FREE VIBRATIONS OF ARBITRARILY-SHAPED BEAMS

摘要

An approach is proposed to examine the free vibration of an arbitrarily-shaped beam. The analysis begins with the separation of the beam in terms of a prismatic beam(main beam) and the remaining partstsub-beams). Then, the beam is regarded as a main beam connected by several sub -beams. Lagrange's equations are used to develop a characteristic equation by applying the mode shapes of the main beam as assumed deflection curves of the arbitrarily-shaped beam(combined beam). The form of resulting equation is not commonly used in structural dynamics. However, the equation can be transformed into the form of a conventional characteristic equation with coupling terms between the main beam and sub-beams. This equation provides insight into the resonance characteristics of an arbitrarily-shaped beam.