Transverse Vibrations Of Non Uniform Free Free Beams

Download or read book Transverse Vibrations of Non-uniform, Free-free Beams written by William F. Bozich and published by . This book was released on 1962 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transverse vibrations in one plane of a non-uniform, free-free beam are considered, which include the effects of rotary inertia, shear deflection, and a constant axial acceleration, which is provided by an axial thrust at one end of the beam. The equations of motion are derived. An energy formulation for approximate solution of the natural frequencies, and a matrix formulation for the approximate solution of the natural frequencies and mode shapes are derived, which include these effects. Both formulations are altered to give the critical axial acceleration for buckling. It is shown that rotary inertia, shear deflection, and axial acceleration all reduce the natural frequency of vibration, however the first two effects are important in short beams, while the latter effect is important in long slender beams.