Mechanical oscillators with dampers defined by implicit constitutive relations. (English) Zbl 1374.34028

Pražák, Dalibor; Rajagopal, Kumbakonam R.

Commentat. Math. Univ. Carol. 57, No. 1, 51-61 (2016).

The authors study the vibrations of a mass-spring-dashpot system with a simple linear spring and a fully implicit constitutive relation between damping force and velocity describing the dashpot. The main point is an investigation of conditions sufficient to ensure uniqueness of the solution. At the end some examples are given where several solutions exist.

Reviewer: Werner M. Seiler (Kassel)

MSC:

34A09	Implicit ordinary differential equations, differential-algebraic equations
70F40	Problems involving a system of particles with friction
34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations

Keywords:

lumped parameter systems; differential-algebraic equations; Coulomb friction; uniqueness of solutions