DYNAMIC ANALYSIS OF CONTINUOUS PLANE TRUSSES WITH EQUIDISTANT SUPPORTS

The natural and forced vibrations of a continuous Warren truss resting on equidistant roller supports are studied. In the analyses, the longitudinal inertial forces are neglected in the equation of motion and the mass of the truss is replaced by two sets of lumped masses at the nodes. In the forced vibration case, the truss is subjected to transverse harmonic loads acting at the nodes. The truss can be considered as an equivalent system with cyclic bi-periodicity: periodicities due to the repetitive units of the truss and the supports respectively. Therefore, the governing equation for such a system can be uncoupled by applying U-transformation twice to form a set of single-degree-of-freedom equations. Such equations can be used to solve for the natural frequencies of the trusses or their responses due to external excitations. Typical Warren trusses are taken as examples to demonstrate the advantages of the proposed method and the accuracy that can be achieved. The response of a truss with six substructures and four supports with a harmonic load acting at the centre node is investigated.