Drgania własne belek z uwzględnieniem wpływu ścinania

The paper presents a new model of tranverse vibrations of uniform beams. Basing on the assumptions concerning the cross-sectional deformation of the beam, the motion equations are presented; a particular case of these equations are the equations given by Timoshenko. Under the assumption that the external loads acting upon the beam produce rotation and warping of its cross-sections, the components of displacement are given by (10). Using the generalized equations of a slender body (15)-(18), the equations of motion (33) for the considered model of the beam have been found as well as the expressions describing the internal forces (34) and external loads (35). Calculation results of eigenfrequencies for two special cases viz. the cantilever beam (Fig. 3) and the simply supported beam (Fig. 4, 5; Table 1, 2) have been presented.