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Free flexural (or bending) vibration analysis of certain of stiffened composite plates or panels in flight vehicle structures

Javanshir Habestan, Jaber
In this study, the “Free Flexural (or Bending) Vibrations of Stiffened Plates or Panels” are investigated in detail. Two different Groups of “Stiffened Plates” will be considered. In the first group, the “Type 4” and the “Type 6” of “Group I” of the “Integrally-Stiffened and/or Stepped-Thickness Plate or Panel Systems” are theoretically analyzed and numerically solved by making use of the “Mindlin Plate Theory”. Here, the natural frequencies and the corresponding mode shapes, up to the sixth mode, are obtained for each “Dynamic System”. Some important parametric studies are also presented for each case. In the second group, the “Class 2” and the “Class 3” of the “Bonded and Stiffened Plate or Panel Systems” are also analyzed and solved in terms of the natural frequencies with their corresponding mode shapes. In this case, the “Plate Assembly” is constructed by bonding “Stiffening Plate Strips” to a “Base Plate or Panel” by dissimilar relatively thin adhesive layers. This is done with the purpose of reinforcing the “Base Plate or Panel” by these “Stiffening Strips” in the appropriate locations, so that the “Base Plate or Panel” will exhibit satisfactory dynamic response. The forementioned “Bonded and Stiffened Systems” may also be used to repair a damaged (or rather cracked) “Base Plate or Panel”. Here in the analysis, the “Base Plate or Panel”, the “Stiffening Plate Strips” as well as the in- between “adhesive layers” are assumed to be linearly elastic continua. They are assumed to be dissimilar “Orthotropic Mindlin Plates”. Therefore, the effects of shear deformations and rotary moments of inertia are considered in the theoretical formulation. In each case of the “Group I” and “Group II” problems, the “Governing System of Dynamic Equations” for every problem is reduced to the “First Order Ordinary Differential Equations”. In other words the “Free Vibrations Problem”, in both cases, is an “Initial and Boundary Value Problem” is reduced to a “Two- Point or Multi-Point Boundary Value Problem” by using the present “Solution Technique”. For this purpose, these “Governing Equations” are expressed in “compact forms” or “state vector” forms. These equations are numerically integrated by the so-called “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. In the numerical results, the mode shapes together with their corresponding non-dimensional natural frequencies are presented up to the sixth mode and for various sets of “Boundary Conditions” for each structural “System”. The effects of several important parameters on the natural frequencies of the aforementioned “Systems” are also investigated and are graphically presented for each “Stiffened and Stiffened and Bonded Plate or Panel System”. Additionally, in the case of the “Bonded and Stiffened System”, the significant effects of the “adhesive material properties” (i.e. the “Hard” adhesive and the “Soft” adhesive cases) on the dynamic response of the “plate assembly” are also presented.