In the paper an approachto determination of the major (first, second, third …) natural frequencies and modal vectors is proposed. A differential transformations method (DTM) is applied, for which the partial differential equations which describe the free vibration of the beam are transformed to homogeneous system of algebraic equations that define the modes of vibrations. Hence analytical expressions for computation are derived. For verification of the theoretical results numerical examples for the same cantilever beam are presented. In case of different angular velocities the time histories of the amplitudes of vibrations, respectively, of the frequencies, show the significant influence of the centrifugal accelerations, as well as coincidence with the analytical computations.
Key words: rotating cantilever beam, modes of vibrations, centrifugal accelerations
Topic: ENGINEERING SCIENCES