Non-linear non-planar vibrations of geometrically imperfect inextensional beams. Part II—Bifurcation analysis under base excitations

摘要: Abstract The non-linear non-planar steady-state responses of a near-square cantilevered beam (a special case inextensional beams) with general imperfection under harmonic base excitation is investigated. By applying the combination multiple scales method and Galerkin procedure to two integro-differential equations derived in part I, modulation coupled first-order differential are obtained for primary resonance one-to-one internal resonance. contain linear imperfection-induced terms addition cubic geometric inertial terms. Variations response amplitude curves different parameters presented. Bifurcation analyses fixed points show that influence on can be significant great extent although small. phenomenon frequency island generation also observed.