Recent Advancements in Fractal Geometric‐Based Nonlinear Time Series Solutions to the Micro‐Quasistatic Thermoviscoelastic Creep for Rough Surfaces in Contact

Abstract

To understand the tripological contact phenomena, both mathematical and experimental models are needed. In this work, fractal mathematical models are used to model the experimental results obtained from literature. Fractal geometry, using a deterministic Cantor structure, is used to model the surface topography, where recent advancements in thermoviscoelastic creep contact of rough surfaces are introduced. Various viscoelastic idealizations are used to model the surface materials, for example, Maxwell, Kelvin-Voigt, Standard Linear Solid and Jeffrey media. Such media are modelled as arrangements of elastic springs and viscous dashpots in parallel and/or in series. Asymptotic power laws, through hypergeometric series, were used to express the surface creep as a function of remote forces, body temperatures and time. The introduced models are valid only when the creep approach of the contact surfaces is in the order of the size of the surface roughness. The obtained results using such models, which admit closed-form solutions, are displayed graphically for selected values of the systems' parameters; the fractal surface roughness and various material properties. Results obtained showed good agreement with published experimental results, where the utilized methodology can be further extended to the utilization for the contact of surfaces within micro- and nano-electronic devices, circuits and systems.

Characteristic Roots of a Class of Fractional Oscillators

“…Denote by ℎ( ) the impulse response function of (24). Then, using the techniques in fractional calculus and differential equations [64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81], we have (see [61] for details)…”

Vibration Control of Fractionally-Damped Beam Subjected to a Moving Vehicle and Attached to Fractionally-Damped Multiabsorbers

“…Future work will involve the following items for the application of the fractional calculus-based approach that is used in this paper within: (1) quantum and nano computing systems [52], (2) nanobeams, materials and medical applications [52][53][54], (3) fractal-based formulations to the microquasistatic thermoviscoelastic creep for rough surfaces in contact [55], and (4) other beam configurations for various types of nonlinearities, damping characteristics, and moving vehicles.…”

Thermal contact conductance of elastically deforming nominally flat surfaces using fractal geometry

“…The multi-scale nature of the surface roughness suggests the use of the second route which is the fractal representation. Various models for the approach of the fractal punches were considered and utilized (Borodich and Mosolov, 1992;Warren and Krajcinovic, 1995;Abuzeid, 2003Abuzeid, , 2004Abuzeid, , 2006Abuzeid, , 2012Abuzeid et al, 2010Abuzeid et al, , 2011Abuzeid and Eberhard, 2007;Abuzeid and Alabed, 2009). In the previously cited published works, different constitutive relations were considered:…”