The effect of boundary conditions on the lowest vibration modes of strongly inhomogeneous beams

Şahin, Onur

doi:10.2140/jomms.2019.14.569

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The effect of boundary conditions on the lowest vibration modes of strongly inhomogeneous beams

Onur Şahin

Vol. 14 (2019), No. 4, 569–585

DOI: 10.2140/jomms.2019.14.569

Abstract

This paper investigates the influence of the boundary conditions on the lowest vibration modes of strongly inhomogeneous beams. It is observed that the softer component of the composite beams asymptotically contributes to an almost rigid-body motion of the stiffer parts and gives rise to one or two nonzero eigenfrequencies contrary to a single beam with free end conditions. An asymptotic procedure is employed to derive the eigenfrequencies as well as the eigenforms in the case of global low frequency regime. The developed model is adapted for two and three-component beams with different end conditions. It is also shown that all eigenforms corresponding to the stiffer components of the beams perform almost rigid body motions. Comparisons of exact and approximate solutions are presented, demonstrating the validity of the proposed approach.

Keywords

composite beam, low frequency vibration, contrast, perturbation, rigid body motion

Milestones

Received: 18 July 2019

Revised: 13 September 2019

Accepted: 28 October 2019

Published: 13 December 2019

Authors

Onur Şahin
Department of Mathematics Giresun University Güre Campus Giresun Turkey

Vol. 14, No. 4, 2019

Onur Şahin

Abstract

Keywords

Milestones

Authors