Free Bending Vibrations of Integrally-Stiffened and/or Stepped-Thickness Rectangular Plates or Panels With a Non-Central Plate Stiffener

The present study is primarily concerned with the “Free Bending Vibrations of Integrally-Stiffened and/or Stepped-Thickness Plates or Panels with a Non-Central Plate Stiffener”. The general theoretical formulation is based on the “Mindlin Plate Theory”. The plate elements of the system are considered to be made of dissimilar orthotropic materials with unequal thicknesses. The transverse shear deformations and the transverse and the rotary moments of inertia of plate elements are included in the analysis. The damping effects, however, are neglected. The dynamic equations of the orthotropic “Mindlin Plates” in combination with the stress resultant-displacement expressions are algebraically manipulated. They are eventually reduced to a set of the “Governing System of the First Order Ordinary Differential Equations” in the “state vectors” form. The resulting differential equations system is numerically integrated by making use of the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. The mode shapes with their dimensionless natural frequencies are presented for various support conditions in the “isotropic” Al-Alloy and in the “orthotropic” composite cases. Additionally, the effect of some of the important parameters such as (“Stiffener Position Ratio”, “Thickness Ratio”, “Stiffener Length (or Width) Ratio)” on the dimensionless natural frequencies are investigated and plotted. Based on the numerical results, some brief but important conclusions are presented.