Nonlinear resonance characterization of parametrically excited pre-buckled elastic struts

A simply supported planar elastic and inextensible strut subjected to a static axial load and a harmonic parametric excitation is studied. A variational formulation leads to a system of nonlinear partial differential equations that are subsequently discretized primarily by the first buckling mode and truncated to cubic order. Steady-state periodic responses and bifurcations are evaluated using numerical continuation and verified through finite element simulations. The analysis identifies five resonance behaviours, distinguished by their bifurcation structure, which partitions the static–dynamic loading parameter plane into regions associated with each resonance type. The present work challenges the widely accepted finding that pre-buckled inextensible struts manifest softening-type resonance under direct or parametric excitation and finds that the behaviour is richer than previous work suggests.