Buckling of an Arbitrary Number of Parallel Timoshenko Beamswith Intermediate Flexible Connections Under a CompressiveAxial Force

Buckling analyzing of a set of parallel Timoshenko beams that areconnected together by intermediate flexible connections is studied inthis article. In order to investigate the buckling, the parallel beams areunder an axial force. In this case, a suitable set of equations is createdthat are applicable to solve the problems of axial loading. The numberof beams and intermediate connections are arbitrary and are consideredas parameters n and m respectively. The existence of the intermediateconnections needs compatibility equations which create coupleddifferential equations along with the Timoshenko beams. The solvingmethod involves a change of variables to decouple the governingdifferential equations. The eigenvalues and the eigenfunctions areobtained adopting transfer matrix method. Natural frequencies of thebeams are obtained by increasing the axial force and different stiffnessof the connections. It is observed that by increasing the axial force, thenatural frequencies decrease and the first frequency of the beams equalszero at the critical buckling force and at this value of force, the bucklingis started. Then the values of the critical axial force are shown forincreasing the length of the beams and increasing the stiffness of theconnections.

Keywords:

Parallel TimoshenkoBeams , Intermediate Flexible Connections , Transfer Matrix Method , Axial Force , Critical Buckling Force