The free bending vibrations of an orthotropic, composite base plate or panel reinforced by a central stiffening plate strip are considered. The orthotropic base plate and the dissimilar, orthotropic, central stiffening plate strip are bonded together with a very thin adhesive layer. The dynamic equations of the lower base plate and the upper stiffening strips are derived according to the 'Mindlin plate theory'. The governing system of partial differential equations is first reduced to a special set of first order ordinary differential equations. Following the elimination of the time variable and one of the space variables, the problem becomes a 'two-point boundary value problem'. Then, the governing system of differential equations are integrated by a 'modified version of the transfer matrix method'. The effects of the 'hard' and the 'soft' adhesive layers on the mode shapes and the natural frequencies of the composite system are investigated and presented. It was also shown that the natural frequencies of plate or panel system gradually increase at first for the increasing values of the 'bending cross stiffness ratio' of the base plate and the stiffening plate strip. Then, for certain values of the 'ratio', the natural frequencies experience a sudden sharp drop and again start going up gradually regardless of the boundary conditions. This unusual 'sudden drop phenomena' is observed for the 'hard' as well as for the 'soft' adhesive layer cases in the composite plate system. Some important conclusions in connection with the 'phenomena' are presented. (C) 2000 Elsevier Science Ltd. All rights reserved.