Vibrações transversais de viga comprimida apoiada sobre sistema massa-mola

Abstract

The principal problem undertaken is this work is the determination of the natural frequencies of lateral vibrations of a beam with axial load, wich carries a concentrated mass and spring located at any point along the length of the beam. The case of a beam with two concentrated masses and springs is also analysed. Exact soluctions for a beam with concentratedmass by classical methods was found by Karman (5) for a simply supported beam with concentrated mass at its mid-point and by Prescott (6) for a cantilever beam with concentrated mass at its free end. The extension of the solutions to include the efect of a spring can be made by classical methods only for the special cases mentioned. Aproximate solutions for the lowest natural frequency of a beam, mass, and spring system may be obtained by the Rayleigh-Ritz (4,8) energy methods but it is not always possible to determine the degree of aproximation. The method adopted makes use of a series expansion in terms of the set of orthogonal functions associated with the normal modes of vibration of a beam. Such a method was used for the particular case of an axially unloaded cantilever beam with mass and spring by Young (1).