Abstract:We study the vibrations of lumped parameter systems, the spring being defined by the classical linear constitutive relationship between the spring force and the elongation while the dashpot is described by a general implicit relationship between the damping force and the velocity. We prove global existence of solutions for the governing equations, and discuss conditions that the implicit relation satisfies that are sufficient for the uniqueness of solutions. We also present some counterexamples to the uniqueness when these conditions are not met.
Keywords: lumped parameter systems; differential-algebraic equations; Coulomb's friction; uniqueness of solutions
DOI: DOI 10.14712/1213-7243.2015.143
AMS Subject Classification: 34A09 70F40 34K32