Exact solution of in-plane vibrations of circular arches with account taken of axial extension, transverse shear and rotatory inertia effects

Exact solution of free in-plane vibrations of circular arches of uniform cross-section is given by considering axial extension, transverse shear and rotatory inertia effects. In contrast with Kirchhoff's beam theory the restrictions of perpendicular cross-section and inextensible arc length are removed. The principal axes of the cross-section are assumed to coincide with the principal normal and binormal vectors of the centerline of the beam. A solution procedure is applied to obtain the fundamental matrix for various end conditions. Natural frequencies and mode shapes are given in figures and tables.