Date of Award

Spring 1995

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Engineering Mechanics

Committee Director

Chuh Mei

Committee Member

A. Aminpour

Committee Member

Gene J.-W. Hou

Committee Member

John Kroll

Committee Member

Duc T. Nguyen


The nonlinear random response of composite plates to the simultaneously applied, combined acoustic/thermal loads are investigated in this dissertation. A finite element formulation for the nonlinear random response is developed. The three-node Mindlin plate element with improved transverse shear is extended and employed. The extension includes the development of the thermal geometric matrix, the mass matrix, the first- order and second-order nonlinear stiffness matrices, and the thermal and mechanical load vectors. An innovative solution procedure has been created which is believed to be the first attempt to analyze nonlinear random response of complex composite panels subjected to simultaneous acoustic and thermal loads. The acoustic pressure can be normal incidence or grazing incidence. The solution procedure starts with obtaining the static and dynamic equations. For the static equation, the Newton-Raphson method was used. A modal transformation followed by the equivalent linearization technique and an iterative scheme was employed for the dynamic equation.

Seven problems of thermal buckling and post buckling were studied in this dissertation. The extension and bending coupling makes the plate bend out of its plane as soon as the plate is heated, without the prebuckling stage. The most interesting phenomenon in this process is the mode shape change during thermal postbuckling. The described solution procedure automatically obtains the mode change in the postbuckling stage as long as the incremental step of temperature change is small enough regardless of the presence of mechanical load. The effects of the number of layers, the ply angles and the aspect ratio of the plate upon the thermoelastic response are studied.

The results show that three or four modes will give converged root mean square (RMS) deflection. Anti-symmetrical modes are not included for normal incidence cases. It is demonstrated that the peaks of the response are very close to the natural frequencies at low sound pressure levels. However, at high pressure levels the response peaks are shifted up and broadened. An interesting observation is that the anti-symmetrical modes about the axis, which is perpendicular to the wave propagation direction, participate in the response of the plate for grazing incident acoustic wave. It is also found that the RMS maximum strain with temperature could be either smaller or larger than the one without temperature. This is due to: (1) the temperature increases the thermal strain component, and (2) the thermal postbuckling increases the nonlinear stiffness which reduces the RMS deflection and it leads to smaller strain component. For plate with initial imperfection in deflection, the nonlinear stiffness due to imperfection reduces the random responses as compared to the flat plate. For a plate with an initial imperfection in deflection which has the same maximum deflection as the thermal postbuckling deflection, the plate with initial imperfection is stiffer and leads to smaller random responses.