Dynamic instability of a disk forced by a pulse of short duration

A dynamic analysis is presented for circumferential buckling of a disk induced by transient axisymmetric flexural deformation from a pulse of short duration. A perturbation solution is adopted in solving the coupled non-linear stability equations, utilizing the asymmetric dynamic eigenfunctions of the disk as trial functions in the Galerkin procedure. Static buckling is treated first to demonstrate the utility of the stability analysis and evaluate how critical stress and circumferential wave number of the buckling mode depend on disk radius and thickness. In the dynamic case, transient response is the evolution in time of an axisymmetric deformation shape bounded by the shear wave front. Dynamic stability from induced inplane stresses of asymmetric perturbations is characterized by their divergence in time. The dynamic buckling mode is that mode growing fastest over a fixed period of time after impact