Nonlinear resonant response of a buckled beam coupled with a boundary massive oscillator

This study focuses on nonlinear modal resonant dynamics of a buckled beam coupled with a boundary massive oscillator. To reveal buckled beam–boundary oscillator coupling effect, extended Hamilton principle is employed to derive a dynamic model with geometric nonlinearity included, and direct multiple-scale method (i.e., attacking directly partial differential equations) is then applied to reduce the original infinite-dimensional beam–support coupled system, leading to nonlinear modulation equations characterizing reduced slow dynamics of the coupled system, by focusing on beam’s one-to-one internally resonant dynamics around its first buckled shape. Time history responses, frequency responses, and Poincaré mapping are employed to investigate stability/bifurcation of nonlinear forced coupled dynamics, with one-to-one internal resonance activated or not.