Bifurcation and buckling analysis of a unilaterally confined self-rotating cantilever beam

摘要

A nonlinear dynamic model of a simple non-holonomic system comprising a self-rotating cantilever beam subjected to a unilateral locked or unlocked constraint is established by employing the general Hamilton's Variational Principle.The critical values,at which the trivial equilibrium loses its stability or the unilateral constraint is activated or a saddle-node bifurcation occurs,and the equilibria are investigated by approximately analytical and numerical methods.The results indicate that both the buckled equilibria and the bifurcation mode of the beam are different depending on whether the distance of the clearance of unilateral constraint equals zero or not and whether the unilateral constraint is locked or not.The unidirectional snap-through phenomenon (i.e.catastrophe phenomenon) is destined to occur in the system no matter whether the constraint is lockable or not.The saddle-node bifurcation can occur only on the condition that the unilateral constraint is lockable and its clearance is non-zero.The results obtained by two methods are consistent.