Free Flexural (or Bending) Vibrations of Composite Mindlin Base Plates or Panels with Two Bonded Stiffening Plate Strips

Abstract

In this study, the primary concern is the Free Flexural (or Bending) Vibrations of Plates or Panels with Two Plate Strips. The Bonded and Stiffened Plate or is composed of an Orthotropic Plate or Panel reinforced by the two dissimilar, orthotropic Stiffening Plate Strips of unequal thicknesses adhesively bonded to the Base Plate or Panel. The entire is analyzed in terms of the Mindlin Plate Theory which takes into account the transverse shear deformations and the transverse and rotary moments of inertia in all its plate elements. The very thin and in+between adhesive layers are considered to b e linearly elastic, each with different material properties. The dynamic equations of each plate element and the stress resultant+displacement equations are combined together. Following some mathematical manipulations, the aforementioned equations are reduced to a new Governing System of the First Order Ordinary Differential Equations in state vector forms. These are numerically integrated by means of the Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials). In the numerical solutions, the Isotropic Al+Alloy system and the Orthotropic Composite system are considered separately in terms of various sets of boundary conditions. The mode shapes and their natural frequencies are accurately computed up to the sixth mode. However, in the present paper, they are graphically presented only up to the fifth mode with the corresponding natural frequencies. Furthermore, the effects on the natural frequencies of some important parameters such as the Stiffeners Length (or Width) Ratio are studied and presented. Also, very significant differences in mode shapes caused by the Hard (or relatively Stiff) and the Soft (or relatively flexible) adhesive layers in the Isotropic Al+Alloy and the Orthotropic Composite systems are shown and presented for a few sets of the boundary conditions. Based on the numerical results obtained, some important conclusions are stated for engineering and design applications.