Dynamic analysis of structural systems using component modes

Abstract

A method is developed for analyzing complex structural systems that can be divided into interconnected components. Displacements of the separate components are expressed in generalized coordinates that are defined by displacement modes. These are generated in three categories: rigid-body, constraint, and normal modes. Rigid-body modes are convenient where displacements are denned in inertial space for dynamic analysis. Constraint modes are included to treat redundancies in the interconnection system. Normal modes define displacements relative to the connections. Generalized mass, stiffness, and damping matrices are determined for each component, as are generalized forces. The requirement of system continuity gives rise to equations of displacement compatibility at the connections. These serve as equations of constraint among the component coordinates and are used to construct a transformation relating component coordinates to system coordinates. This transformation is used to derive system properties and forces from component properties and forces. System equations of motion are formulated and solved to determine system response. Component responses are found using the transformation. Connection forces are computed from the component equations. Each component can then be isolated and treated separately.