Out-of-plane instability and vibrations of a flexible
circular arch under a moving load
X.W. Zhao & G.H.M. van der Heijden
Flexible lightweight arched structures are finding increasing use as
components in smart engineering applications. Such structures are prone to
various types of instability under moving transverse loads. Here we study
deformation and vibration of a hinged circular arch under a uniformly moving
point load using geometrically-exact rod theory to allow for large pre- and
post-buckling deformations. We first consider the quasi-statics problem,
without inertia. We find that for arches with relatively large opening angle
(~ 160°) a sufficiently large traversing load will induce an out-of-plane
flopping instability, instead of the in-plane collapse (snap through) that
dominates failure of arches with smaller opening angle. In a subsequent
dynamics study, with full account of inertia, we then explore the effect of
the speed of the load on this lateral buckling. We find speed to have a
delaying (or even suppressing) effect on the onset of three-dimensional
bending-torsional vibrations and instability. Based on numerical
computations we propose a power law describing this effect. Our results
highlight the role of inertia in the onset of elastic instability.
keywords: circular arch, out-of-plane buckling, large deformation, Cosserat
rod, moving load, generalised-alpha method, delay effect
Int. J. Struct. Stab. Dyn., 2550049 (2025)