The second harmonic and the validity of Duffing’s equation for vibration of beams with large displacements

Most analytical and numerical investigations on the transverse vibration of beams with large displacements only find odd harmonics in the response. However, experimental research indicates that the second harmonic is also present in the response and in this paper an explanation for this is sought. Two possibilities are explored. First, the in-plane inertia is not neglected and, therefore, the equations of motion have quadratic and cubic non-linearities, i.e., they are not equations of Duffing type. Secondly, small perturbations, characteristic of experimental work, are included in the excitation and the ensuing vibration is analysed.