A residual flexibility approach for decoupled analysis of nonlinear, nonclassically damped systems of combined components

A residual flexibility approach for the analysis of systems comprised of multiple components subjected to dynamic loading is presented. In it, the reactive forces at the junctions of the components are computed directly without the synthesis of component modes or the determination of system modes. This is accomplished by expressing the displacements at the junction coordinates of the components in terms of the retained component free-junction normal modes and a first-order account of the residual flexibility of the unretained modes. Once the components are represented in this manner, the requirement of displacement compatibility and force equilibrium at the junction coordinates is enforced. This leads to a set of junction-sized, simultaneous algebraic equations, similar in form to that of the flexibility formulation in statics, in terms of the unknown junction forces. The computed forces at a given time-step then serve to base-drive each component's equations of motion separately, hence the term decoupled analysis. Due to the formulation of the method, the nonlinear, nonclassically damped problem becomes a natural progression. The new method compares well to the traditional method of Component-Mode Synthesis for solutions to a nonclassically damped fixed-fixed beam comprised of two classically damped cantilevered beam components