Vibration Control of H-Shaped Planar Frames Based on the Classical Euler-Bernoulli and the Advanced Timoshenko Bending Theories

Abstract

Coupled bending and longitudinal vibrations in H-shaped planar frames are controlled from a wave standpoint, in which vibrations are described as waves traveling along uniform structural waveguides, and being reflected and transmitted at structural discontinuities. Active discontinuities are created using active control forces/moments both along structural elements and at structural joints to control vibration waves. The bending vibrations are modeled and controlled using the classical Euler-Bernoulli as well as the advanced Timoshenko theories. Numerical examples are presented. Comparisons are made between the results obtained using the classical Euler-Bernoulli model and the advanced Timoshenko model. Good agreements have been reached at low frequencies. However, discrepancies are significant at higher frequencies, typically when the transverse dimensions are not negligible with respect to the wavelength. This study addresses the importance of taking into account the effects of rotary inertia and shear distortion at high frequencies.