Numerical-perturbation technique for the transverse vibrations of highly prestressed plates

Under the usual assumptions of small strains with moderately large rotations, the problem of the transverse vibrations of highly prestressed nonuniform annular plates is reduced to the solution of the differential equation governing the transverse vibration of the corresponding prestressed membrane subject to modified boundary conditions that account for the effects of bending. The method of composite expansions is used to determine these modified boundary conditions. The agreement of the present solution or results with known exact solutions for simple geometries demonstrates the efficiency of this method when compared with other well-known numerical techniques.