Date of Award


Document Type


Degree Name

Master of Science (MS)


Mechanical & Aerospace Engineering


Engineering Mechanics

Committee Director

Earl A. Thornton

Committee Member

Chuh Mei


A numerical integration technique, a modified version of the Newmark method, is applied to transient motion problems of systems with mass, stiffness, and small nonlinear damping. The nonlinearity is cast as a pseudo-force to avoid repeated recalculation and decomposition of the effective stiffness matrix; thus, the solution technique is dubbed the "pseudo-force Newmark method." Comparisons with exact and perturbation solutions in single-degree-of-freedom problems and with a Gear-method numerical solution in a cantilevered Timoshenko beam finite element problem show the solution technique to be efficient, accurate, and, thus, feasible provided the nonlinear damping is small. As a preliminary step into the investigation of the active control of large space structures, a problem involving a free-free Timoshenko beam with nonlinear structural damping is solved. As expected, small damping is shown to be of little importance in the prediction of low-frequency vibrations while being of utmost importance in the prediction of high-frequency vibrations.