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 different examples of engineering gadgets operating in several kinematic and dynamic environments.
Topics lined in 5 self-contained chapters learn non-steady dynamic phenomena that are made up our minds through key components: i.e., warmth conduction, thermal stresses, and the volume of donning. New to this monograph is the significance of the inertia issue, that is thought of on par with thermal stresses.
* specific monograph to handle the subject of dynamic touch difficulties in thermoelasticity, which have in mind inertial results and impact of thermoelastic coupling for types of solids involved
* Mathematical modeling tools are illustrated and utilized to useful engineering difficulties: e.g., for bettering the reliability and sturdiness of machines and mechanisms lower than friction, warmth, and volume of damage in contact
* offers strategies that describe many attention-grabbing nonlinear effects
Nonsmooth Dynamics of Contacting Thermoelastic Bodies is an interesting available functional reference for engineers (civil, mechanical, commercial) and researchers in theoretical and utilized mechanics, utilized arithmetic, physicists, and graduate students.
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Extra resources for Nonsmooth Dynamics of Contacting Thermoelastic Bodies
2 Mathematical formulation of the problem 39 τ ˙ ) − ϕ(τ |φ(τ ˙ )|p(τ )dτ, uw (τ ) = k w 0 < τ < τc . 23) 0 The cylinder radial displacement is ⎡ r 1 1 ⎣ θ(η, t)ηdη − u(r, τ )/r = 2(1 − ν1 ) r2 0 ⎤ 1 θ(η, t)ηdη ⎦ − 0 U0 hU (τ ) + uw (τ ). 23), one should know time-dependent velocities of the bush and shaft. 23) are mutually adjoined and require simultaneous solution. 3 Rotational motion of the shaft Let axis Z coincide with the shaft axis. 24) B1 ϕ¨1 ∈ M − Mf r , where Mf r = f (Vr )2πR12 P (t) denotes the moment of friction force, M is the moment acting on the shaft, and ϕ1 (t) stands for the angle of the shaft position.
Furthermore, radial springs are initially compressed and they have stiﬀness coeﬃcients k1 , whereas tangential springs are characterised by nonlinear stiﬀness k2 , k3 of Duﬃng type per unit bush (pad) length. In the tangential direction, the bush (pad) is driven by the damping force measured per bush length unit (c denotes the viscous damping coeﬃcient) and force F2 = F∗ cos(ω t) is also measured per bush length unit. It is assumed that (i) the cylinder (shaft) rotates at an angular velocity ϕ˙ 1 (t) such that centrifugal forces can be neglected in our system; (ii) the cylinder angular J.
1966), Osiński (1979), Nayfeh (1981), Awrejcewicz (1989), (1996)]. 24). As has already been mentioned, the material systems of bodies in contact can show self-excited vibrations. , Oden, Martins (1985), Awrejcewicz, Pyryev (2005), (2007)]. Self-excited vibrations belong to nonextinguishing vibrations that are supported by external energy sources in a nonlinear conservative system. Self-excited stick-slip vibrations occur in many mass-elastic systems with slip friction, both in technology and in everyday life.