Date of Award

Spring 5-1994

Document Type

Thesis - Open Access

Degree Name

Master of Science in Aerospace Engineering


Graduate Studies

Committee Chair

Habib Eslami

Committee Member

Frank Radosta

Committee Member

Yechiel J. Crispin


The purpose of this thesis is to study the nonlinear forced vibration of an unsymmetrically laminated composite beam. Two cases are considered: unsymmetrical angle-ply and unsymmetrical cross-ply composite beams. The nonlinear governing partial differential equations of motion are obtained by taking into account the von-Karman geometrical nonlinearity. These equations are transformed into nonlinear ODE (Ordinary Differential Equations) by means of the Galerkin method. For both cases the forced Duffing equation was obtained. It is to be noted that only for the unsymmetrical cross-ply laminate simply-supported case are both quadratic and cubic nonlinearities present. The resulting equations for both cases are then solved using the Method of Multiple Scales (MMS). The boundary conditions considered here are simply-supported with immovable edges and clamped at both edges. For both cases the frequency response of the beam associated with the primary resonance was studied. In addition, the subharmonic and superharmonic resonances were analyzed for a simply-supported unsymmetrically laminated angle-ply composite beam. In order to compare the effects of different modes of vibrations, a one-mode solution and a two-mode solution were investigated.