The fundamental modal response of elastically connected parallel Timoshenko beams

Abstract

We study the modal matrix differential equation of an elastically coupled double-beam Timoshenko system. Its general solution is determined by using the matrix basis generated by a fundamental matrix response. This later is found, through convolution, to be a perturbation of the uncoupled Timoshenko double-beam system. This approach allows to identify elements belonging to each beam and make use of knowledge already established for single beams. The fundamental matrix response as an initial value problem with impulsive conditions is split into the matrix response of a Timoshenko double-beam system and a forced response due to the elastic connection. Eigenanalysis is formulated in terms of the fundamental matrix response. Simulations were performed for classical and non-classical boundary conditions. Their mode shapes were compared with those of a single beam.