Abstract

The analysis of the free vibration of rectangular sandwich plates with viscoelastic cores is purposed. The analysis focuses on evaluating two displacement theories of sandwich plates for various geometric and material properties and boundary conditions. The first theory was developed for the vibratory bending of unsymmetrical sandwich plates by Rao and Nakra1. The theory is a layerwise theory that models the displacement of the face layers with classic plate theory (i.e. normals to the midplane remain normal to the midplane and undeformed after deformation of the plate) and the continuity of the displacements at the interfaces between the face layers and the core used to derive the displacements of the core. The core is assumed to be in a state of pure transverse shear and in-plane strains are considered negligible. This theory is not only restricted by the assumed displacement field, but is specific to a sandwich plate composed of three isotropic layers. The second theory is a third order plate theory that was developed for composite plates that required the inclusion of transverse strains by Reddy2. The theory assumes a cubic displacement in terms of the thickness resulting in quadratic transverse shear stresses that vanish at the free surfaces of the plate. The advantage of this displacement field is that it does not require shear correction factors which are dependent on the specific plate materials and boundary conditions like first order plate theories (e.g. Mindlin plates). The theory is an equivalent single layer theory that integrates the displacement of the plate over the thickness, resulting in generalized stiffnesses that apply to a general plate composed of monoclinic layers. Both theories are analyzed and compared to finite element models generated in ANSYS for simply supported boundary conditions. The purpose of the simply supported analysis is to determine the characteristics of each theory with respect to variations of the geometric and material properties of the sandwich plate. Damping is introduced to the sandwich plate using the linear elastic-viscoelastic correspondence principle for harmonic analysis and loss factors are calculated for several specific geometries of the simply supported plates. The cantilever plate is also examined for both theories using the semi-analytical superposition method with a state space approach. The closed form superposition method developed by Gorman3 for classic plate theory is extended to both sandwich plate theories and a new semi-numerical approach is taken. The only numerical error introduced in the analysis is the calculation of the eigenvalues and corresponding eigenvectors for the state space solutions that are superimposed to solve for the cantilever boundary conditions. Fourier series solutions are obtained for the mode shapes such that each term of the series exactly satisfies the prescribed boundary conditions. The approach is directly compared to finite element models generated in ANSYS for the cantilever plate. 1 Rao, Y.V.K.S. and Nakra, B.C. 1973 Archive of Mechanics 25, 213-225. Theory of vibratory bending of unsymmetrical sandwich plates. 2 Reddy, J.N. 1984 Journal of Applied Mechanics 45, 745-752. A simple higher-order theory for laminated composite plates. 3 Gorman, D. J. 1982 Free Vibration Analysis of Rectangular Plates New York: Elsevier

Publication Date

2005

Document Type

Thesis

Student Type

Graduate

Degree Name

Mechanical Engineering (MS)

Department, Program, or Center

Mechanical Engineering (KGCOE)

Advisor

Hany Ghoneim

Advisor/Committee Member

Josef Török

Advisor/Committee Member

Agamemnon Crassidis

Comments

I, Devlin Hayduke, prefer to be contacted each time a request for reproduction is made.

Campus

RIT – Main Campus

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