"Free Vibrations of Centrally Bonded Symmetric Lap Joint (or Symmetric Doubler Joint) With a Gap in Mindlin Plates or Panels"

Abstract

*† In this study, the “Free Flexural Vibrations of Composite Mindlin Plates or Panels with a Centrally Bonded Symmetric Lap Joint (or Symmetric Doubler Joint) with a Gap” is investigated in some detail. The dissimilar, orthotropic, plate “adherends” are centrally joined by means of a dissimilar, orthotropic, symmetric “doubler” plate and the in-between adhesive layer discontinued in the “Gap” area. The “adherends” and the “doubler” are considered as the “Mindlin Plates” with the transverse shear deformations and the transverse and rotary moments of inertia. The very thin adhesive layer is linearly elastic continuum with the transverse normal and shear stresses. The dynamic equations of the “adherends”, and the “doubler” and the adhesive layer, after some combinations and manipulations, are finally reduced to a set of the “Governing System of the First Order Ordinary Differential Equations” in terms of the “state vectors” of the problem. Aforementioned system of equations is numerically integrated by means of the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. Several very interesting and quite different mode shapes with their natural frequencies corresponding to the “hard” and the “soft” adhesive cases are presented. The mode shapes (and the corresponding natural frequencies) are greatly influenced by the elastic constants of the adhesive layer. Also, some parametric studies showing the effects of the “Doubler Length Ratio” and the “Gap Length Ratio” on the natural frequencies are included in the present study .