Vibration and buckling of a multiple-Timoshenko beam system joined by intermediate elastic connections under compressive axial loading

Free vibration and buckling of a set of parallel Timoshenko beams joined by intermediate flexible connections under axial loading are assessed in this paper. The numbers of beams and intermediate connections are arbitrary. Through axial loading, a new set of equations is extracted, applicable in solving the axial loading problems. The existence of the intermediate connections and the related compatibility equations allow for the introduction of coupled partial differential equations. The solution involves a change of variables to uncouple the governing differential equations. The natural frequencies and mode shapes are calculated through the transfer matrix method. By presenting an appropriate equation, it is observed that the general formulation studied here, regarding the separated flexible connections, can easily cover the issue of parallel beams joined by Winkler elastic layers in a continuous manner presented in the literature. The effects of different parameters such as the number of beams, number and stiffness of elastic connections and axial loading are assessed on the natural frequencies and the critical buckling force.