Nonlinear Dynamics of Structures Via Residual Flexibility of Components

Abstract

An approach for the analysis of systems comprising multiple components subjected to dynamic loading is presented. It allows for an efficient treatment, stepwise in time, of linear and nonlinear connections between components. The constraint forces at the junctions of the components are computed directly without the synthesis of component modes of the determination of system modes. This is accomplished by expressing the displacements at the junction coordinates of the components in terms of the retained unconstrained normal modes and the residual flexibility of the unretained modes, in conjunction with a Newmark algorithm representation of nodal kinematics within a time step. This leads to a set of junction-sized equations, similar in form to that of the flexibility formulation in statics, in terms of the unknown junction forces. For the linear problem, the connection forces are solved for directly. For the nonlinear problem, the connection forces are determined in an iterative manner. The approach is applied to a problem involving the dynamic response of a Mini-Pressurized Logistic Module (MPLM) rack in a Space Shuttle liftoff event. The results of the proposed approach are compared with pertinent results derived by relying on component-mode synthesis.