Stability and postcritical behavior of a multilink system of rigid bodies subjected to nonpotential loading

A multilink system of rigid bodies is considered, the links of which are loaded by dead forces (inertia forces). The rear link is loaded by a follower force (thrust force) directed along the axis of the lowest link. The links are connected to each other by viscoelastic elements the characteristics of which are assumed to be linear. The principal axes of these elements are orthogonal to each other. In the unloaded state, the planes of these axes (principal planes) are orthogonal to the axes of the links of the system and parallel to each other. In the loaded state, the axes are turned relative to each other in the principal planes. The stability of the trivial solution of the problem, for which the deviation of the longitudinal axes of the links from the vector of acceleration of the center of mass of the system is zero, is analyzed. The boundaries of the divergence and flutter domains are constructed. The postcritical behavior of the system is analyzed numerically. In particular, the dynamic behavior of the system under slowly changing thrust force is analyzed. This analysis made it possible to establish the types of dynamic behavior, find the bifurcations of the modes, and determine the domains of chaotic behavior of the system. The behavior of elastic systems subjected to nonpotential (in particular, follower) forces has been studied fairly thoroughly [1-6]. However, quite a lot of problems still remain, which are of interest from the standpoint of the nonlinear dynamics. One of such problems is that of the dynamic behavior of a system of rigid bodies (links) connected by viscoelastic elements and loaded by dead and follower forces. An example of dead forces are the inertia forces, provided that the direction of the vector of acceleration of the center of mass is constant. A follower force is the thrust force. In this system, the quasistatic (divergence) and dynamic (flutter) types of loss of stability are possible. It is of interest to analyze the combination of these types. In this case, the effect of secondary flutter is possible in the divergence domain. This effect was first observed for aeroelastic systems [7] and then thoroughly analyzed [8-10]. In the present study, the complete systematic analysis of both the equilibrium states of divergence kind and the motions in the flutter domain is performed for a system of three links. Major attention is given to the analysis of stability of the direction of the acceleration of the center of mass of the system.