Strange dynamics of bilinear oscillator close to grazing Ekaterina Pavlovskaia 1 , James Ing 1 , Soumitro Banerjee 2 and Marian Wiercigroch 1 1 Centre for Applied Dynamics Research, School of Engineering, King’s College, Aberdeen University, Aberdeen, AB24 3UE, UK E-mail: e.pavlovskaia@abdn.ac.uk, j.ing@abdn.ac.uk, m.wiercigroch@abdn.ac.uk 2 Department of Electrical Engineering, Indian Institute of Technology, India E-mail: soumitro.banerjee@gmail.com Keywords: Impact Oscillator, Grazing Bifurcations, Chaos SUMMARY. In this work strange behaviour of an impact oscillator with a one sided elastic con- straint discovered experimentally [1, 2] is compared with the predictions obtained using its math- ematical model. Particular attention is paid to the chaos recorded near grazing frequency when a non-impacting orbit becomes an impacting one under increasing excitation frequency. Extensive experimental investigations undertaken on the rig developed at the Aberdeen University [1, 3] reveal different bifurcation scenarios under varying excitation frequency near grazing which were recorded for a number of values of the excitation amplitude. It was found that the evolution of the attractor is governed by a complex interplay between smooth and non-smooth bifurcations. In some cases the occurrence of coexisting attractors is manifested through a discontinuous transition from one orbit to another through boundary crisis. One of those bifurcation scenarios is explained here based on numerical simulation. 1 INTRODUCTION Simple piecewise systems have been studied extensively in the past. While much work has been devoted to finding normal forms and classifying the possible types of bifurcations in such systems, [4, 5, 6, 7] and references therein, comparatively little has been devoted to experimental verification of these, [3, 8, 9, 10, 11], and then only to a limited extent, or with simple rigid impact assumptions. This study presents detailed analysis of one of the bifurcation scenarios close to grazing in terms of the nonlinear bimodal maps that result from solving the linear equations in each subspace. The normal form 3/2 map resulting from grazing is often either the cause of or a direct precursor to a smooth bifurcation. Detailed simulations are shown to be in good correspondence with experiments both qualitatively and quantitatively. 1.1 Experimental set up The experimental investigations were carried out on the impact oscillator [1, 2] shown in figure 1 which consists of a block of mild steel supported by parallel leaf springs providing the primary stiffness and preventing the mass from rotation. The secondary stiffness provided by an elastic beam is mounted on a separate column. Contact between the mass and the beam is made when their relative displacement is equal to zero. In practice, the contact is through a bolt which is attached to the beam. The length of the bolt can be adjusted to control the gap, g. The oscillator rig was mounted on an electro-dynamic shaker which provided harmonic excitation through the base. Displacement of the oscillator was measured with an eddy current probe displacement transducer mounted over one leaf spring. The acceleration of the oscillator was measured using an accelerometer mounted directly on the mass. A Savitzky-Golay algorithm was used to smooth the data, where a second 1