Dynamic Analysis of Large Systems by Complex Mode Synthesis

Abstract

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.

Stability Analysis of Rotor-Bearing Systems Using Component Mode Synthesis

“…Hasselman and Kaplan [3] recently presented a component mode synthesis formulation for a general second order system. Their formulation differs from the component mode synthesis discussed above in that it does not include consideration of component constraint modes.…”

Substructure synthesis and its iterative improvement for large nonconservative vibratory systems

“…The equations of motion for the assembled system are the conditions for stationarity of the functional (£i m5 )df \o_/ ' (12) where the stationarity conditions are subject to constraints in the form of internal boundary compatibility conditons between adjacent substructures. Before writing L explicitly, it is necessary to recognize that the vectors rj ls and ij* s in Eq.…”

“…On the other hand, Ref. 12 introduced the idea of using complex substructure eigenvectors to represent each substructure of a general nongyroscopic nonconservative system. There the substructures are coupled together to form a whole structure model before introducing substructure eigenvectors, a process which is often undesirable.…”

A free interface component mode synthesis method for viscoelastically damped systems

“…However, the increasing use of nonclassically damping in mechanical systems led the simplifications of undamped or proportional damping do not appropriate in these cases. As a result, the works of CMS method for non-classically damped systems have been studied by some researchers [9][10][11]. Due to the fact that it is difficult and unnecessary to obtain all the eigenpairs of a large-scaled model, the high-order modal truncation problem is frequently encountered and leads to errors.…”