Abstract
The free bending vibrations of beams with a concentrated mass subjected to axial forces caused by axial acceleration are analyzed by the Galerkin method, introducing the mode shape functions which are the sum of the products of the finite power series and the trigonometrical function. This analytical method makes it easy to construct the equations of motion in each boundary condition only by exchanging the coefficients of the finite power series. Numerical calculations are carried out under four sets of boundary conditions combined with simply supported and clamped edges. The natural frequencies and the corresponding modes of vibration are determined under both various locations of the concentrated mass and axial forces. it is found that the transverse inertia force and the axial force, due to the concentrated mass, have significant effects on the change of the natural frequencies for beams. Furthermore the distinction of boundary conditions gives predominant influence to the variation of natural frequencies.
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