A Residual Flexibility Approach for Decoupled Analysis of Systems of Combined Components

A residual flexibility approach for the analysis of systems involving multiple components subjected to dynamic loading is presented. The reactive forces at the junctions of the components are computed directly without synthesis of component modes or determination of system modes. This is accomplished by expressing the displacements at the junction coordinates of the components in terms of the retained component modes and a first-order account of the residual flexibility of the unretained modes. Once the components are represented in this manner, the requirements of displacement compatibility and force equilibrium at the junction coordinates are enforced. This leads to a set of junction-sized simultaneous algebraic equations for the unknown forces, similar in form to that of the flexibility formulation in statics; this is done by invoking the Newmark integration algorithm. The computed reactive forces at a given time point are used to integrate the equations of motion of the individual components separately for that time point, hence the terminology decoupled analysis. The new method compares well with traditional Component-Mode Synthesis approach for a nonclassically damped fixed-fixed beam consisting of two classically damped cantilevered beam components.