Coupled axial and flexural vibration of 1-D members

The method of characteristics is used to model vibrations of one-dimensional members in the presence of coupling between axial and flexural waves. Only small deflections are considered and so the couple F_xδ_y is large only when the axial force F_x is large. Alternative numerical schemes are presented for the integration of terms describing coupling and a suitable explicit scheme is identified. The analysis is used to illustrate the influence of axial loads on frequencies and amplitudes of lateral oscillations of cantilever structures. Strong parametric behaviour is reproduced for a single-storey shear structure, including unstable resonance at double the linear natural frequency.