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The present analysis deals with the ground taxiing of aircrafts and considers, in particular, their turning at rather low speed with very small path radii among obstacles that may be very close to each other, for example inside the hangars or on the flight decks of the aircraft carriers where other planes stand stationary. To succeed in this operation, it is crucial to optimize the path and avoid dangerous collisions or, more generally, the interference in the ground projection between the obstacles and the band enclosing all the point trajectories of the plane. The essential innovation here proposed for this purpose consists in making all the wheels of the undercarriage steerable, assuming electrically motorized struts, and in searching for the best correlation among the steering angles in order to optimize the path. The geometrical and dynamical nonlinearities due to the relatively large steering angles, to the changes of the cornering stiffness with the vertical loads on the wheels and to the inertial and the aerodynamic forces will be included in the analysis. The rollover critical speeds will be calculated on varying the path radius.

When designing articulated tractor-trailer systems, engineers should take care to contrast some undesired phenomena associated with the lateral dynamics: the path off-tracking, namely the trajector...

Comparing with the tractor-trailer systems for the road haulage, which must cope with some typical undesired trends, such as high-speed instability, over- or under-steering and off-tracking, the multi-trailer systems for the transport of luggage in the airports or in the railway stations, or for the transfer of goods in the warehouses, run at quite low speeds, but must manage to steer clear of the many obstacles encountered along their path. This type of vehicle is not subject to tire cornering phenomena, because the speed is just low and the wheels are generally stiff. Hence, the vehicle movement is in practice ruled by the non-holonomic rolling constraint of the wheels and by the steering device mounted on the trailers, which may consist in drawbars integrated with the front axles and rotating around a central pin (dolly-semitrailer systems), or else in roulettes set back with respect to their vertical connection pins to the trailer chassis (caster-trailer systems). The present analysis addresses all the interconnected aspects of the mechanical behaviour of these types of multi-trailer systems in an organic whole, starting from the kinematical analysis of the possible paths and their stability, giving guidelines for the proper layout of the vehicle units to eliminate the steady off-track, and ending with the calculation of the traction forces through the various links and the road forces at the ground prints, in order to gain information useful to check the stress state of the various structural elements.

We discuss the process of particle creation in the case of a scalar quantum field confined to a small cavity, initially at rest, which is suddenly dropped in a static gravitational field. We show that, due to the transition from a Schwarzschild to a Minkowski background, as perceived by a comoving observer, field particles are excited out of the quantum vacuum. The density of the created quanta depends on the proper gravitational acceleration as well as on a parameter α≃1/Δt, with Δt representing the typical time duration of the transition. For the specific acceleration profile considered, the energy spectrum of the created quanta roughly resembles a two-dimensional Planckian distribution, whose equivalent temperature mimics the Hawking-Unruh temperature, with the detector acceleration (or the black hole surface gravity) replaced by the parameter cα. We briefly comment on possible issues related to local Lorentz symmetry.

In Cosmology and in Fundamental Physics there is a crucial question like: where the elusive substance that we call Dark Matter is hidden in the Universe and what is it made of? that, even after 40 years from the Vera Rubin seminal discovery [1] does not have a proper answer. Actually, the more we have investigated, the more this issue has become strongly entangled with aspects that go beyond the established Quantum Physics, the Standard Model of Elementary particles and the General Relativity and related to processes like the Inflation, the accelerated expansion of the Universe and High Energy Phenomena around compact objects. Even Quantum Gravity and very exotic Dark Matter particle candidates may play a role in framing the Dark Matter mystery that seems to be accomplice of new unknown Physics. Observations and experiments have clearly indicated that the above phenomenon cannot be considered as already theoretically framed, as hoped for decades. The Special Topic to which this review belongs wants to penetrate this newly realized mystery from different angles, including that of a contamination of different fields of Physics apparently unrelated. We show with the works of this ST that this contamination is able to guide us into the required new Physics. This review wants to provide a good number of these “paths or contamination” beyond/among the three worlds above; in most of the cases, the results presented here open a direct link with the multi-scale dark matter phenomenon, enlightening some of its important aspects. Also in the remaining cases, possible interesting contacts emerges. Finally, a very complete and accurate bibliography is provided to help the reader in navigating all these issues, The original research described in this work has been partially funded by INFN through the IS QGSKY

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

A crucial problem of turbomachinery is the oil film instability on increasing the angular speed, which is correlated with the asymmetry of the bearing stiffness matrix and resembles the hysteretic instability somehow. As a beneficial effect is exerted on the latter by the anisotropy of the support stiffness, some favorable effects have been recently found by the author also for the former, whence a systematic analysis has been undertaken. The instability thresholds may be detected by the usual conventional methods, but a detailed analysis may be carried out by closed-form procedures in the hypothesis of symmetry of the rotor-shaft-support system, which condition approaches the real working of turbomachines quite often. Altogether, the results point out an improvement of the rotor stability for low Sommerfeld numbers by softening and locking the support stiffness in the vertical and horizontal directions, respectively. Nonetheless, the partial support release on one plane implies lower instability thresholds for large Sommerfeld numbers, but this drawback may be obviated by a sort of “two-mode” stiffness management, with some vertical flexibility for heavy loads and full blocking for light loads. Otherwise, it is possible to combine the anisotropic supports with journal bearing types that offer favorable stability behavior in the range of large Sommerfeld numbers. Basing on approximate but realistic models, the present analysis elucidates the changes of the rotor-shaft unstable trend on varying the external stiffness of the supports and gives tools for a rapid calculation of the expected instability thresholds.

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

When planning the road vehicles for the transport of passengers or goods, engineers should take care to contrast some undesirable phenomena in the lateral dynamics, such as high-speed instability or off tracking. While the former is less troubling in the slow heavy vehicles, the latter is a serious problem due to the risk of invading the neighbouring lanes. The use of multi-wheel steering may completely cancel this drawback and, pursuing an optimized correlation among the steering angles, a functional inter-dependence based on the cubic “witch of Agnesi” is found to be very promising. Simple control systems with electromechanical or electronic components may be easily implemented for the mutual interlocking of the steering angles.

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.

In this paper, the figure of Elia Ovazza, professor of TMM in Palermo around the end of the 19th century, is presented, along with his valuable legacy in regard to his activities in teaching, research, design and technology transfer. Short biographical notes outline his foremost life events and an illustrated survey explains his contributions.

The internal friction of a rotor–shaft-support system is mainly due to the shaft structural hysteresis and to some possible shrink-fit release of the assembly. The experimentation points out the destabilizing effect of the internal friction in the over-critical rotor running. Nevertheless, this detrimental influence may be efficiently counterbalanced by other external dissipative sources located in the supports or by a proper anisotropic configuration of the support stiffness. The present analysis considers a rotor–shaft system which is symmetric with respect to the mid-span and is constrained by viscous-flexible supports with different stiffness on two orthogonal planes. The cylindrical and conical whirling modes are easily uncoupled and separately analysed. The internal dissipation is modelled by nonlinear Coulombian forces and moments, which counteract the translational and rotational motion of the rotor relative to a frame rotating with the shaft ends. The nonlinear equations of motion are solved by averaging approaches of the Krylov–Bogoliubov type. In both the over-critical whirling motions, cylindrical and conical, stable limit cycles may be attained whose amplitude is as large as the external dissipation applied by the supports is low. The stiffness anisotropy of the supports may be recognised as quite beneficial for the cylindrical whirl.

We discuss the Casimir effect in a small cavity, moving in a circular orbit around an Ellis wormhole. We show that the interplay between the spacetime geometry and the cavity orbital motion gives rise to a distortion in the Casimir energy density, causing a reduction of its absolute value. Quite interestingly, such effect can be observed also when the cavity moves on a circular geodesic (albeit unstable) orbit at the wormhole throat, where a comoving observer becomes locally inertial (namely, the observer’s reference frame reduces to a geodesic, Fermi-Walker transported one). In that respect, the discussed effect appears as a nonlocal quantum effect by means of which some properties of the underlying spacetime geometry, hidden to local classical measurements, can be captured and unveiled.

In this paper we discuss the Casimir effect in a small cavity at rest in the weak gravitational field of a massive, non-rotating source. We propose a new approach, based upon Schwinger’s effective action method, showing that the gravitational interaction induces a small correction in the vacuum energy density, in full agreement with the result we obtained in a previous work (Sorge 2005 Class. Quantum Grav. 22 5109), following a standard field mode decomposition technique. The present result reinforces the belief that gravity can indeed be effective in modifying the vacuum energy of a quantum field confined to the cavity, against the recent claim appeared in Lima et al (2019 J. Cosmol. Astropart. Phys. JCAP07(2019)11) that a weak gravitational field has no influence on the Casimir energy.

This book treats several subjects from the History of Mechanism and Machine Science, and also contains an illustrative presentation of the Museum of Engines and Mechanisms of the University of Palermo, Italy, which houses a collection of various pieces of machinery from the last 150 years. The various sections deal with some eminent scientists of the past, with the history of industrial installations, machinery and transport, with the human inventiveness for mechanical and scientific devices, and with robots and human-driven automata. All chapters have been written by experts in their fields. The volume shows a wide-ranging panorama on the historical progress of scientific and technical knowledge in the past centuries. It will stimulate new research and ideas for those involved in the history of Science and Technology

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 destabilizing influence of the internal friction on the supercritical rotor whirl can be efficiently counterbalanced by other external dissipative sources and/or anisotropic suspension systems. The theoretical approach may take the internal dissipation into consideration either by dry or viscous models. Nevertheless, several numerical results and a new perturbation technique of the averaging type prove that similar rotor motions and stability limits are achievable by both models, whence the linear viscous assumption appears preferable. Thus, the internal hysteretic force may be expressed by the product of an equivalent viscous coefficient and the rotor centre velocity relative to a reference frame rotating with the shaft end sections. After calculating the natural frequencies and the response to dynamic imbalances, the stability of the steady motion is checked by the Routh-Hurwitz criterion, focusing the analysis on the individual influence of several characteristic properties, like the gyro structure, the stiffness anisotropy of the supports and their asymmetry, and searching for the external damping level needed for stability. A fairly interesting result is that the benefit of the suspension anisotropy is most effective for a symmetric rotor mounted at the shaft mid-span and decreases significantly on increasing the configuration asymmetry, even moderately. It is also observed how the stability may somehow be associated with the coupling between progressive and retrograde precession motions.

Most of the undesired whirling motions of rotating machines can be efficiently reduced by supporting journal boxes elastically and controlling their movement by viscous dampers or by dry friction surfaces normal to the shaft axis, which rub against the frame. In the case of dry dampers, resonance ranges of the floating support configuration can be easily cut off by planning a motionless adhesive state of the friction surfaces. On the contrary, the dry friction contact must change automatically into sliding conditions when the fixed support resonances are to be feared. Moreover, the whirl amplitude can be restrained throughout the speed range by a proper choice of the suspension-to-shaft stiffness ratio and of the support-to-rotor mass ratio. This theoretical research deals firstly with the natural precession speeds and looks for Campbell plots in dependence on the shaft angular speed, for several rotor-suspension systems. Then, the steady response to unbalance is investigated, in terms of rotor and support orbits and of conical path of the rotor axis. In this search, the ranges of adhesive or sliding contact are identified in particular for system with dry friction damping. At last, the destabilizing influence of the shaft hysteresis in the supercritical regime is focalized and the counterbalancing effect of the other dissipative sources is verified. In the nonlinear case of dry friction dampers, the control of linear stability is fulfilled by a perturbation procedure, checking the magnitude of Floquet characteristic multipliers on the complex plane. Moreover, the nonlinear stability far from steady motion is tested by the direct numerical solution of the full motion equations. The comparison configuration of suspension systems with viscous dampers and no dry friction is examined through an analytical first approximation approach and closed-form results for stability thresholds are derived in particular for the symmetric case.

An efficient and automatic attenuation technique for the whirling motion of rotating machinery can be achieved by supporting the journal boxes elastically and providing them with suitable rubbing surfaces subject to dry friction normal to the shaft axis. The critical flexural speeds are easily cut off and the whirl amplitude is minimized throughout the frequency range. Confining the usual operative angular speed of the rotor in the range of adhesive contact between the dry friction surfaces, there is no significant increase of power dissipation or heat production as a whole due to this type of suspension system, whose task is just to suppress the resonant peaks when passing the critical speeds. Moreover, the wear of the rubbing surfaces can be easily compensated by use of suitable spring loading systems for the friction contact. The dry friction damping is also compared with an equivalent viscous damping, where the equivalence has to be understood in terms of work dissipated per single revolution of the rotor. As for other conventional cases, the shaft hysteresis is found to exert a destabilizing effect above the first critical speed, which however can be compensated by the other dissipation sources. The system stability is here studied perturbing the periodic motion and applying the Floquet theory.

We propose a new approach to the study of spin-flip probability for massive Dirac neutrinos orbiting around a Schwarzschild black hole, recently considered by Dvornikov (2006 Int. J. Mod. Phys. 15 1017). Inspired by the paper by Papini and Lambiase (2002 Phys. Lett.A 294 175), we employ a reference frame comoving with the particle in the curved spacetime background. Using a suitable tetrad adapted to a comoving observer, we discuss the gravito-inertial effects (curvature plus spin rotation or Mashhoon effect) on the massive neutrino spin-flip probability. At variance with some recent claims, we find non-null results, in very good agreement with those obtained in [19], although through quite a different approach. Such results suggest a sort of competition between gravity and inertia. Taking into account the possible anomalous magnetic moment μν of a massive Dirac neutrino, we also briefly consider the interplay between gravito-inertial and magnetic effects, in the presence of some external strong magnetic field in the Schwarzschild geometry (which is believed to be a typical scenario in the case of Active Galactic Nuclei (AGN) or neutron stars). We find some evidence that the actual poor knowledge about the bounds on μν cannot rule out the possibility of some relevant competition between the two effects.

We deduce the explicit form of a phase-locked (PL) tetrad, adapted to a small spinning particle (a test gyroscope) following an arbitrary geodesic orbit in the Schwarzschild geometry of a gravitational source. We subsequently obtain the analytic expression of the gyroscopic precessional velocity Ω in a non-circular orbit, by means of the Fermi rotation coefficients related to the tetrad’s transport law. As an application, we compute the orbital shift in the spin vector, considering a spinning test particle (the gyroscope) in a slightly non-circular orbital motion in the weak gravitational field limit. We compare our results with those of other previous works.

Measuring the passage of time has intrigued humankind throughout the centuries. Ancient times witnessed the appearance and development of clepsydras and water clocks, whose place was subsequently taken by mechanical clocks in the Middle Ages. It is really surprising how the general architecture of mechanical clocks has remained almost unchanged in practice up to the present time. Yet the foremost mechanical developments in clock-making date from the 17th century, when the discovery of the laws of pendular isochronism by Galilei and Huygens permitted a higher degree of accuracy in the measuring of time.

We investigate the Dynamical Casimir Effect (DCE) in the case of a scalar field enclosed in a box which undergoes a phase of strong acceleration (a kick) during its motion. Following a general-relativistic approach, we describe the acceleration field as a time-dependent space–time metric in the frame of a comoving, noninertial observer. Assuming a nonrelativistic motion of the box, we perturbatively solve the Klein–Gordon equation for the matter field, evaluating the β-Bogolubov coefficients, related to the particle creation. We show that, after the kick, a (small) number of created quanta is found inside the box. The resulting spectrum carries, in principle, information about the details of the box acceleration phase. The present approach can serve to shed light on the close relationship between DCE and Unruh–Hawking effect.

We investigate the effects of a weak gravitational wave, modelled as a gaussian wavepacket, on the polarization state of an electromagnetic field enclosed in a cavity. Our approach is semiclassical, in that the electromagnetic field is described as a quantum field, while the gravitational perturbation is treated classically, as a slightly curved background spacetime. Assuming that before the interaction the electromagnetic field has been prepared in a given polarization state, we show that – due to the gravitational scattering with the wave – some photons having different polarization states are found in the cavity at late times. Such polarization scattering has some resemblance with Thomson scattering, well-known in Quantum Electrodynamics: hence the motivation for the title. We give a numerical estimate of the resulting photon polarization spreading in the case of a typical gravitational burst from a final supernova rebound. We also briefly comment about the possible influence of such gravitational scattering on the Cosmic Microwave Background (CMB) polarization.

We study the Casimir vacuum energy density for a massless scalar field confined between two nearby parallel plates (a cavity) in a slightly curved, static spacetime background, employing the weak-field approximation. Following an order-by-order perturbative approach, we evaluate the gravity-induced correction to Casimir energy. We find evidence for a small shift in the (negative) vacuum energy. As a consequence, the (attractive) force between the cavity walls is expected to weaken. Although derived in the weak-field approximation, and too small to be detected with the current technology, such gravitationally induced shift in vacuum energy seems nevertheless interesting from a theoretical point of view, since it might play a role in a cosmological scenario (e.g., gravitational influence on the Λ-term) as well as at a microscopic level (quark confinement) in strong gravitational fields. Finally, the analysis of the possible gravitational effects on Casimir cavities faces the open issue concerning the limits of validity of general relativity at small distances.

In this paper, we consider the effects of a magnetic field on the dynamics of the early universe. As predicted by Matravers and Tsagas (2000 Phys. Rev. D 62 103519) we find that the coupling between spatial curvature and primordial magnetic field permeating a perfectly conducting barotropic fluid can inhibit the accelerated expansion but may also induce acceleration in a variety of cases not considered in the above paper.

We study the motion of magnetized particles near a rotating black hole. The main result is that the spacetime curvature and electromagnetic field conspire to allow for the existence, inside the ergosphere, of stable circular orbits occupied by particles with negative total energy and angular momentum. Since these particles would never populate stable orbits were they not magnetized, a large binding energy is required to let them exist. A simple model of a magnetized belt in the ergosphere of a massive black hole with a strong magnetic field, shows that it can store a binding energy as high as 1054 erg, an amount comparable with the energy detected in gamma ray bursts. Besides the above astrophysical considerations, this paper contains a formal deduction, from an appropriate Hamiltonian, of the equations of motion of a neutral and magnetized fluid made of spinless dust particles interacting with a magnetic field. This analysis does not appear to have been done before.

We study the motion of a magnetized particle orbiting around a supermassive Schwarzschild black hole, surrounded by a strong (asymptotically uniform) magnetic field. Using the Hamilton–Jacobi formalism, we solve in a fully analytical way the problem of finding the innermost circular orbits. We show that, for suitable values of the parameters controlling the magnetic interaction, these orbits may become stable near r = 3M, hence giving rise to a possible mechanism for particle confinement and energy storage. We argue that any sudden change in the above parameters could allow for abrupt release of large amounts of energy from such innermost orbits.

The mechanical response of pneumatic artificial muscles is analyzed in transient and periodic conditions, assuming the inextensibility of the sheathing fibres and considering the influence of the texture geometry, of the dissipation due to the mutual sliding between the braids and of the stress field inside the bladder thickness, where the constituent elastomer is regarded as a two-parameter Mooney–Rivlin material. The polytropic exponent of the thermodynamic air evolution inside the muscle during the charging and discharging phases may be properly chosen depending on the working frequency. The muscle end shape is taken into account profiling the meridian section by a simple m-degree parabolic law. The estimate of the mechanical and geometrical parameters of each individual muscle permits simulating its response in several unsteady operations and identifying its hysteretic behaviour under periodic pressure excitation. The comparison with several experimental results present in the literature shows a very acceptable agreement.

We study the behaviour of a small gyroscope moving on a circular trajectory in the field of a weak gravitational plane wave. In order to monitor the precessional velocity we introduce an observer comoving with the gyroscope and an observer-adapted frame optically defined by means of light rays and not Fermi-Walker transported. From such a frame we infer some physical information about the gravitational-wave-induced frame dragging, which the observer will detect looking at the small perturbations on the gyroscopic precession. We find evidence of gyroscope sensitivity to the polarization state of the gravitational wave. As expected, the general relativistic precession of the compass of inertia and the `memory effect' which are discussed in this paper are very small and hardly detectable with modern technology; however, they are operationally well defined and therefore not ignorable for future considerations.

Solving the Klein-Gordon equation for a free scalar field in a curved spacetime in the weak-field approximation we rederive the results of Gibbons et al: no particle creation from the interaction between scalar fields and gravitational waves. We show, however, that particle creation would really occur when the matter field is constrained in space by some boundaries. Such an effect is likely to be related to the uncertainty principle, in connection with a sort of dimensional reduction (as in the Kaluza-Klein theory) that causes the field to acquire a mass term, also responsible for conformal symmetry breaking in a spatially flat FRW spacetime. Although derived in the weak-field approximation, the results seem also to be reasonably valid in the presence of exact gravitational waves.

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.

The internal friction associated with the shaft hysteresis or with the possible release of some shrink-fit coupling exerts a destabilizing effect on the over-critical rotor running, but may be efficiently counteracted by other external dissipative sources or by a proper anisotropic configuration of the support stiffness. The present analysis considers a symmetric rotor-shaft system on viscous-flexible supports with different stiffness on two orthogonal planes containing the bearing axis. The internal friction of the shaft is described either by a linear hysteretic model or by a nonlinear Coulombian force contrasting the rotor motion relative to the shaft ends. The nonlinear equations of motion are solved using an averaging approach of the Krylov–Bogoliubov type, which yields the steady orbit depending on the support dissipation applied to damp the whirl motion, for various working conditions. The beneficial influence of the support stiffness anisotropy is clearly identified.

Simple formulas can relate axial thrust and torque of rubber V-belt drives, taking into consideration the radial penetration of the belt.

A simplified formulation is adopted for the theoretical problem of tension distribution and radial penetration of a V-belt along the pulley groove. The trajectory portrait of the second order differential system describing the belt behavior is carefully analyzed and asymptotic approximations for the tension solutions are derived which are well suited for design purposes.

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.

Turbocompressor surge in a line with a long suction duct and plenum chamber is analysed using a distributed parameter propagation model which accounts for dynamic damping. The results, though obtained with simplifying assumptions, show very good agreement with experimental data.

The rotary aero engine is a special type of air-cooled radial engine, where the cylinders are arranged like the spokes of a wheel and turn around the crankshaft. The propeller is connected to the cylinders, while the crankshaft is fixed to the frame. The rotary aero engine, developed in 1908, set new standards of power and light weight within the aircraft industry. It was adopted by many pioneer aviators and widely used to set records of endurance, speed and height. Many aero engine manufacturers produced different models and variants of this type of engine, which was extensively used until the end of the First World War. The latest evolution of the rotary engine was the counter-rotary arrangement, which was devised and designed by the Siemens-Halske company. The distinctive feature of this type of engine was that the engine body (with cylinders and propeller) rotated in one direction while the crankshaft rotated in the opposite one. This result was obtained by using a bevel gear mechanism. However, rotaries were quickly and definitively replaced in 1918 by new kinds of conventional engine, which were developed in the same period by other manufacturers. The main features of rotary and counter-rotary aero engine and the performance limits that caused their decline will be described in this paper. The rotary engine will be compared with the conventional one in terms of power output, specific consumption, weight and inertia loads transferred to the frame.

This paper deals with a new pneumatic control strategy for the roll damping enhancement of marine U-tank stabilizers. The proposed technique consists in a three-mode operation, where the control is active only within a limited resonant range around the ship natural frequency, whereas the control valves are kept closed in the remaining frequency range. Moreover the connection valve between the two air chambers is either closed or partially opened for the low or high frequencies, respectively. The pressurized air for the active control is fed by a turbo-blower set aboard and operates accelerating the motion of the water mass in the U-duct. The theoretical analysis is conducted in the hypothesis of harmonic excitation and includes an equivalent linearization procedure for the turbulent air flow through the upper valve regulating the efflux from the one to the other tank. The application of the laws of thermodynamics to the open air system overhanging the water in each tank chamber reveals the negligibility of the heat transfer through the tank wall in comparison with the mass transfer effects. As a practical result, the mathematical model permits developing a suitable optimization process with the aim at the best damping operation, which however must be subjected to two fundamental constraints: the system stability and the pre-imposed limit power absorbable from the control equipment. Comparing with natural damped passive systems, a reduction of the order of 20–40% can be roughly attained for the resonant roll amplitude, depending on the supplied control power.

A very common configuration of V-belt variators for motorcycles considers the correction of the belt tensioning depending on the resistant torque by means of suitable helical-shaped tracks allowing the driven half-pulleys to close/open. The theoretical model for belt-pulley coupling is rather complex for this configuration, where one half-pulley may run in advance and the other one behind with respect to the belt, and requires the repeated numerical solution of a strongly nonlinear differential system by a sort of shooting technique, until all the operating conditions are fulfilled (angular contact extent, torque, and axial force). After solving the full equations, the present study develops closed-form approximations, which are characterized by an excellent correspondence with the numerical plots, and suggests a simple and practical formulary for the axial thrust as a function of the torque and of the tension level. Then, the results of a theoretical–experimental comparison are also reported, and they indicate a fine agreement between the model and the real operation.

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).

A new technique for the rotor whirl damping in rotating machinery, based on the elastic suspension of the journal boxes and the use of dry friction surfaces normal to the shaft axis between their supports and the frame, is here analysed theoretically for several cases of rotor systems characterized by mass and constraint asymmetry, where gyroscopic effects are to be expected and conical whirl motions may grow up. The critical flexural speeds can be easily cut off by an adhesive state of the supports and the whirl amplitude can be minimized as well throughout the remaining sliding range. Confining the operative angular speed of the rotor in the range of adhesive contact between the dry friction surfaces, no significant increase of power dissipation or heat production has to be ascribed as a whole to this type of suspension system, whose task is just to suppress the resonant peaks when passing the critical speeds. On the other hand, the rubbing surface wear can be easily compensated in the long run by use of suitable spring devices to close the friction contact. The uniqueness and the stability of the steady motion are proved, both in the absence and in the presence of possible additional viscous sources of dissipation. It is also shown how the destabilizing influence of the shaft material hysteresis can be counterbalanced by the other external dissipative forces. r 2008 Elsevier Ltd. All rights reserved.