An original framework for triply-coupled bending-torsion dynamics of beams. (February 2021)

• Record Type: Journal Article
• Authors: Burlon, Andrea; Failla, Giuseppe
• Is Part Of: Thin-walled structures. Volume 159(2021)
• Publication Date: 2021-02
• Subjects: Triply-coupled bending-torsion -- Green's functions -- Frequency response functions -- Modal response functions -- Transversal stiffeners -- External supports -- External dampers; Thin-walled structures -- Periodicals; 690.1
• DOI: 10.1016/j.tws.2020.107317
• Languages: English
• ISSNs: 0263-8231

Abstract

Abstract: 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. Highlights: Triply-coupled bending-torsional dynamics of beams with asymmetric cross section is addressed. An original framework is introduced for bare beams and generalized to beams with attachments. Exact dynamic Green's functions and frequency response functions are obtained by a novel approach based on Laplace Transform. Appropriate orthogonality conditions are derived and used to build the exact modal responses. Solutions are derived in presence of proportional and non-proportional damping.