Bifurcations and chaos in a forced zero-stiffness impact oscillator. (English) Zbl 0714.73049

Li, G. X.; Rand, R. H.; Moon, F. C.

Int. J. Non-Linear Mech. 25, No. 4, 417-432 (1990).

Summary: We study a simple model of a structure having a pin joint with “play”. The model consists of a zero-stiffness impact oscillator. For small forcing we analyse two types of simple periodic solutions: symmetric and asymmetric. Saddle-node and pitchfork bifurcations are found for both types of solutions, while period-doubling bifurcations are found for the asymmetric periodic solutions. For large forcing it is numerically shown that the system exhibits chaos.

MSC:

74H45	Vibrations in dynamical problems in solid mechanics
70K50	Bifurcations and instability for nonlinear problems in mechanics
74M20	Impact in solid mechanics
34C23	Bifurcation theory for ordinary differential equations

Keywords:

space truss structures; smooth pin joints; small forcing; simple periodic solutions; symmetric; asymmetric; Saddle-node; pitchfork bifurcations; period-doubling bifurcations

Software:

MACSYMA