By Boresi A.P., Schmidt R.J.
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Extra resources for Advanced mechanics of materials
Fig. 2 Contact Dynam Let us define the dynam of the mechanical action of contact of B1 on B2 , simply called the contact dynam of B1 on B2 or the constraint dynam of B1 on B2 . Let o be a reference point. D The contact dynam of B1 on B2 is defined by its elements of reduction, at o, namely: L(1→2) = ∫ l dS (1-5) M 0(1→2) = ∫ op ∧ l dS . (1-6) S S It is denoted by L(1→2) (1→2) . M o Statics 49 Remark 1. The contact dynam is obtained from the stress l of B1 on B2 known at every point of S.
Present in (rough) surfaces of two solids in contact. This type of friction is sometimes called Coulomb friction because, in 1781, Charles de Coulomb developed elementary laws describing dry frictions. 3a Friction Force and a Classic Experiment Before showing the Coulomb’s laws, we consider the following classic experiment. A solid block B2 of mass m is in rest on a horizontal plane B1 . The contacting surfaces show a certain extent of roughness. Fig. 12 The experiment consists in exerting on B2 a given horizontal force F with an increasing magnitude in order to set the block in motion.
Since we know that the transport velocity 1 of q is (v q ) T = (v O ) e + ω ∧ Oq , (0-11b) we say: PR18 The absolute velocity is the sum of the relative velocity and the transport velocity. In the same manner, the absolute acceleration of q is de de (a q ) e = (v q ) e = [(v q ) E + (v O ) e + ω ∧ Oq ] dt dt such that the terms of the sum are successively: de dE (v q ) E = (v q ) E + ω ∧ (v q ) E dt dt 1 Called Vitesse d’entraînement in French. 23 Requirements de (v O ) e = ( a O ) e , dt de d eω d E Oq (ω ∧ Oq ) = ∧ Oq + ω ∧ ( + ω ∧ Oq ) , dt dt dt and by denoting the relative acceleration as follows: dE (a q ) E = (v q ) E , dt we obtain the following expression of the absolute acceleration of q: d eω (a q ) e = (a q ) E + [(a O ) e + ∧ Oq + ω ∧ (ω ∧ Oq )] + 2ω ∧ (v q ) E .
Advanced mechanics of materials by Boresi A.P., Schmidt R.J.