Chaotic vibrations of a magnet near a superconductor

The forced vibration of a small permanent magnet near the surface of a high temperature superconducting ceramic disc is shown to produce period doubling oscillations and chaos. The source of these anomalous vibrations is the nonlinear, hysteretic force between the magnet and the superconductor. These forces are believed to be related to flux pinning and flux dragging effects in the superconductor in the type II state. A return map, based on the displacement of the magnet, reveals a single hump polynomial function which under iteration exhibits a bifurcation structure similar to the experimental results.     

Chaotic vibrations of a vocal fold model with a unilateral polyp

A nonlinear model was proposed to study chaotic vibrations of vocal folds with a unilateral vocal polyp. The model study found that the vocal polyp affected glottal closure and caused aperiodic vocal fold vibrations. Using nonlinear dynamic methods, aperiodic vibrations of the vocal fold model with a polyp were attributed to low-dimensional chaos. Bifurcation diagrams showed that vocal polyp size, stiffness, and damping had important effects on vocal fold vibrations. An increase in polyp size tended to induce subharmonic patterns and chaos. This study provides a theoretical basis to model aperiodic vibrations of vocal folds with a laryngeal mass.     

Chaotic response of a limit cycle

External periodic modulation of a nonlinear oscillator may lead to chaotic behavior. This phenomenon is attributed to the existence of a strange attractor, which embodies essentially a folding motion as is met within the Bernoulli shift or the baker's transformation. The results obtained for the Brussels model are discussed from this viewpoint.     

Aerodynamic vibrations of a maglev vehicle running on flexible guideways under oncoming wind actions

This paper intends to present a computational framework of aerodynamic analysis for a maglev (magnetically levitated) vehicle traveling over flexible guideways under oncoming wind loads. The guideway unit is simulated as a series of simple beams with identical span and the maglev vehicle as a rigid car body supported by levitation forces. To carry out the interaction dynamics of maglev vehicle/guideway system, this study adopts an onboard PID (proportional-integral-derivative) controller based on Ziegler-Nicholas (Z-N) method to control the levitation forces. Interaction of wind with high-speed train is a complicated situation arising from unsteady airflow around the train. In this study, the oncoming wind loads acting on the running maglev vehicle are generated in temporal/spatial domain using digital simulation techniques that can account for the moving effect of vehicle's speed and the spatial correlation of stochastic airflow velocity field. Considering the motion-dependent nature of levitation forces and the non-conservative characteristics of turbulent airflows, an iterative approach is used to compute the interaction response of the maglev vehicle/guideway coupling system under wind actions. For the purpose of numerical simulation, this paper employs Galerkin's method to convert the governing equations containing a maglev vehicle into a set of differential equations in generalized systems, and then solve the two sets of differential equations using an iterative approach with the Newmark method. From the present investigation, the aerodynamic forces may result in a significant amplification on acceleration amplitude of the running maglev vehicle at higher speeds. For this problem, a PID+LQR (linear quadratic regulator) controller is proposed to reduce the vehicle's acceleration response for the ride comfort of passengers.     

Chaotic dynamics of flexible beams with piezoelectric and temperature phenomena

The Euler–Bernoulli kinematic model as well as the von Kármán geometric non-linearity are used to derive the PDEs governing flexible beam vibrations. The beam is embedded into a 2D temperature field, and its surface is subjected to action of the electric potential. We report how an increase of the exciting load amplitude yields the beam turbulent behavior, and how the temperature changes a scenario from a regular/laminar to spatio-temporal/turbulent dynamics. Both classical Fourier analysis and Morlet wavelets are used to monitor a strong influence of temperature on regular and chaotic beam dynamics.     

Destabilization of deep-water risers by a heaving platform

Offshore gas and oil fields are being discovered and exploited nowadays in water depths of more than 2000 m. In order to convey the hydrocarbon to the sea level, a steel slender pipe is installed between wellhead at the sea bed and floating platform. If used in deep waters, these pipes are commonly referred to as deep-water risers. The heave (vertical motion) of a floating platform induces a fluctuation in time of the axial tension of the riser. A possible and undesirable phenomenon is the excitation of a transverse riser vibration caused by this fluctuation. Owing to this fluctuation, the governing equation of transverse motion of the riser is a nonlinear partial differential equation containing a time-dependent coefficient. As a first step, this equation is linearized around the straight equilibrium, and stability of this equilibrium is investigated using the Galerkin method and the Floquet theory. Then, the dynamic equilibrium is studied that the riser reaches if its straight equilibrium is unstable. This is done using a numerical time-domain technique. Two qualitatively different mechanisms of stability loss are distinguished, discussed and exemplified. The first is classical parametric resonance that occurs solely due to periodic time variation of the axial tension. The second mechanism occurs if the amplitude of vibration of the platform is large enough to change tension into compression in a segment of the riser for a part of the vibration cycle. It is shown that the second mechanism can cause dangerously large dynamic stresses in the riser.     

Vibrational response of a moving suspension-slider loading system exciting a rotating flexible disk

To investigate the vibrational response of the magnetic read/write head in hard disk drives this paper models a rotating flexible disk excited by a moving suspension-slider system which is considered to be a mass-dashpot-spring loading system, with the initial unstressed transverse runout integrated into the rotating disk dynamic model. The slider motion on the disk surface is driven by the suspension rotating at a constant speed. By subtracting the steady-state deflection component from the instantaneous deflection response of the rotating disk system, the relative vibration transverse deflection of the slider caused by the motion of the suspension-slider loading system is obtained. The effects of the slider initial and final positions, speed of movement, the disk rotational speed, and the disk mode of the initial transverse runout on the maximum amplitude of the relative vibration deflection are analyzed.     

Open loop control of vortex-induced vibration of a circular cylinder

In this paper both numerical and experimental investigations have been carried out to suppress the vortex-induced vibration (VIV) of a circular cylinder in an electrically low-conducting fluid. The electromagnetic forces (Lorentz forces) in the azimuthal direction were generated through the mounted electrodes and magnets locally on the surface of the cylinder, which have been proved having an accelerating effect to the fluid on the surface of the cylinder. Results of computations are presented for synchronous vibration phenomenon of a cylinder at Re=200, which are in good agreement with previous computational results. With the Lorentz forces loaded, the VIV of the cylinder has been suppressed successfully. Experimental results have also shown the same tendency and are in reasonable agreement with the numerical results.     

Maximal violation of Bell's inequalities is generic in quantum field theory

Under weak technical assumptions on a net of local von Neumann algebras {A(O)} in a Hilbert space , which are fulfilled by any net associated to a quantum field satisfying the standard axioms, it is shown that for every vector state in there exist observables localized in complementary wedge-shaped regions in Minkowski space-time that maximally violate Bell's inequalities in the state . If, in addition, the algebras corresponding to wedge-shaped regions are injective (which is known to be true in many examples), then the maximal violation occurs in any state on () given by a density matrix.     

垂直载荷下颗粒物质的声波探测和非线性响应

对于玻璃珠组成的颗粒介质样品,本文测量了横波和纵波声速,同时分析了剪切模量(G)与体积模量(B)的比值(G/B)随压强的变化规律.结果表明,在低压强下,颗粒体系的纵波声速(C_L)明显大于横波声速(c_T),且体系的CL,CT及G/B均随压强p变化呈幂律标度,即CL∝p~(0.3817),CT∝p~(0.2809)G/B∝p~(-0.4539),幂指数与文献[1]中预言的-1/2非常接近,暗示在我们实验压强范围内的颗粒样品处于L玻璃状态.此外,本文还利用快速傅里叶变换法测量了玻璃珠样品中的声学衰减特性及二阶谐波随压强的变化,发现:纵波声衰减系数(α)、接收端二倍频振幅(μ_(2ω))与基频振幅(μ_(1ω))平方的比值(μ_(2ω)/μ_(1ω)~2)均随压强的增大而幂率减小,分别为α∝p~-(-0.1879),和μ_(2ω)/μ_(1ω)~2∝p~(-0.866).     

Thermoelastic vibrations of a semi-infinite strip

The forced vibrations of a thermoelastic strip (x₁ϵ [0, l], x₂ ⩾ 0) produced by a prescribed heating at the boundary x₂ = 0 are considered. The analysis is based on classical coupled thermoelastic theory (plane strain) and finite Fourier transforms. The solution of the problem under discussion is expressed in terms of the Lamé scalar and vector potentials.