INSTABILITY OF ACCELERATED ELASTIC METAL PLATES

When subjected to rapid acceleration, a metal plate that is not perfec tly hat displays a type of Rayleigh-Taylor instability, which is affec ted by shear strength. We investigate the initial stage of this instab ility assuming that the deviation from flatness is small and the press ure producing the acceleration is moderate. Under these assumptions, t he plate can be modeled as elastic and incompressible, and the lineari zed form of the governing are valid. We derive a linear initial/bounda ry-value problem that models the flow and obtain analytical formulae f or the solutions. Our solutions exhibit vorticity inside the plate, an important feature caused by shear strength that was omitted in previo us solutions. The theoretical relationship between the acceleration an d the critical perturbation wave length, beyond which the flow is unst able, agrees quantitatively with results of numerical simulations and experiments.