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Free flexural( or bending) vibrations analysis of doubly stiffened, composite, orthotropic base plates and panels (in aero-structural systems)

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2003
Çil, Kürşad
In this Thesis, the problem of the أFree Vibrations Analysis of Doubly Stiffened Composite, Orthotropic and/or Isotropic, Base Plates or Panels (with Orthotropic Stiffening Plate Strips)ؤ is investigated. The composite plate or panel system is made of an أOrthotropic and/or Isotropic Base Plateؤ stiffened or reinforced by adhesively bonded أUpper and Lower Orthotropic Stiffening Plate Stripsؤ. The plates are assumed to be the أMindlin Platesؤ connected by relatively very thin adhesive layers. The general problem under study is considered in terms of three problems, namely أMain PROBLEM Iؤ, أMain PROBLEM IIؤ and أMain PROBLEM IIIؤ. The theoretical formulation of the أMain PROBLEMSؤ is based on a أFirst Order Shear Deformation Plate Theory (FSDPT)ؤ that is, in this case, the أMindlin Plate Theoryؤ. The entire composite system is assumed to have simple supports along the two opposite edges so that the أClassical Levy̕s Solutionsؤ can be applied in that direction. Thus, the transverse shear deformations and the rotary moments of inertia of plates are included in the formulation. The very thin, yet elastic deformable adhesive layers are considered as continua with transverse normal and shear stresses. The damping effects in the plates and the adhesive layers are neglected. The sets of the systems of equations of the أMindlin Plate Theoryؤ are reduced to a set of the أGoverning System of First Order Ordinary Differential Equationsؤ in the أstate vectorؤ form. The sets of the أGoverning Systemؤ for each أMain PROBLEMؤ constitute a أTwo-Point Boundary Value Problemؤ in the y-direction which is taken along the length of the plates. Then, the system is solved by the أModified Transfer Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials)ؤ which is a relatively semi-analytical and numerical technique. The numerical results and important parametric studies