On triply coupled vibrations of axially loaded thin-walled composite beams

Free vibration of axially loaded thin-walled composite beams with arbitrary lay-ups is presented. This model is based on the classical lamination theory, and accounts for all the structural coupling coming from material anisotropy. Equations of motion for flexural–torsional coupled vibration are derived from the Hamilton’s principle. The resulting coupling is referred to as triply coupled vibrations. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results are obtained for thin-walled composite beams to investigate the effects of axial force, fiber orientation and modulus ratio on the natural frequencies, load–frequency interaction curves and corresponding vibration mode shapes.