A similarity transformation for numerical integration of piecewise-linear second-order differential equations without damping*

Abstract

The rigid and flexible dynamic behavior of many systems in aerospace structures can be modeled by a set of coupled non linear second-order differential equations. In these systems, the mass matrix function of the system, which contains the masses of the different modules in the structure, its moment of inertia tensors, and its bending moment coefficients (finite number of modes), exhibits eigenvalue dispersion between four and nine orders of magnitude. In addition, due to small gravity gradient and aerodynamic forces and moments, these systems are acted on by small or negligible damping forces and moments. The two characteristics alluded to above imply that the differential equa tions representing these systems have poor numerical stability properties. This study is concerned with the development of a similarity transformation on the variables of integration which results in an equivalent system with higher damping and conse quently better numerical stability than the original one.