The title problem is investigated, emphasizing two effects that are usually ignored in the literature. These are (i) nonlinear plate stiffness and (ii) mutual interaction between the plate and external and/or internal (cavity) air flow. The method of analysis employs modal expansions for the plate and cavity (air) motions, with the solution effected in the time (rather than the frequency) domain. The external flow pressure perturbations due to the plate motion are assumed to be described adequately by classical acoustic theory including convection effects. A discussion is given as to when the two effects will be important and a practical, numerical example is worked out to illustrate the method. © 1969, Acoustical Society of America. All rights reserved.