Basin boundaries of plane model of impacting coin

Basin boundaries of plane model of impacting coin

Petr FrantíkPetr Frantík

Michal ŠtafaMichal Štafa

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MotivationMotivationSimulation of a coinSimulation of a coin

Probability of achieving ofProbability of achieving of standing standing coincoin..

Testing of numerical representation of Testing of numerical representation of impactimpact forces. forces.

Final state dependency on Final state dependency on initial initial conditionsconditions. .

ModelModelBasic assumptionsBasic assumptions

AbsolutelyAbsolutely rigid rigid ideal coin.ideal coin.

Contact is reduced to penetration of Contact is reduced to penetration of corner pointscorner points..

Elastic surface modeled as Elastic surface modeled as Winkler Winkler foundationfoundation..

Linear viscous damping Linear viscous damping acting only acting only during impact. during impact.

ModelModelActing forcesActing forces

Dynamical systemDynamical systemNumerical solutionNumerical solution

ByBy Symplectic Euler Symplectic Euler method. Two approaches were used: method. Two approaches were used: full time numerical solving and full time numerical solving and semi-analyticalsemi-analytical solving (free solving (free fall and contact case).fall and contact case).

Dynamical simulationDynamical simulationParameters and solutionsParameters and solutions

DiameterDiameter 2 cm, 2 cm, thicknessthickness 2 mm, 2 mm, weightweight 3.14 g, foundation 3.14 g, foundation stiffnessstiffness 10000 N/m, 10000 N/m, dampingdamping coefficient 0.5 Ns/m. coefficient 0.5 Ns/m.

Static statesStatic statesStability comparisonStability comparison

Rigid Rigid contact contact ElasticElastic contact contact

Basin boundariesBasin boundariesInitial conditionsInitial conditions

0.24%0.24%

This outcome has been achieved with the financial support This outcome has been achieved with the financial support of the project No. of the project No. FAST-S-12-34FAST-S-12-34..

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