Theory of scattering between two rigid rotors

The scattering problem for two rigid rotors is formulated. Expanding the potential into a series of bipolar harmonics and using the framework of helicity formalism we derive simple final formulae for practical use.     

Dynamic stability of rotating flexible disk perturbed by the reciprocating angular movement of suspension-slider system

To simulate the dynamic process of a magnetic head reading/writing data in a hard disk drive, a rotating flexible thin disk perturbed by the reciprocating angular movement of a suspension-slider system is modelled, where the suspension-slider system is considered as a mass-damping-spring loading system. A system dynamic model is formulated as a parametrically excited system, and its dynamic stability is studied by Hill’s method involving harmonic balance. The reciprocating angular movement of the suspension-slider system causes system parametric instability at some angular movement frequencies. The large-amplitude angular movement is especially dangerous, and angular movement frequency must be reduced when the slider works at large radii of the disk. The parametric instability can be avoided or suppressed by operating at: low-frequency and small-amplitude reciprocating angular movement, small mass, large natural frequency and damping of the suspension-slider system, and low-speed rotation of the disk.     

两连通气泡的平衡稳定性

针对气泡连通装置的平衡稳定性分析,引入"气泡坐标"概念,并采用最小能量法定量分析气泡初始状态对两连通气泡平衡稳定性的影响,准确解释了对此类问题的定性分析结果.同时,实验表明数值计算结果与实验测量结果之间误差极小,从而进一步验证了使用最小能量法分析气泡连通装置平衡稳定性的有效性与准确性.     

Secondary critical speed of flexible rotors with inertia slots

Rotors of two-pole generators have longitudinal slots for the electric windings and thus have dual flexural rigidity. Second order (or twice per revolution) forced vibrations are excited by the weight of the rotor and the problem of secondary critical speed, at half of the normal critical speed, arises. To overcome this difficulty transverse saw cuts or inertia slots are made in the pole faces in order to restore equality of the flexural rigidity of the rotor. In this paper, the critical speeds of rotors with inertia slots are calculated by using the transfer matrix method. The flexural rigidity of the element used in the transfer matrix method is determined by a three-dimensional finite element method. The secondary critical speeds of asymmetric rotors with inertia slots were measured experimentally thus demonstrating the validity of the present analysis.     

Dynamics and stability of rigid rotors levitated by passive cylinder-magnet bearings and driven/supported axially by pointwise contact clutch

A stable rotor—supported laterally by passive magnetic bearings and longitudinally by magnetic forces and a clutch—loses suddenly its contact to the clutch and executes abruptly longitudinal movements away from its original equilibrium position as a result of small increases in angular velocity. Such an abrupt unstable behaviour and its reasons are thoroughly theoretically as well as experimentally investigated in this work. In this context, this paper gives theoretical as well as experimental contributions to the problem of two dimensional passive magnetic levitation and one dimensional pointwise contact stability dictated by mechanical–magnetic interaction. Load capacity and stiffness of passive multicylinder magnetic bearings (MCMB) are thoroughly investigated using two theoretical approaches followed by experimental validation. The contact dynamics between the clutch and the rotor supported by MCMB using several configurations of magnet distribution are described based on an accurate nonlinear model able to reliably reproduce the rotor-bearing dynamic behaviour. Such investigations lead to: (a) clear physical explanation about the reasons for the rotor's unstable behaviour, losing its contact to the clutch and (b) an accurate prediction of the threshold of stability based on the nonlinear rotor-bearing model, i.e. maximum angular velocity before the rotor misses its contact to the clutch as a function of rotor, bearing and clutch design parameters.     

Modal balancing of flexible rotors with bow and distributed unbalance

Unbalance and bow are found to be one of the most common causes of synchronous machinery vibrations in rotating systems. Concentrated lumped mass models are adopted in most of the finite element approach for modeling unbalances and subsequent balancing in rotating systems. But this assumption may not be appropriate for long slender rotors with unbalances distributed along the length of the rotor. A polynomial curve for eccentricity distribution with finite element modeling is used to identify the distributed unbalance. The unbalance eccentricity distributions are estimated using the measured vibration responses at a speed below the balancing speed. Modal correction mass required to balance a rotor at its first bending critical speed, having both distributed unbalance and bow is computed knowing the amplification factor at critical speed. The rotor is balanced at its first bending critical speed using modal balancing method in a single trial run and using a single balancing plane. The method thus avoids multiple trial runs required for modal balancing of flexible rotors. This method is verified on an experimental rotor having both bow and unbalance. The concept of quantifying the distributed unbalance using ‘Norm’ of eccentricity polynomial function is also introduced for the first time.     

Entanglement between two atoms in two distant cavities connected by an optical fiber beyond strong fiber-cavity coupling

This paper investigates entanglement between two atoms in two distant cavities, which are connected by an optical fiber. We give an exact expression of the evolution of the whole system, and study the entanglement between the two atoms. We find that even the fiber-cavity coupling constant is smaller than the atom-cavity coupling constant, high degree entanglement between the two atoms is obtainable. This result gives a new prospect for experimental realization.     

Dynamic coupling between two paramagnetic spin species induced by resonant phonons

Results of paramagnetic relaxation studies conducted at ≈11 GHz and liquid helium temperature, involving lanthanum magnesium nitrate doped with Ce³⁺ and Pr³⁺ in spatially separated regions, are presented. The Ce transition alone was excited by fast passage, and the Pr paramagnetic resonance signal was observed. The spectral separation of the center frequencies of the two transitions, and the time during which the separation was maintained, could be independently adjusted. In this way both the temporal and spectral properties of the phenomenon could be studied.     

Aeroelastic stability of complete rotors with application to a teetering rotor in forward flight

The derivation of a set of non-linear coupled flap-lag-torsion equations of motion for moderately large deflections of an elastic, two-bladed teetering helicopter rotor in forward flight is concisely outlined. The following degrees of freedom are included in the mathematical model: rigid body flapping, rigid body lead-lag, elastic bending in flap and lead-lag, blade root torsion, and shaft torsion. Quasi-steady aerodynamic loads are considered and the effects of reversed flow are included. The aeroelastic stability of the complete rotor is investigated by using a linearized system of equations of motion. The equilibrium position about which the equations are linearized is obtained by considering the trim state of the helicopter, in true or simulated forward flight conditions. The sensitivity of the aeroelastic stability boundaries to interblade structural and mechanical coupling is illustrated by comparing the complete rotor stability boundaries with those obtained from a single blade analysis for a number of hover and forward flight cases.     

Non-Markovian transmission through two quantum dots connected by a continuum

We consider a transport setup that contains a double-dot connected by a continuum. Via an exact solution of the time-dependent Schrödinger equation, we demonstrate a highly non-Markovian quantum-coherence-mediated transport through this dot–continuum–dot (DCD) system, which is in contrast with the common premise since in typical case a quantum particle does not reenter the system of interest once it irreversibly decayed into a continuum (such as the spontaneous emission of a photon). We also find that this DCD system supports an unusual steady state with unequal source and drain currents, owing to electrons irreversibly entering the continuum and floating there.     

Dynamic fragmentation of solid particles interacting with a rigid barrier

Fragmentation of small solid particles as a result of collision with a rigid barrier is considered. It is shown that the application of the Griffith energy approach to dynamic fracture is characterized by specific surface energy differing from its value determined from static tests. The existence of the threshold fragmentation velocity is established and the method for its prediction is proposed. The method for experimental estimation of the fracture incubation time is also proposed.     

Analytical research on structural-acoustic coupling of a cavity surrounded by flexible panel

The structural-acoustic coupling characteristics, mechanisms, effect of structural-acoustic coupling on natural mode and natural frequencies of the system are analyzed theoretically and numerically. Formulae for the natural frequencies of the coupled system are derived. Some new conclusions are obtained. Analytical results demonstrate that the strongly coupled system indicates obvious closed-loop feedback characteristics, whereas the weakly coupled system indicates obvious feedforward characteristics, and it is because of the presence of the feedback loop that the natural characteristics and natural frequencies are changed. Cluster coupling characteristic between the structural and acoustic modes for the regular cavity and panel system is found, which determines the coupling interaction between the flexible panel and cavity. Any mode in one mode cluster only interferes the modes and the modal natural frequencies in the same cluster independently. The modal cluster coupling changes not only the natural frequencies of the system but also the modal order and structural mode shape.     

Dynamic stability of thermoelastic coupling moving plate subjected to follower force

The dynamic characteristics and stability of the moving thermoelastic coupling rectangular plate subjected to uniformly distributed tangential follower force are investigated. Based on the heat conduction equation containing the thermoelastic coupling term and the thin plate theory, the thermoelastic coupling differential equation of motion of the rectangular plate under the action of uniformly distributed tangential follower force is established. Dimensionless complex frequencies of the moving thermoelastic coupling rectangular plate with four edges simply supported, two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method. The effects of the dimensionless thermoelastic coupling factor and dimensionless moving speed on the stability and critical load of the moving plate are analyzed. The results show that the divergence loads of the first order mode increase with the increase of the dimensionless thermoelastic coupling factor, and decrease with increasing the dimensionless moving speed.     

Free vibrations of two rods connected by multi-spring-mass systems

This study deals with the longitudinal free vibrations of a system in which two rods are coupled by multi-spring-mass devices. The dynamics of this system are coupled through the motion of the masses. By using the transfer matrix method and considering the compatibility requirements across each spring connection position, the eigensolutions (natural frequencies and mode shapes) of this system can be obtained easily for different boundary conditions. The characteristic equation encompasses a function of the eigenvalues, the location of the spring connection positions, the ratio of the stiffness of the springs, the ratio of the lengths of the rods, the ratio of the sectional properties of the rods and the suspended masses. Some numerical results are presented to demonstrate the method proposed in this article.     

Interfacial enhancement of flexible PVC-silica composites by silane coupling agents

Enhancement of a flexible poly(vinyl chloride) (PVC)-silica composite interface was studied by the application of γ-aminopropyltrimethoxysilane on silica. Composites containing silica and silanized silica up to 25.6 phr (per hundred resin) and prepared by sol-gel technology were subjected to water and water vapor attacks similar to that in their daily use. Silane application resulted in diminishing liquid water and water vapor sorption by about 24.0% and 11.9%, respectively. Equilibrium weight gain values of the composites having different amounts of silica correlated well with a peak at 3400 cm^-1 in the IR spectra which was attributed to the stretching vibration of the O-H group of water. Liquid water and water vapor diffusivities in composites determined by the evaluation of weight gain against time data were about 0.4 x 10^-13 and 0.4 x 10^-12 m² s^-1, respectively. Inhibition of dioctyl phthalate (DOP) migration from composites by silane application was also determined as 24% using UV measurements. The most impressive merit of silane enhancement was observed as the retention of ultimate tensile strength (UTS) under wet conditions. While the untreated silica composite reduced its UTS by about 21.2%, silanized silica composite reduced its UTS by only about 13.6%, on wetting.     

Dynamic behaviour of in-line shear walls connected by floor slabs

Experimental and theoretical investigations are presented for two models consisting of pairs of in-line shear walls connected by floor slabs. The results are compared and recommendations made for the analysis of this type of structure.     

Resonance frequencies and stability of two flexible permanent magnetic beams facing each other

This paper aims at investigating the interaction of two flexible permanent magnet beams facing each other. The governing equations of motion are obtained based on the Euler–Bernoulli beam model along with Hamilton's principle. Assuming that the beams' tips are far enough, each magnet beam is considered as a series of dipole segments and the external force and moment distributions over each beam due to the magnetic field of the other one is calculated in the deformed configuration. The transverse deflections of the beams are written as series expansions of the mode shapes of an unloaded cantilever beam and the Galerkin method is applied to determine the stability and resonance frequencies. Using the obtained model, the stability regions of the beams for both cases of opposite poles and same poles facing each other are obtained. Also the effect of magnet's strength and flexibility of the beams on the stability boundaries are illustrated.     

Ground-state energy of a two level system with phonon coupling

The coupling of a two-level system to quantized boson modes has been the focus of many researchers for a number of years. Applications to exciton motion, molecular polaron formation, chaos in quantum systems as well as a number of other effects in condensed matter physics have also been studied. Here we investigate the interaction of bosonic modes with a two-level fermionic system. This quantum system is used as a testing ground for a recently developed Generalized Moments Expansion, GMX(m,n), of which the well-known Connected Moments Expansion (CMX) and Alternate Moments Expansion (AMX) are special cases. The convergence and viability of this scheme are discussed and comparisons are made with a related Canonical Sequence Method (CSM) as well as a Lanczos tridiagonal truncation scheme.