The problem of the "Free Transverse Vibrations of Orthotropic Composite Mindlin Plates or Panels with a Non-Centrally Bonded Symmetric Lap Joint (or Symmetric Doubler Joint)" is theoretically analyzed and solved with some numerical results. The "Bonded Joint" system is composed of two dissimilar, orthotropic plate "adherends" non-centrally bonded and connected by a dissimilar, orthotropic "doubler" plate through a very thin and elastic adhesive layer. The "adherends" and the single "doubler" are taken into account as the "Mindlin Plates" with the transverse shear deformations and the transverse and the rotary moments of inertia. The adhesive layer is considered as a linearly elastic continuum with the transverse normal and shear stresses. The damping effects are neglected. The dynamic equations of the plate "adherends", the "doubler" plate and the adhesive layer in combination with the stress resultant-displacement expressions, after some algebraic manipulations, are finally reduced to a set of the "Governing System of the First Order Ordinary Differential Equations" in matrix form in terms of the "state vectors" of the problem. The aforementioned set of the "Governing Equations" is integrated by means of the "Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)". Several mode shapes with their corresponding natural frequencies are presented for the "hard" and the "soft" adhesive cases. It was found that there are significant differences in mode shapes and natural frequencies corresponding to the "hard" and the "soft" adhesive cases. Additionally, some parametric studies such as the effects of the "Bonded Joint Length Ratio" and the "Bonded Joint Position Ratio" on the natural frequencies are included in this first study.

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