Statics of the Non-Rotating Structure

To assess and compare the performance of different configurations, it is sufficient to regard the static behavior of the non-rotating structure in conjunction with the voltage source driven actuator application, as discussed in Section 4.5. With the subsequently described restrictions, it is possible to derive an analytic solution. 

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To determine the equations of equilibrium as well as the constitutive relations of the beam, the principle of virtual work may be applied and its individual contributions be examined, respectively. Thus, the foundations for an analytic solution with regard to the statics of the non-rotating structure can be provided. Furthermore, the principle of virtual work will serve to set up the equations of motion in consideration of the dynamics of the rotating structure. This, in addition, requires the study of inertia effects and the inclusion of stiffening effects due to kinematic non-linearity with reference to relatively slender and flexible beams. The derivation of the principle of virtual work for the general case is presented in Section 3.4, and it will now be adapted and extended to depict adaptive thin-walled beams. Therefore, the various virtual work contributions will be discussed individually. 

The static behavior of the non-rotating structure will be examined by means of the properties outlined above. These can be summarized as follows ... 

In neutron scattering, the elastic part reflects the static correlations (Bragg peaks reveal the unit cell structure and the diffuse pattern shows the non-periodic, local disorder). The inelastic scattering is due to the periodic motions of atoms or ions (phonons) and the quasi-elastic scattering is caused by any kind of non-periodic motion (or magnetic disorder). The transition between low frequency periodic motions (translational and rotational oscillation) and diffusive motion (non-periodic) is not well understood. 

In this chapter, the binary mixture of GB particles of different aspect ratios has been studied by molecular dynamics simulation. The composition dependence of different static and dynamic properties has been studied. The radial distribution function has been found to show some interesting features. Simulated pressure and overall diffusion coefficient exhibit nonideal composition dependence. However, simulated viscosity does not show any clear nonideality. The mole fraction dependence of selfdiffusion coefficients qualitatively signals some kind of structural transition in the 50 50 mixture. The rotational correlation study shows the non-Debye behavior in its rank dependence. The product of translational diffusion coefficient and rotational correlation time (first rank) has been found to remain constant across the mixture composition and lie above the stick prediction. 

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