An original framework for triply-coupled bending-torsion dynamics of beams

Triply-coupled bending-torsion in beams with asymmetric cross section is an interesting yet challenging problem in dynamics. In this study, a comprehensive framework is introduced to obtain the response in frequency and time domains under arbitrary loads, considering warping effects. First, a Laplace Transform approach provides the dynamic Green's functions of the beam, which can be used to obtain the frequency response to arbitrary loads by applying simple integration rules of the theory of generalized functions. Next, on deriving suitable orthogonality conditions for the undamped coupled bending-torsion modes, modal impulse and modal frequency response functions are obtained for any load. The solutions are derived under the assumption of proportional damping; they are exact and easy to implement. Finally, the proposed framework is formulated for beams with in-span transversal stiffeners, external supports and is generalized to non-proportional damping including the presence of in-span external dampers.