Nonsmooth Dynamics of Contacting Thermoelastic Bodies by Jan Awrejcewicz, Yuriy Pyr'yev

By Jan Awrejcewicz, Yuriy Pyr'yev

This paintings is dedicated to an extensive research in touch mechanics, treating the nonsmooth dynamics of contacting our bodies. Mathematical modeling is illustrated and mentioned in several examples of engineering gadgets operating in several kinematic and dynamic environments.

Topics lined in 5 self-contained chapters study non-steady dynamic phenomena that are decided through key elements: i.e., warmth conduction, thermal stresses, and the quantity of donning. New to this monograph is the significance of the inertia issue, that's thought of on par with thermal stresses.

Principal features:

* exact monograph to handle the subject of dynamic touch difficulties in thermoelasticity, which keep in mind inertial results and impression of thermoelastic coupling for types of solids involved

* Mathematical modeling equipment are illustrated and utilized to sensible engineering difficulties: e.g., for bettering the reliability and sturdiness of machines and mechanisms less than friction, warmth, and volume of damage in contact

* offers suggestions that describe many fascinating nonlinear effects

Nonsmooth Dynamics of Contacting Thermoelastic Bodies is a fascinating obtainable functional reference for engineers (civil, mechanical, commercial) and researchers in theoretical and utilized mechanics, utilized arithmetic, physicists, and graduate students.

Show description

By Jan Awrejcewicz, Yuriy Pyr'yev

This paintings is dedicated to an extensive research in touch mechanics, treating the nonsmooth dynamics of contacting our bodies. Mathematical modeling is illustrated and mentioned in several examples of engineering gadgets operating in several kinematic and dynamic environments.

Topics lined in 5 self-contained chapters study non-steady dynamic phenomena that are decided through key elements: i.e., warmth conduction, thermal stresses, and the quantity of donning. New to this monograph is the significance of the inertia issue, that's thought of on par with thermal stresses.

Principal features:

* exact monograph to handle the subject of dynamic touch difficulties in thermoelasticity, which keep in mind inertial results and impression of thermoelastic coupling for types of solids involved

* Mathematical modeling equipment are illustrated and utilized to sensible engineering difficulties: e.g., for bettering the reliability and sturdiness of machines and mechanisms less than friction, warmth, and volume of damage in contact

* offers suggestions that describe many fascinating nonlinear effects

Nonsmooth Dynamics of Contacting Thermoelastic Bodies is a fascinating obtainable functional reference for engineers (civil, mechanical, commercial) and researchers in theoretical and utilized mechanics, utilized arithmetic, physicists, and graduate students.

Show description

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Additional resources for Nonsmooth Dynamics of Contacting Thermoelastic Bodies

Example text

Fremond (2002)]). Again the approach can be oriented to modelling of nonsmooth processes mainly with convex or more 30 1 Introduction sophisticated mathematical analysis. The study is devoted to different systems and does not present complex dynamical behaviours. 2. Aim and scope The study comprises the formulation of the models of motion of material systems with one and two degrees-of-freedom, with tribological processes taken into account. The analysis of both regular and chaotic vibrations is also presented in this book.

2. Aim and scope The study comprises the formulation of the models of motion of material systems with one and two degrees-of-freedom, with tribological processes taken into account. The analysis of both regular and chaotic vibrations is also presented in this book. The following objectives are formulated in this monograph. • Modelling the dynamics of contact systems with one and two degrees-offreedom with friction, taking into account the inertia of the bodies, heat generated by friction, and wear, and the analysis of their influence on the solutions of certain problems • Drawing up the methodology of a nonlinear problem of the motion of thermoelastic bodies in contact • Examining the phenomena of stick-slip motion in self-excited systems, taking tribological processes into account, and determining the influence of the system parameters on the character of regular vibrations, as well as determining the critical values of parameters, for which a qualitative change in the system’s behaviour occurs • Showing that for external mechanical and harmonic kinematical excitations the system may pass to chaotic motion in certain circumstances • Determining the conditions of the occurrence of frictional thermoelastic instability • The analysis of the kinetics of contact characteristics during starting, motion, and braking of the bodies in contact For the determination of regular vibrations of systems, the analytical method of perturbations is applied, whereas chaotic vibrations are analysed with the use of Melnikov and frequency spectrum methods.

1966), Neimark (1978)]. In works of [Pyryev et al. (1995), Pyryev, Grilitskiy (1995)], the so-called thermoelastic contact between a rotating cylinder and a fixed noninertial pad has been studied. Further on, a more complicated axially symmetric problem of both regular and chaotic self-excited vibrations (caused by friction) and wear of the rotating cylinder and bush (fixed to a frame by springs and viscous damping elements) is investigated. 1. Analysed system An elastic and heat-transferring cylinder (shaft) with radius R1 is inserted into the bush (full bush or braking pad) with initial compression value of U0 hU (t) (hU (t) → 1, t → ∞).

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