Date of Award

Winter 2002

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Engineering Mechanics

Committee Director

Chuh Mei

Committee Member

Colin Britcher

Committee Member

Gene Hou


A finite element time domain modal formulation for analyzing flutter behavior of aircraft surface panels in hypersonic airflow has been developed and presented for the first time. Von Karman large deflection plate theory is used for description of the structural nonlinearity and third order piston theory is employed to account for the aerodynamic nonlinearity. The thermal loadings of uniformly distributed temperature and temperature gradients across the panel thickness are incorporated into the finite element formulation. By applying the modal reduction technique, the number of governing equations of motion is reduced dramatically so that the computational time of direct numerical integration is dropped significantly. All possible types of panel behavior, including flat, buckled but dynamically stable, limit cycle oscillation (LCO), periodic motion, and chaotic motion can be observed and analyzed. As examples of the applications of the proposed methodology, flutter responses of isotropic, specially orthotropic and laminated composite panels are investigated. Special emphasis is put on the boundary between LCO and chaos, as well as the routes to chaos. A systematic mode filtering procedure that helps mode selection without specific knowledge of the complex mode shapes is presented and illustrated. Influences of aerodynamic parameters, including aerodynamic damping and Mach number, on the panel flutter responses are studied. The importance of nonlinear aerodynamic terms is examined in detail. The supporting conditions and panel aspect ratio on the onset condition of chaos are also investigated as an illustration of optimization among different design options.

Several mathematical tools, including the time history, phase plane plot, Poincaré map, and bifurcation diagram are employed in the chaos study. The largest Lyapunov exponent is also evaluated to assist in detection of chaos. It is found that at low or moderately high nondimensional dynamic pressures, the fluttering panel typically takes a period-doubling route to evolve into chaos, whereas at high nondimensional dynamic pressure, the route to chaos generally involves bursts of chaos and rejuvenations of periodic motions. Various bifurcation behaviors, such as the Hopf bifurcation, pitchfork bifurcation, and transcritical bifurcation, are observed.

On the basis of the successful applications presented, the proposed finite element time domain modal formulation and the mode filtering procedure have proven to be an efficient and practical design tool for designers of hypersonic vehicles