Analysis of Rotatory Inertia and Shear Deformation on Transverse Vibration of Beams
Anderson Soares1; Simone dos Santos Hoefel1
1 Universidade Federal do Piauí
doi:10.20906/CPS/CON-2016-1101
Resumo
In the classical Bernoulli-Euler theory flexural vibrations of beam, the effect of rotatory inertia and shear are neglected. However, the equations obtained on these assumptions are inadequate for short and thin-webbed beams and for beams where higher modes are required, considerable errors may be incurred by use of equations. When a beam is subjected to lateral vibration so that depth of the beam is a significant proportion of the distance between two adjacent nodes, rotatory inertia of beam and transverse deformation arising from the severe contortions of the beam during vibration make significant contributions to the lateral deflection. Therefore rotatory inertia and shear effects must be taken into account in the and analysis of high-frequency vibration of all beams, and in all analyses of deep beams. In this work, the effect of rotatory inertia and transverse-shear deformation on beams are introduced and analysed. Frequency equation for each case are developed in terms of dimensionless parameters of rotatory and shear. Numerical examples presented in literature are re-examined.
Palavras-chave: beam theory; critical frequency; dispersion relation; rotatory inertia; shear deformation