VIBRATIONS OF OPEN-SECTION CHANNELS: A COUPLED FLEXURAL AND TORSIONAL WAVE ANALYSIS

Abstract An exact analytical method is presented for the analysis of forced vibrations of uniform, open-section channels. The centroid and the shear center of the channel cross-sections considered do not coincide; hence the flexural and the torsional vibrations are coupled. In the context of this study, the type of any existing coupling is defined in terms of the independent motions which are coupled through mass and/or stiffness terms. Hence, if the flexural vibrations in one direction are coupled with the torsional vibrations, the resulting coupling is called double-coupling. On the other hand, if the flexural vibrations in two mutually perpendicular directions and the torsional vibrations are all coupled, the resulting coupling is referred to as triple-coupling. The study also takes the effects of cross-sectional warping into consideration but, since it is derived from torsional characteristics, the warping is not treated as an independent motion. Wherever necessary, the admission of warping is characterized by the inclusion of warping constraint. The current work uses the wave propagation approach in constructing the analytical model. Single-point force excitation has been considered throughout and the channels are assumed to be of Euler–Bernoulli beam type. Both double- and triple-coupling analyses are performed. The coupled wavenumbers, various frequency response curves and the mode shapes are presented for undamped and structurally damped channels.