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Casimir energy in presence of a weak gravitational field is discussed taking into account the issues related to energy and its conservation in a curved background. It is well-known that there are inherent difficulties in defining energy in General Relativity, essentially due to its non-localizability. Using the concept of quasi-local mass and energy, it is shown that it is possible to attribute a Tolman mass to a massless scalar field confined to a Casimir cavity. Such non-local mass coincides - as expected - with the Casimir energy. The present approach offers an alternative derivation of the vacuum buoyancy force acting on a Casimir cavity, confirming the results presented by Calloni {\em et al.} in a series of papers devoted to explore the possibility of experimentally weighting the Casimir vacuum (the so-called Archimedes Experiment)., Comment: 20 pages. Accepted in Class. Quantum Grav

In this work, we consider a Casimir apparatus that is put into free fall (e.g., falling into a black hole). Working in 1+1D, we find that two main effects occur: First, the Casimir energy density experiences a tidal effect where negative energy is pushed toward the plates and the resulting force experienced by the plates is increased. Second, the process of falling is inherently nonequilibrium and we treat it as such, demonstrating that the Casimir energy density moves back and forth between the plates after being "dropped,'' with the force modulating in synchrony. In this way, the Casimir energy behaves as a classical liquid might, putting (negative) pressure on the walls as it moves about in its container. In particular, we consider this in the context of a black hole and the multiple vacua that can be achieved outside of the apparatus., 18 pages, 5 figures

The two main sources of internal friction in a rotor-shaft system are the shaft structural hysteresis and the possible shrink-fit release of the assembly. The internal friction tends to destabilize the over-critical rotor running, but a remedy against this effect may be provided by a proper combination of some external damping in the supports and an anisotropic arrangement of the support stiffness, or at most by the support damping alone, depending on the system geometry. The present analysis reported here considers a general asymmetric rotor-shaft system, where the rotor is perfectly rigid and is constrained by viscous–flexible supports having different stiffnesses on two orthogonal planes. The internal friction is modelled by nonlinear Coulombian forces, which counteract the translational motion of the rotor relative to a frame rotating with the shaft ends. The nonlinear equations of motion are dealt with using an averaging approach based on the Krylov-Bogoliubov method with some adaptation to address the multi-degree-of-freedom nature of the problem. Stable limit cycles may be attained by the overcritical whirling motions, whose amplitudes are inversely proportional to the external dissipation applied by the supports. A noteworthy result is that the stiffness anisotropy of the supports is recognized as beneficial in reducing the natural whirl amplitudes, albeit mainly in the symmetric configuration of the rotor at the mid span and, to a rather lesser extent, in the asymmetric configuration, which then requires a stronger damping action in the supports.

The three main requirements of a vehicle-trailer connection system are: en route stability, over- or under-steering restraint, minimum off-tracking along curved path. Linking the two units by four-bar trapeziums, wider stability margins may be attained in comparison with the conventional pintle-hitch for both instability types, divergent or oscillating. The stability maps are traced applying the Hurwitz method or the direct analysis of the characteristic equation at the instability threshold. Several types of four-bar linkages may be quickly tested, with the drawbars converging towards the trailer or the towing unit. The latter configuration appears preferable in terms of self-stability and may yield high critical speeds by optimising the geometrical and physical properties. Nevertheless, the system stability may be improved in general by additional vibration dampers in parallel with the connection linkage. Moreover, the four-bar connection may produce significant corrections of the under-steering or over-steering behaviour of the vehicle-train after a steering command from the driver. The off- tracking along the curved paths may be also optimized or kept inside prefixed margins of acceptableness. Activating electronic stability systems if necessary, fair results are obtainable for both the steering conduct and the off-tracking.

The internal friction due to the shaft hysteresis or the shrink fitting release exerts a destabilizing effect on the overcritical rotor whirl, but may be counteracted by other external dissipative sources and/or by proper anisotropy of the support stiffness. The internal friction effect may be treated by either dry or viscous models, obtaining similar results in the hypothesis of small dissipation levels, provided that proper equivalence criteria are defined between the two approaches. The equivalence is here stated by imposing the same energy dissipation over a large number of shaft revolutions. Approximate closed-form autonomous solutions for a symmetric rotor arrangement subject to Coulombian non-linear friction are derived by an averaging approach of the Krylov-Bogoliubov type, in order to ascertain the result similarity between the two dissipative assumptions. Summing up, the viscous equivalent linear assumption appears conservative in general and may be accepted for a straightforward analysis of the overall rotor dynamics in the whole speed range.

The mechanical response of pneumatic artificial muscles is analyzed assuming the inextensibility of the sheathing braids and taking into account the stress field inside the rubber bladder, which is regarded as a Mooney-Rivlin hyperelastic material. The end effects are simulated by heuristically profiling the meridian section. After estimating the constitutive parameters by traction tests on rubber specimens, the theoretical results are compared with experiments and a satisfactory accordance may be detected.

Horizontal rotor systems on lubricated journal bearings may incur instability risks depending on the load and the angular speed. The instability is associated with the asymmetry of the stiffness matrix of the bearings around the equilibrium position, in like manner as the internal hysteretic instability somehow, where some beneficial effect is indeed obtainable by an anisotropic configuration of the support stiffness. Hence, the idea of the present analysis is to check if similar advantages are also obtainable towards the oil film instability. The instability thresholds are calculated by usual methods, such as the Routh criterion or the direct search for the system eigenvalues. The results indicate that the rotor performances may be improved in the range of low Sommerfeld numbers by softening the support stiffness in the vertical plane, and hardening it on the horizontal one, up to the complete locking, though this advantage has to be paid by rather lower instability thresholds for large Sommerfeld numbers. Nevertheless, a "two-mode" arrangement is conceivable, with some vertical flexibility of the supports for large journal eccentricity, and complete locking for small eccentricity. As another alternative, the support anisotropy may be associated with the use of step bearings, whose particular characteristic is to improve the stability for small eccentricities.

Starting from a previous model for the shift mechanics of rubber belt variators, this lecture elaborates practical design formulas for the torque and the axial thrust making use of the very close resemblance of the belt path to a linear spiral of Archimedes along a large part of the arc of contact. In addition, as an alternative to the modern calculus tools, it is shown how the drive variables can be equally calculated applying some propositions of Archimedes’ classical treatise πeρί ‘eλίκων (On Spirals).

The mechanical behavior of V-belt variators during the speed ratio shift is different from the steady operation as a gross radial motion of the belt is superimposed to the circumferential motion. The theoretical analysis involves equilibrium equations similar to the steady case, but requires a re-formulation of the mass conservation condition making use of the Reynolds transport theorem. The mathematical model of the belt-pulley coupling implies the repeated numerical solution of a strongly non-linear differential system. Nevertheless, an attentive observation of the numerical diagrams suggests simple and useful closed-form approximations for the four possible working modes of any pulley, opening/closing, driver/driven, whose validity ranges over most practical cases. The present analysis focuses on the development of such simplified solutions, succeeding in an excellent matching with the numerical plots, and on the comparison of the theory with some experimental tests on a motorcycle variator, revealing a very good agreement.Copyright © 2009 by ASME

International audience; In this paper we study the Josephson tunneling for a quantum fluid (a Bose-Einstein condensate) in presence of a weak gravitational wave. Starting from a lagrangian formulation in the framework of linearized gravity, we deduce the Gross-Pitaevskii equation for the fluid in a weak gravitational background. We use such equation to investigate the influence of a gravitational wave on Josephson effect. Considering a double-well trap, made of two identical boxes placed orthogonally each other and weakly coupled through a small junction, we show how the trap geometry influences the coupling between the gravitational wave and the quantum field modes in the two sides of the trap. Namely, the macroscopic wavefunction of the condensate acquires a different phase shift in the two sides, hence giving rise to a gravitationally-induced ac-Josephson effect through the trap junction. Although small, such effect is theoretically interesting, since it represents the influence of a gravitational wave on a mesoscopic quantum system. Also, the effect exhibits polarimetric properties. Possible experimental detection of such effect is briefly discussed at the end of the paper.