In-plane vibration and stability of shallow circular arches subjected to axial forces

Natural frequencies and buckling loads of a simply supported shallow circular arch with sufficiently sma.11d epth-to-radius of curvature ratio (H/R CC 1) subjected to initial axial tensile and/or compressive forces are analysed. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a one-dimensional higher-order arch theory for in-plane vibration problems of shallow circular arches is derived through Hamilton’s principle. Several sets of truncated approximate theories which can take into account the effects of both shear deformations with depth changes and rotary inertia are applied to solve the eigenvalue problems of an elastic arch. Convergence properties of the natural frequency and the buckling load of simply supported shallow circular arches are examined in detail. The present approximate theories can predict the natural frequencies and buckling loads of shallow circular arches with small length-todepth ratio L/H more accurately compared with previously published results.