Variable angle tow-steered fibres based rotating composite beam with rotary oscillations – Parametric excitation/instability analysis

Abstract

This study is concerned with the stability analysis for various vibrational motions of tow-steered variable angle fibres based composite rotating beam with time varying speed. The formulation combines a higher order theory introducing sine function along with finite element methodology. It satisfies the plane stress condition in width direction of beam. The displacement kinematics are generic in the sense it includes various possible vibrational motions like chord and flap wise motions, torsional and axial vibration behaviours. The equilibrium equations for the proposed problem evolved adopting virtual dynamic work are then transformed into the equations of Mathieu-Hill type considering time varying harmonic rotational speed. Using Bolotin’s procedure coupled with C1 continuity-based beam element, the parametric resonance zones along with boundary limits are numerically evaluated. The eigenvalue type of solution methodology applied for the detailed study is validated for accuracy and computational efficiency against the time domain dynamic response analysis. Based on in-depth analysis, dynamic instability characteristics in terms of resonance range and origin of instability of composite beam subjected to the chord and flap wise, torsional and axial motions are studied considering curvilinear fibre path angles, beam cross section, hub radius, thickness ratio and mean rotary speed.