Reduced-order modeling of geometrically nonlinear structures. Part I: A low-order elimination technique

A general methodology for reduced-order modeling of geometrically nonlinear structures is proposed. This approach is built upon equivalent elimination of low-order nonlinear terms by employing a key concept termed 'passive patterns', defined to be essential dynamic features of nonlinear structures, produced by, namely slaved to, the active mode via low-order nonlinear effects. Thus, besides the active/dominant structural mode, passive patterns are regarded as secondary 'energy-containing' features. Their asymptotic construction procedure is explicitly presented in a weakly nonlinear framework. It is pointed out that both active mode and passive patterns are non-trivial dynamic features of nonlinear structures, and reduction errors of routine Galerkin truncation method are due to incomplete characterization of these passive patterns. Through elimination of their low-order sources (like nonlinearity), the proposed technique fully captures the passive patterns in an equivalent manner and thus leads to refined reduced-order models (ROMs) of the nonlinear structures, while its connection with other existing nonlinear reduction methods is detailed in Part II (Guo and Rega in Nonlinear Dyn, 2023) via an expanded theoretical correspondence.