Transient Response Analysis of Nonlinear Modally Coupled Structural Dynamics Equations of Motion

Abstract

The solution of the structural dynamics matrix differential equations of motion in the presence of general structural damping, aerodynamic stiffness and damping, and nonlinear generalized forces is discussed. An intuitive and easy-to-use method of Picard iteration by Dawson is shown to provide exponential convergence to the exact solution of quasilinear second-order matrix differential equations with general modal coupling, and the first mathematical proof of convergence is presented. It is demonstrated, for the special case of general structural damping without aerodynamic forces but with forcing functions that depend only on time, that the method of Picard iteration agrees to within machine accuracy with the method of linear modal velocity of Henkel and Mar. Thomson's coupled damping problem is solved using both methods and percent errors resulting from ignoring modal coupling are quantified. Possible areas of future research are discussed.