Dynamic Analysis of Large Systems by Complex Mode Synthesis

The method of component mode synthesis, originally conceived for application to lightly damped structures, is extended to include linear, autonomous, holonomic dynamical systems in general. When written in terms of generalized coordinates, the equations of motion may have completely arbitrary constant coefficients. The work was initially developed for the analysis of high speed trains which exhibit discrete damping in their suspension systems, and nonsymmetry of the coefficient matrices due to wheel-rail interaction and the possibility of Coriolis coupling from spinning wheels and rotors. The object of component mode synthesis is to minimize the number of equations which must be solved for either stability analysis of dynamic response analysis of multi-component systems. Formulation of the equations in terms of the modal vectors associated with isolated subsystems is found to satisfy this objective. The modes are considered to be complex in general as opposed to the classical normal modes in structural dynamics which are always real. A method for computing the frequency response of a system to sinusoidal excitation is described. It is valid over a frequency range determined by the component modes included in the analysis. An example is discussed which illustrates the effectiveness of this approach in terms of reducing the computational effort required to obtain accurate modes for the complete system.