This study is mainly concerned with a “General Approach” to the “Theoretical Analysis and the Solution of the Free Vibrations Response of Integrally-Stiffened and/or Stepped-Thickness Plates or Panels with Two or more Integral Plate Stiffeners”. In general, the “Stiffened System” (regardless of the number of “Plate Stiffeners”) is considered to be composed of dissimilar “Orthotropic Mindlin Plates” with unequal thicknesses. The dynamic governing equations of the individual plate elements of the “System” and the stress resultant-displacement expressions are combined and algebraically manipulated. These operations lead to a new “Governing System of the First Order Ordinary Differential Equations” in “state vector” forms. The new “Governing System of Equations” facilitates the direct application of the present method of solution, namely, the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. As shown in the present study, the “MTMM” is sufficiently general to handle the “Free Vibrations Response” of the “Stiffened System” (with, at least, one or up to three or four “Integral Plate Stiffeners”). The present analysis and the method of solution are applied to the typical “Stiffened Plate or Panel System with Two Integral Plate Stiffeners”. The mode shapes with their natural frequencies are presented for the “Isotropic Al-Alloy” and “Orthotropic Composite” cases and for several sets of support conditions. As an additional example, the case of the “Stiffened Plate or Panel System with Three Integral Plate Stiffeners” is also considered and is shown in terms of the mode shapes and their natural frequencies for one set of the boundary conditions. Also, some parametric studies of the natural frequencies versus the “Stiffener Thickness Ratio” and the “Stiffener Length (or Width) Ratio” are investigated and are graphically presented.
Numerical and Experimental Approach for Identifying Elastic Parameters in Sandwich Plates