams with free-free and free-hinged ends. The rigorous analysis of uniform beams vibration with free-free and free-hinged ends conditions defines these missing lowermost natural frequencies and normal modes and ascertains the frequencies and modes for all uniform beams with various end conditions into the ordered system. The lowermost mode of vibration of a beam with free-free ends, caused by ocean choppiness and determined in this investigation, is paramount for estimation of the ships structural strength, particularly important for the tankers.
-
References
[1] L. H. Donnell, “Beams, Plates and Shellsâ€, McGraw-Hill Book Co.,New York, 1976.
[2] F. R. Gantmacherand M. G. Krein, “Period of frequency matrices kernel and small vibrations vibrations of mechanical systemsâ€, pp. 142 – 143, Gostechizdat, Moscow, 1950.
[3] J. Kozesnik, “Dynamika Stroju, (Vybrane stati)â€, Statni Nakladatelstvi Technicke Literature, PRAHA, 1958.
[4] W. S. Rayleigh,“The Theory of Soundâ€, 2-nd revised edition, vol.1, Dover Publication, New York, 1945.
[5] E. J. Routh,“Advanced Rigid Dynamicsâ€, MacMillon, London, 49, 1892.
[6] A. G. Piersol and T. L Paez “Harris’s Shock and Vibration, Handbookâ€,sixth ed. The McGraw-Hill Co. Inc., 2010. ISBN: 9780071508193.
[7] S. P. Timoshenko,“Vibration Problems in Engineeringâ€, D.Van Nostrand, Inc., Prinston, NJ, 1937.
[8] S. S. Rao, “Vibration of Continuous Systemsâ€, John Wiley and Sons, Inc. New Jersey, 2007, 11-5.
[9] American Bureau of Shipping, “ABS Guidance Notes on Ship Vibrationâ€, p.37, 2014.
[10] Iwer Asmussen, Wolfgang Menzel, Holger Humm, “Ship vibration, Germanisher Lloydâ€, Hamburg, 2001.
[11] Vikipedia (Image Results), Science, vol.314, p. 1861, Dec. 22, 2006
[12] V.V. Lugovsky, “Dynamics of Seaâ€, Publishing House Shipbuilding, Leningrad, 1976.
[13] Waves in the Ocean - University of South Florida fcit.usf.edu/florida/teacher/science/mod2/resources/waves.pdf.
[14] G. Z. Forristall, “Wave crest distributions: Observations and second order theoryâ€. J. of Phys. Oceanography, 30, pp.1931-1943, 2000.
-
Downloads
-
How to Cite
Shulemovich, A. (2017). Revised dynamic characteristics of uniform beams with free - hinged and free - free end conditions. International Journal of Engineering & Technology, 6(2), 41-44. https://doi.org/10.14419/ijet.v6i2.7465Received date: 2017-03-12
Accepted date: 2017-04-24
Published date: 2017-05-17