An Efficient Response Analysis Method for a Non-Linear/Parameter Changing System Using Sub-Structure Modes

Abstract

An efficient state-space method is presented to determine time domain forced responses of a structure using the Lagrange multiplier based sub-structure technique. Compared with the conventional mode synthesis methods, the suggested method can be particularly effective for the forced response analysis of a structure subjected to parameter changes with time, such as a missile launch system, and/or having localized non-linearities, because this method does not need to construct the governing equations of the combined whole structure. Both the loaded interface free-free modes and free interface modes can be employed as the modal bases of each sub-structure. The sub-structure equations of motion are derived using Lagrange multipliers and recurrence discrete-time state equations based upon the concept of the state transition matrix are formulated for transient response analysis. The suggested method is tested with two example structures, a simple lumped mass model with a non-linear joint and an abruptly parameter changing structure. The test results show that the suggested method is very accurate and efficient in calculating forced responses and in comparing it with the direct numerical integration method.