Date of Award

Spring 1987

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Engineering Mechanics

Committee Director

Chuh Mei

Committee Member

John S. Mixson

Committee Member

Surendra N. Tiwari

Committee Member

Gene Hou

Committee Member

J. M. Dorrepaal


Effects of both nonlinear damping and large deflection stiffness are included in the theoretical analysis in an attempt to explain the experimental phenomena of aircraft panels excited at high sound pressure levels; that is the broadening of the strain response peak and the increase in modal frequency. Beams and symmetrically laminated plates subjected to acoustic excitation are considered in the analyses. The excitations are ergodic and Gaussian with zero mean. A polynomial containing both linear and nonlinear damping terms is considered as a damping model. Galerkin's method is used to derive modal equations. Direct equivalent linearization is used to solve nonlinear differential equations which contain both nonlinear stiffness and nonlinear damping terms to determine mean square maximum deflection, mean square maximum strain and spectral density function of maximum strain for the structures.

For beams, simply supported and clamped, three modes are considered in the analysis. Isotropic material is considered for beams. It is shown that the choice of linear damping is important for multiple modes analysis and has more influence on root mean square (RMS) strains than on RMS deflections. Nonlinear damping has maximum influence on the first mode and has considerable influence on deflection and strain and modal frequency.

For laminated plates, simply supported and clamped, only single mode analysis is carried out. Immovable and movable inplane edge conditions are considered. Graphite/Epoxy is the material used. It is shown that small values of nonlinear damping coefficient have significant influence on panel RMS deflection and strains and modal frequency.

It is identified that nonlinear structural damping causes the broadening behavior of the strain response peaks at high sound pressure levels. Nonlinear analysis (large deflection with nonlinear damping) would yield more accurate and realistic predictions on panel random response. And also it is shown that by the inclusion of nonlinear damping, the linearized frequencies and RMS deflections and strains will be more realistic.

This analytical investigation will help to broaden the basic understanding of the role of nonlinear damping on random response of structures and lead to better sonic fatigue design criteria.