zbMATH — the first resource for mathematics

Some remarks on a vibro-impact scheme. (English) Zbl 1134.74392
Summary: We consider a mechanical system subject to a unilateral constraint for which an impact law is defined. The impact process is considered to be instantaneous and the behavior at the impact is described through a restitution coefficient \(e\). We solve this problem using an algorithm developed and used by Paoli and Schatzman. We show that this algorithm develops numerical instabilities related to the restitution coefficient used in the impact law. Finally, we propose a new scheme which introduces some numerical damping in order to avoid the numerical instabilities.

74M20 Impact in solid mechanics
74S99 Numerical and other methods in solid mechanics
35L35 Initial-boundary value problems for higher-order hyperbolic equations
35L85 Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators
65L99 Numerical methods for ordinary differential equations
Full Text: DOI