The problem of the “Free Flexural Vibrations of Bonded and Centrally Doubly Stiffened Composite Orthotropic Base Plates or Panels” is formulated and investigated. The composite plate or panel system is made up of an orthtropic base plate reinforced or doubly stiffened by the upper and lower stiffening orthotropic plate strips. The stiffening plate strips are at the mid-center and are adhesively bonded to the base plate. The base plate and the stiffening plate strips are considered as dissimilar orthotropic Mindlin plates. Thus, the analysis is based on a “First Order Shear Deformation Plate Theory (FSDPT)” of Mindlin type. In the very thin, linearly elastic adhesive layers, the transverse normal and shear stresses are included. The sets of the dynamic equations and other equations of plates and adhesive layers are finally reduced to a “Governing System of the First Order Ordinary Differential Equations.” Then, this system is integrated by means of the “Modified Transfer Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials).” The mode shapes and the associated natural frequencies are calculated and some parametric studies are presented. Also, the influences of the “hard” and the “soft” adhesive layers on the natural frequencies and the mode shapes are shown.

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