DYNAMIC BUCKLING OF A BEAM WITH TRANSVERSE CONSTRAINTS

A nonlinear dynamic system with continuously distributed mass is studi ed using several approaches: experimentally, numerically as well as an alytically. The nonlinearity of the system consists of geometrical con straints imposed on the motion. It is harmonically loaded and it is de monstrated that for certain choices of the loading parameters, periodi c, quasi-periodic or chaotic behaviour may occur depending on the init ial conditions. An important issue is to investigate the number of deg rees of freedom needed in order to analytically model the system accur ately enough that the important characteristics of the motion are reta ined in the solution. It is found that the impact conditions at the co nstraints are of crucial importance and a new approach is proposed for modelling of the impacts. The method is based on the fact that the fr ee motion can be approximated with quite a few degrees of freedom, whi le at impact all the infinite number of degrees of freedom are conside red.