Transverse vibration and buckling of a cantilevered beam with tip body under axial acceleration

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The transverse vibration and buckling of a cantilevered beam subject to constant axial acceleration with rigid tip body is investigated. Two classes of tip bodies are recognized: those with mass centers located along the beam tip tangent line, and those with mass centers having an arbitrary offset with respect to the beam attachment point (but not lying along the beam tip tangent line). For the former class, the critical buckling loads and shapes as well as the natural frequencies and mode shapes are determined analytically. It is shown that for the latter class of tip bodies, steady state solutions exist except for certain critical values of acceleration. The free vibration problem for this later class of tip bodies is addressed. Numerical comparisons are made between the exact analysis and a Rayleigh-Ritz procedure for the first three natural frequencies for values of base acceleration between zero and the first critical buckling value.