Modal analysis-based reduced-order models for nonlinear structures-an invariant manifold approach

An approach is outlined that can be used to define and construct normal modes of motion for a wide class of nonlinear vibratory systems. Furthermore, an extension of these ideas is used to develop a mode-based model reduction method for multidegree-of-freedom nonlinear systems. The approach makes use of invariant manifolds in the system phase space, and it reduces to the well-known results in the linearized case. An explicit construction method for weakly nonlinear systems allows for the automated generation of a set of reduced-order equations of motion for the nonlinear modes and, in the single-mode case, it systematically produces the amplitude dependent mode shapes. Results from some illustrative examples are presented. The paper closes with a discussion of some topics of current and future interest and some conclusions.