Near Grazing Dynamics of Piecewise Linear Oscillators

Near Grazing Dynamics of Piecewise Linear Oscillators
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This is a past event

Impacts in mechanical systems are ubiquitous. These can be intrinsic; such as suspension cables in bridges acting as one-sided springs, unintentional; such as lateral 'Hunting' motions of trains causing loss of contact with the track, a result of wear or manufacturing errors; such as dead zones or gear rattles or a design feature; such as a contact bearing for rotating shafts. Such impacts can cause large changes to the observed motion, often effectively making other sources of nonlinearity negligible. There also remains a somewhat open debate as to how these impacts should be modeled, especially as the duration of impact becomes small.

In this talk I present detailed experimental studies of various bifurcation scenarios of a single degree of freedom harmonic

oscillator undergoing elastic impact with one or two secondary springs. The parameters were chosen so that the details of the bifurcation structure close to the 'grazing' trajectory of the non-impacting response were revealed. At these parameters continuous vs discontinuous models for a relatively hard impact can be compared. Experimental stability analysis can be used to justify the use of a piecewise model, and explain the atypical jumps as well as smooth bifurcations which were observed.

Simulations are shown in order to fill in the details of the observed bifurcations. These were conducted by solving each of the linear equations and stitching them together to obtain the Poincar'e maps. Features observed in the lab which cannot be explained by a discontinuous model are shown to be caused by the interaction of smooth local and non-local bifurcations in a piecewise linear model.

Speaker
Dr. James Ing, School of Engineering, CADR, University of Aberdeen
Hosted by
School of Engineering
Venue
Room G011, Fraser Noble Building