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- W1993695512 abstract "This paper describes the transverse vibration of an Euler-Bernoulli vertical uniform cantilever, with account taken of the effect of self-weight. It is shown that the natural frequencies depend not only on the conventional geometric and/or natural boundary conditions but also on which of the two boundaries is axially restrained. This property results in the classification of vertical cantilevers into two types: they are cantilevers axially restrained at the “clamped” end and referred to as “clamped-free” (CL-FR) beams and those axialy restrained at the “free” end and referred to as “free-clamped” (FR-CL) beams. The transverse vibration of CL-FR beams has been investigated in the past. The published results are based on Galerkin, Rayleigh-Ritz and other numerical methods. In this paper CL-FR and FR-CL beams are considered. The solution to the mode shape differential equation is expressed as the superposition of four independent functions. The exact frequency equations are then derived and solved numerically for the first three natural frequencies. “Standing” and “hanging” positions are considered. Buckling under self-weight is investigated as the limiting case at which the natural frequency is zero. All results are presented in tabular form to preserve the accuracy of the results." @default.
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- W1993695512 date "1991-04-01" @default.
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- W1993695512 title "Vibration of a vertical cantilever with and without axial freedom at clamped end" @default.
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- W1993695512 doi "https://doi.org/10.1016/0022-460x(91)90758-c" @default.
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