Variable angle tow-steered curvilinear fibres-based rotating arbitrarily layered composite beams- a coupled vibration of chordwise-flapwise-torsional motions by higher-order beam theory

Abstract

In the present work, variable angle tow-steered curvilinear fibres-based straight composite rotating beam is studied for its coupled vibrational behaviours from different beam planes by a higher-order beam formulation satisfying plane stress situation and combining with finite element methodology. The structural theory is extended to include all the vibrational motions including chord- and flap-wise motions, axial and torsional vibrations of beam. The centrifugal force stiffening and gyroscopic effects stemming from rotational motions are taken into the formulation. The generic differential equations of equilibrium for the proposed structural theory are evolved adopting virtual dynamic work, Hamilton’s principle and a suitable C1 continuity based elemental equations are obtained. The newly constructed finite element formulation is tested for solved problems that are known in the literature. Based on in-depth analysis, vibration features of curvilinear fibre-based rotating generally layered composite beam including coupled dynamic motions in terms of vibrational modes and their frequencies pertaining to chord- and flap-wise, axial, torsional motions are detailed presuming variable angles along the curvilinear fibre path at the centre and layer edge, short and long beams, hub-radius, beam cross-section, and high rotational speed effects.