Analytical and experimental investigation of bend-twist coupling on the vibrational response of multi-layered stepped composite beams

This paper investigates the bend-twist coupling analysis of multi-layered stepped generally orthotropic composite beams subjected to mixed end-of-beam and mid-span supports. Specifically, an analytical closed-form model was developed based on first-order shear deformation theory (FSDT), which discretizes the domain into elements based on the step change of geometry, laminate configuration, or mid-span boundary supports. Hamilton's principle was used to derive the governing equations within each element and connection and boundary equations. The state-Space approach was then utilized to provide an analytical solution. Moreover, an experimental investigation was conducted to validate the mode shapes and natural frequencies of the beam subjected to several mixed boundary conditions. The results are also validated with the literature and a finite element model developed using ANSYS. Comparisons demonstrate the reliability and accuracy of the analytical model.