Date of Award

Summer 2003

Document Type


Degree Name

Doctor of Philosophy (PhD)


Aerospace Engineering

Committee Director

Chuh Mei

Committee Member

Travis L. Turner

Committee Member

Robert L. Ash

Committee Member

Brett A. Newman


This work presents a finite element modal formulation for large amplitude free vibration of arbitrary laminated composite shallow shells. The system equations of motion are formulated first in the physical structural-node degrees of freedom (DOF). Then, the system is transformed into general Duffing-type modal equations with modal amplitudes of coupled linear bending-inplane modes. The linear bending-inplane coupling is due to the shell curvature as well as unsymmetric lamination stacking. Multiple modes, inplane inertia, and the first-order transverse shear deformation for composites are considered in the formulation. A triangular shallow shell finite element is developed from an extension of the triangular Mindlin (MIN3) element with the improved shear correction factor. Time numerical integration is employed to determine nonlinear frequency of vibration. An iterative procedure to determine the judicious initial conditions for periodic panel response is developed and presented. By neglecting the inplane inertia effect, the general Duffing modal equations in functions of modal amplitudes of linear bending modes only are also formulated and presented. This approach is used for comparison of results with existing classic analytical methods. The differences in characterizing a shallow shell behavior with modal amplitudes of coupled linear bending-inplane and bending only modes are demonstrated and discussed.

Then the finite element modal formulation for large amplitude random response of shallow shell panels to acoustic excitation and elevated temperature is presented. Reduced order integration is used to determine strains. Rainflow counting method and S-N curves are combined by means of damage accumulation theory to predict panel fatigue life. Factors contributing the softening effect, namely unsymmetrical lamination and curvature are investigated along with their impact on the fatigue life. Two types of excitation inputs are considered. Responses and fatigue life estimations to simulated band-limited Gaussian white noise and to in-flight recorded pressure fluctuation microphone data are presented and compared.