Simple model of bouncing ball dynamics. Displacement of the limiter assumed as a cubic function of time

Nonlinear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered and the Poincare map, describing evolution from an impact to the next impact, is described. Displacement of the limiter is assumed as periodic, cubic function of time. Due to simplicity of this function analytical computations are possible. Several dynamical modes, such as fixed points, 2 - cycles and chaotic bands are studied analytically and numerically. It is shown that chaotic bands are created from fixed points after first period doubling in a corner-type bifurcation. Equation for the time of the next impact is solved exactly for the case of two subsequent impacts occurring in the same period of limiter's motion making analysis of chattering possible.Comment: 8 pages, 1 figure, presented at the DSTA 2011 conference, Lodz, Polan

Simple model of bouncing ball dynamics: displacement of the table assumed as quadratic function of time

Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles and chaotic bands are studied analytically and numerically. It is shown that chaotic bands appear due to homoclinic structures created from unstable 2 - cycles in a corner-type bifurcation.Comment: 11 pages, 6 figure

Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints : computational and experimental approaches

The main objective of this work is to present a computational and experimental study on the contact forces developed in revolute clearance joints. For this purpose, a well-known slider-crank mechanism with a revolute clearance joint between the connecting rod and slider is utilized. The intra-joint contact forces that generated at this clearance joints are computed by considered several different elastic and dissipative approaches, namely those based on the Hertz contact theory and the ESDU tribology-based for cylindrical contacts, along with a hysteresis-type dissipative damping. The normal contact force is augmented with the dry Coulomb’s friction force. In addition, an experimental apparatus is use to obtained some experimental data in order to verify and validate the computational models. From the outcomes reported in this paper, it is concluded that the selection of the appropriate contact force model with proper dissipative damping plays a significant role in the dynamic response of mechanical systems involving contact events at low or moderate impact velocities.Fundação para a Ciência e a Tecnologia (FCT

Wrinkling of a circular elastic plate stamped by a spherical punch

Large deflection theory is used to determine when wrinkling occurs in a simply supported circular elastic plate loaded at the center by a spherical punch. If the edges are free to displace radially, thin plates stamped by intermediate radius punches will develop radial wrinkles near the edge at a central deflection approximately equal to four plate thicknesses, w0 h ≈ 4. Initially, there are either three or four wrinkles, but the number increases if the central deflection is increased. With larger radius punches, thin plates do not wrinkle. It is calculated that elastic wrinkling occurs in thin plates ( a h > 80) when a2 Rh > 8, where a is the plate radius and R is the punch radius

Oblique elastic-plastic impact between rough cylinders in plane strain

International Journal of Engineering Science37197-122IJES

Stamping rectangular plates into doubly-curved dies

Shallow spheroidal shell segments have been press formed from rectangular plates by stamping between a die and matching punch that have two degrees of curvature. Experiments on mild steel, copper and aluminum plates that were not clamped in the die have measured the punch force, contact regions and final curvature distribution. The sequence of deformation modes has been identified; initially, these are bending but in later stages, in-plane forces predominat

Effects of nonhomogeneity, cell damage and strain-rate on impact crushing of a strain-softening cellular chain

International Journal of Impact Engineering124585-602IJIE

Dynamic crushing of strain-softening cellular structures. A one-dimensional analysis

Journal of Engineering Materials and Technology, Transactions of the ASME1124398-405JEMT

Dynamic modes of plastic deformation for suddenly loaded, curved beams

International Journal of Impact Engineering911-18IJIE