FORCED VIBRATIONS OF TRIPLY COUPLED, PERIODICALLY AND ELASTICALLY SUPPORTED, FINITE, OPEN-SECTION CHANNELS

An exact analytical method is presented for the analysis of forced vibrations of uniform, open-section, single- and multi-bay periodic channels. The centre of gravity and the shear centre of the channel cross-sections do not coincide, and hence the flexural vibrations in two mutually perpendicular directions and the torsional vibrations are all coupled. The ends of the channels and the periodic intermediate supports are modelled with springs having finite flexural and torsional stiffnesses. Single-point force excitation has been considered throughout the study, although the developed method is also capable of dealing with multi-point excitation. The channels are assumed to be of Euler–Bernoulli type beams. The study also takes the effects of cross-sectional warping into consideration. The developed method is suitable for structurally damped analysis and in addition to yielding forced vibration characteristics; it also straightforwardly reveals the free vibration properties like the mode shapes.