The free and forced transverse vibrations of a class of non-uniform beams, which includes as special cases the wedge and cone, are considered. Receptances, frequency equations, mode shapes and natural frequencies are presented for simple end conditions.
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References
1.
TimoshenkoS.Vibration problems in engineering3rd edition, 1955, 324 (D. Van Nostrand, New York).
2.
BishopR. E. D.JohnsonD. C.The mechanics of vibration1960, chapter 7 (Cambridge University Press).
3.
KirchhoffG.Über die Transversalschwingungen eines Stabes von veränderlichem Querschnitt, Gesammelte Abhandlungen1882, 339 (J. A. Barth, Leipzig). Also Monatsbericht der Akad. d. Wiss. zu Berlin 1879 2 (October).
4.
WardP. F.‘The transverse vibrations of a rod of varying cross-section’, Phil. Mag.191325 (Series 6), 85.
5.
WrinchD. M.‘On the lateral vibration of bars of variable cross-section’, Phil. Mag.192346 (Series 6), 273.
6.
MononobeN.‘Die Eigenschwingungen eingespannter Stäbe von veränderlichen Querschnitt’, Z. angew. Math. Mech.19211, 444.
7.
ConwayH. D.DubilJ. F.‘Vibration frequencies of truncated-cone and wedge beams’, J. appl. Mech., Trans. Am. Soc. mech. Engrs196587 (3), 932.
