In-plane transient responses of arch with variable curvature using dynamic stiffness method

A procedure combining the dynamic stiffness method with the Laplace transform is proposed to obtain accurate transient responses of an arch with variable curvature. The dynamic stiffness matrix and equivalent nodal force vector for an arch with variable curvature subjected to distributed loading are explicitly formulated based on a series solution. The effects of shear deformation, rotary inertia, and damping are considered. As examples, the accurate transient responses of a parabolic and a semielliptic arch subjected to either point loading or base excitation are given. The effects of the shapes of the arches and the phase-shift in the multiple input for base excitation are also discussed.