Existence for a thermoviscoelastic beam model of brakes

Kuttler, Kenneth; Shillor, Meir; Fernández, José R.

doi:10.1016/j.nonrwa.2004.03.003

Cited by 8 publications

(12 citation statements)

References 23 publications

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“…It is our conjecture that this model is in fact a model valid to describe the axial deformation of a linearized viscoelastic beam with long-term memory (see Remark 3.7). The same comments apply to the equations for the bending of a linearized viscoelastic beam (7.15) (which can be found in [20], for example) and (7.20) which is of the long-term memory form.…”

Section: (722)mentioning

confidence: 89%

Mathematical justification of viscoelastic beam models by asymptotic methods

Rodríguez-Arós

Viaño

2010

Journal of Mathematical Analysis and Applications

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Section: (722)mentioning

confidence: 89%

Mathematical justification of viscoelastic beam models by asymptotic methods

Rodríguez-Arós

Viaño

2010

Journal of Mathematical Analysis and Applications

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“…It is our conjecture that this model is in fact a model valid to describe the axial deformation of a linearized viscoelastic beam with long-term memory (see Remark 3.7). The same comments are apply to the equations for the bending of a linearized viscoelastic beam (7.15) (which can be found in [15], for example) and (7.20), which is of the long-term memory type.…”

Section: Conclusion: Comparison With Classical Theoriesmentioning

confidence: 99%

Mathematical justification of Kelvin–Voigt beam models by asymptotic methods

Rodríguez-Arós

Viaño

2011

Z. Angew. Math. Phys.

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“…Derivation of various models with thermal effects and wear, from thermodynamic considerations, can be found in [22]. A simplified model for a braking system in which frictional heat generation was taken into account was studied in [2,13], where the friction coefficient was assumed to be slip rate and temperature-dependent.…”

Section: Introductionmentioning

confidence: 99%

A model of a spring-mass-damper system with temperature-dependent friction

Migórski¹,

Ochał²,

Shillor

et al. 2013

Eur. J. Appl. Math

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Link to this article: http://journals.cambridge.org/abstract_S0956792513000272 How to cite this article: S. MIGORSKI, A. OCHAL, M. SHILLOR and M. SOFONEA (2014). A model of a spring-massdamper system with temperature-dependent friction .This work models and analyses the dynamics of a general spring-mass-damper system that is in frictional contact with its support, taking into account frictional heat generation and a reactive obstacle. Friction, heat generation and contact are modelled with subdifferentials of, possibly non-convex, potential functions. The model consists of a non-linear system of first-order differential inclusions for the position, velocity and temperature of the mass. The existence of a global solution is established and additional assumptions yield its uniqueness. Nine examples of conditions arising in applications, for which the analysis results are valid, are presented.

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Existence for a thermoviscoelastic beam model of brakes

Cited by 8 publications

References 23 publications

Mathematical justification of viscoelastic beam models by asymptotic methods

Mathematical justification of viscoelastic beam models by asymptotic methods

Mathematical justification of Kelvin–Voigt beam models by asymptotic methods

A model of a spring-mass-damper system with temperature-dependent friction

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