Friction damping

Figure 18-11. Frictional damping in a metal-disc coupling.

Suppose we idealize the polymeric chain as bang a linear array of Z masses m, each separated by a distance a, coupled by springs of force constant a. Let there be N such macromolecules per c.c. and let / be the frictional damping factor associated with the motion of each particle. 

Kerwin, E. M., Jr. In Internal Friction Damping and Cyclic Plasticity ASTM Special Technical Publication No. 378 American Society for Testing and Materials Philadelphia, 1965 pp 125-149. 

Since frictional damping always is present but has been neglected in the derivation of equation (80), a source of excitation, such as a suitably... 

The general principle of BD is based on Brownian motion, which is the random movement of solute molecules in dilute solution that result from repeated collisions of the solute with solvent molecules. In BD, solute molecules diffuse under the influence of systematic intermolecular and intramolecular forces, which are subject to frictional damping by the solvent, and the stochastic effects of the solvent, which is modeled as a continuum. The BD technique allows the generation of trajectories on much longer temporal and spatial scales than is feasible with molecular dynamics simulations, which are currently limited to a time of about 10 ns for medium-sized proteins. 

Note that the spin-echo attenuation depends in a characteristic way on the NMR parameters A and S, as well as on the self-diffusion constant D and the frictional damping f. Equation (75) is quite general and applies to all time intervals. 

We next point out that the near equilibrium physics of the slow variable regime gives rise to a very simple picture of particle motion and underlies the traditional concept of frictional damping. 

The traditional concept of frictional damping as due to a retarding force linear in the particle s velocity x first emerged from macroscopic phenomenology. However it is now clear that its physical origin is as follows ... 

For all wavelength, t) shows coherent oscillations well beyond the 3 ps time mark. This contrasts with experimental results showing an exponential damping of the time correlation function within this time scale. Such a damping might be due to frictional damping or static disorder on the RCs. 

Cucchetti, A., Ying, S.C. Memory effects in the frictional damping of diffusive and vibrational motion of adatoms, Phys. Rev. B 1996, 54,3300. 

Figure 3. Amplitudes, x and x", of the in-phase and 90 -out-of-phase components of the steady-state displacement of a frictionally damped, massless spring driven by a sinusoidal force, Fq cos( wt).

Laminar fluid flow regime in which inertial effects become negligible compared with frictional damping. 

The Coulomb friction damping due to slip among the unbonded, debrmded and... 

Brownian dynamics obtain when the molecular system on the energy surface is subject to random impulses, as if from a solvent, and to a frictional damping term. In such a study of butane in water, sufficient transitions of the conformational barrier were obtained during the relaxation of an excess trans population to permit the evaluation of a rate constant. Kramers classical diffusion treatment is in agreement with these results. 

The mass of the base is measured to be 38 kg. The stifi iess of the linear springs attached coaxially with the sliding isolator is measured using servo-hydraulic testing machine. The stiffness of each of the springs is found to be 2.162kN/m. A nonlinear frictional damping is... 

COSMOSIM (Structural Research Analysis Corp., Santa Monica, CA) Provides finite element analysis with capabilities in interfaces that are for structural (static, dynamic, etc.), nonlinear (plasticity, friction, damping, etc.), materials (isotropic, orthotropic, etc.), elements (3-D beams, sandwich shells, springs, etc.), heat transfer (steady state, convection, etc.), design optimization (miniweight, stress constraints, etc.), and CAD interfaces and others. 

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