Date of Award

Spring 1983

Document Type

Thesis

Department

Mechanical & Aerospace Engineering

Program/Concentration

Engineering Mechanics

Committee Director

Chuh Mei

Committee Member

Earl A. Thornton

Committee Member

J. Mark Dorrepaal

Call Number for Print

Special Collections; LD4331.E57S53

Abstract

A finite element formulation is presented for analyzing large amplitude free flexural vibrations of symmetrically laminated composite plates of arbitrary shape. Linear and nonlinear fundamental frequencies are determined from the analysis. The laminates are made of multiple generally or specially orthotropic layers and symmetrically disposed about the middle surface, hence there is no coupling between bending and extension. Linearized stiffness equations of motion governing large amplitude oscillations of laminates, linear element stiffness matrix, quasi-linear geometrical element stiffness matrix, and solution procedures are presented. The linearized geometrical stiffness matrix for a 18 degrees-of-freedom high precision triangular anisotropic plate element is evaluated by using a seven-point numerical integration. Linear and nonlinear fundamental frequencies for square, triangular, and circular laminated plates with symmetric angle-ply or cross-ply are obtained. Both simply supported and/or clamped edges are considered. Results are compared with a modified Galerkin approximate solution. The present formulation gives results entirely adequate for many engineering purposes.

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DOI

10.25777/89kr-ht68

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