In this study, the primary concern is the "Free Flexural (or Bending) Vibrations of Composite Mindlin Base Plates or Panels with Two Bonded Stiffening Plate Strips". The "Bonded and Stiffened Plate or Panel System" is composed of an "Orthotropic Mindlin Base Plate or Panel" reinforced by the two dissimilar, orthotropic "Stiffening Plate Strips" of unequal thicknesses adhesively bonded to the "Base Plate or Panel". The entire "System" is analyzed in terms of the "Mindlin Plate Theory" which

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... into account the transverse shear deformations and the transverse and rotary moments of inertia in all its plate elements. The very thin and in-between adhesive layers are considered to be linearly elastic, each with different material properties. The dynamic equations of each plate element and the stress resultant-displacement equations are combined together. Following some mathematical manipulations, the aforementioned equations are reduced to a new "Governing System of the First Order Ordinary Differential Equations" in "state vector" forms. These are numerically integrated by means of the "Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)". In the numerical solutions, the "Isotropic Al-Alloy" system and the "Orthotropic Composite" system are considered separately in terms of various sets of boundary conditions. The mode shapes and their natural frequencies are accurately computed up to the sixth mode. However, in the present paper, they are graphically presented only up to the fifth mode with the corresponding natural frequencies. Furthermore, the effects on the natural frequencies of some important parameters such as the "Stiffeners Length (or Width) Ratio" are studied and presented. Also, very significant differences in mode shapes caused by the "Hard" (or relatively "Stiff") and the "Soft" (or relatively "flexible") adhesive layers in the "Isotropic Al-Alloy" and the "Orthotropic Composite" systems are shown and presented for a few sets of the boundary conditions. Based on the numerical results obtained, some important conclusions are stated for engineering and design applications.