Chaotic vibrations of a beam with non-linear boundary conditions

TLDR: Forced vibrations of an elastic beam with non-linear boundary conditions are shown to exhibit chaotic behavior of the strange attractor type for a sinusoidal input force as mentioned in this paper, where the beam is clamped at one end, and the other end is pinned for the tip displacement less than some fixed value and is free for displacements greater than this value.

Abstract: Forced vibrations of an elastic beam with non-linear boundary conditions are shown to exhibit chaotic behavior of the strange attractor type for a sinusoidal input force The beam is clamped at one end, and the other end is pinned for the tip displacement less than some fixed value and is free for displacements greater than this value The stiffness of the beam has the properties of a bi-linear spring The results may be typical of a class of mechanical oscillators with play or amplitude constraining stops Subharmonic oscillations are found to be characteristic of these types of motions For certain values of forcing frequency and amplitude the periodic motion becomes unstable and nonperiodic bounded vibrations result These chaotic motions have a narrow band spectrum of frequency components near the subharmonic frequencies Digital simulation of a single mode mathematical model of the beam using a Runge-Kutta algorithm is shown to give results qualitatively similar to experimental observations