Previous |  Up |  Next


Title: Mechanical oscillators with dampers defined by implicit constitutive relations (English)
Author: Pražák, Dalibor
Author: Rajagopal, Kumbakonam R.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 57
Issue: 1
Year: 2016
Pages: 51-61
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: lumped parameter systems
Keyword: differential-algebraic equations
Keyword: Coulomb's friction
Keyword: uniqueness of solutions
MSC: 34A09
MSC: 34K32
MSC: 70F40
idZBL: Zbl 06562195
idMR: MR3478338
DOI: 10.14712/1213-7243.2015.143
Date available: 2016-04-12T05:03:36Z
Last updated: 2020-01-05
Stable URL:
Reference: [1] Darbha S., Nakshatrala K., Rajagopal K.R.: On the vibrations of lumped parameter systems governed by differential algebraic systems.J. Franklin I. 347 (2010), 87–101. MR 2581302, 10.1016/j.jfranklin.2009.11.005
Reference: [2] Rajagopal K.R.: A generalized framework for studying the vibrations of lumped parameter systems.Mech. Res. Commun. 17 (2010), 463–466. 10.1016/j.mechrescom.2010.05.010
Reference: [3] Pražák D., Rajagopal K.R.: Mechanical oscillators described by a system of differential-algebraic equations.Appl. Math. 57 (2012), no. 2, 129–142. MR 2899728, 10.1007/s10492-012-0009-8
Reference: [4] Meirovitch L.: Elements of Vibration Analysis.second edition, McGraw-Hill, New York, 1986.
Reference: [5] Vrabie I.I.: Differential Equations. An Introduction to Basic Concepts, Results and Applications.World Scientific Publishing Co. Inc., River Edge, NJ, 2004. MR 2092912, 10.1142/5534
Reference: [6] Granas A., Dugundji J.: Fixed Point Theory.Springer Monographs in Mathematics, Springer, New York, 2003. Zbl 1025.47002, MR 1987179
Reference: [7] Francfort G., Murat F., Tartar L.: Monotone operators in divergence form with $x$-dependent multivalued graphs.Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 7 (2004), no. 1, 23–59. MR 2044260


Files Size Format View
CommentatMathUnivCarolRetro_57-2016-1_5.pdf 229.0Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo