Amplitude Plane Research Articles

Nonequilibrium Phase Transition in Spin-S Ising Ferromagnet Driven by Propagating and Standing Magnetic Field Wave

The dynamical response of spin-S (S=1, 3/2, 2, 3) Ising ferromagnet to the plane propagating wave, standing magnetic field wave and uniformly oscillating field with constant frequency are studied separately in two dimensions by extensive Monte Carlo simulation. Depending upon the strength of the magnetic field and the value of the spin state of the Ising spin lattice two different dynamical phases are observed. For a fixed value of S and the amplitude of the propagating magnetic field wave the system undergoes a dynamical phase transition from propagating phase to pinned phase as the temperature of the system is cooled down. Similarly in case with standing magnetic wave the system undergoes dynamical phase transition from high temperature phase where spins oscillate coherently in alternate bands of half wavelength of the standing magnetic wave to the low temperature pinned or spin frozen phase. For a fixed value of the amplitude of magnetic field oscillation the transition temperature is observed to decrease to a limiting value as the value of spin S is increased. The time averaged magnetisation over a full cycle of the magnetic field oscillation plays the role of the dynamic order parameter. A comprehensive phase boundary is drawn in the plane of magnetic field amplitude and dynamic transition temperature. It is found that the phase boundary shrinks inwards for high value of spin state S. Also in the low temperature (and high field) region the phase boundaries are closely spaced.

Wings as impellers: honey bees co-opt flight system to induce nest ventilation and disperse pheromones.

Honey bees (Apis mellifera) are remarkable fliers that regularly carry heavy loads of nectar and pollen, supported by a flight system - the wings, thorax and flight muscles - that one might assume is optimized for aerial locomotion. However, honey bees also use this system to perform other crucial tasks that are unrelated to flight. When ventilating the nest, bees grip the surface of the comb or nest entrance and fan their wings to drive airflow through the nest, and a similar wing-fanning behavior is used to disperse volatile pheromones from the Nasonov gland. In order to understand how the physical demands of these impeller-like behaviors differ from those of flight, we quantified the flapping kinematics and compared the frequency, amplitude and stroke plane angle during these non-flight behaviors with values reported for hovering honey bees. We also used a particle-based flow visualization technique to determine the direction and speed of airflow generated by a bee performing Nasonov scenting behavior. We found that ventilatory fanning behavior is kinematically distinct from both flight and scenting behavior. Both impeller-like behaviors drive flow parallel to the surface to which the bees are clinging, at typical speeds of just under 1 m s-1 We observed that the wings of fanning and scenting bees frequently contact the ground during the ventral stroke reversal, which may lead to wing wear. Finally, we observed that bees performing Nasonov scenting behavior sometimes display 'clap-and-fling' motions, in which the wings contact each other during the dorsal stroke reversal and fling apart at the start of the downstroke. We conclude that the wings and flight motor of honey bees comprise a multifunctional system, which may be subject to competing selective pressures because of its frequent use as both a propeller and an impeller.

Instability of Viscoelastic Plates with Longitudinally Variable Speed and Immersed in Ideal Liquid

The instability of longitudinally variable speed viscoelastic plates in contact with ideal liquid is studied for the first time. The effect of free surface waves is taken into account in the present study. The viscoelasticity is considered by using the Kelvin–Voigt viscoelastic constitutive relations. The classical theory of thin plate is utilized to derive the governing equation of variable speed plates. The fluid is assumed to be incompressible, inviscid and irrotational. Additionally, the velocity potential and Bernoulli’s equation are utilized to describe the fluid pressure acting on the vibrating plates. The fluid effect on the vibrational plates is described as the added mass of the plates which can be formulated by the kinematic boundary conditions at the structure–fluid interfaces. Parametric instability is analyzed by directly applying the method of multiple scales to the governing partial-differential equations and boundary conditions. The unstable boundaries are derived from the solvability conditions and the Routh–Hurwitz criterion for principal parametric, sum-type and difference-type combination resonances. Based on the numerical simulation, the effects of some key parameters on the unstable boundaries are illustrated in the excitation frequency and excitation amplitude plane in detail.

Design, fabrication and kinematics of a bio-inspired robotic bat wing

The current work is oriented toward the development of a novel biologically inspired bat aerial robot with morphing wings. Based on the flight characteristics data of natural bats (Eptesicus fuscus), a novel four degrees of freedom robotic bat wing was developed to emulate the movements of bat wing. The design, fabrication, programing and wind tunnel experiments of the robot bat wing are described in this paper. Based on this robotic wing, the influence of flap amplitude, wind speed, flight frequency, downstroke ratio and stroke plane angle as well as the contributions of flap, elbow, sweep and wrist motions on the aerodynamic force and mechanical power were studied and analyzed. Results of wind tunnel experiments validated that higher lift would bring greater power consumption, and the flap motion would generate the most force and need more energy expenditure compared with other motions of bat. The experimental results suggest that the flap and fold motions are indispensable to make a robotic bat wing that has a better flight performance. This study provides some implications and a better understanding for the future robotic bat.

Measurement of large amplitude plane vibrations of two dimensional structures

In the paper large amplitude plane vibrations of an elastic structure are investigated experimentally by using the method of time averaged geometric moiré. Investigations of a two-dimensional problem are performed. Experimental setup is developed and the results obtained by using the experimental procedure are analyzed. On the basis of a one-dimensional model graphical relationships for linear variation with respect to longitudinal coordinate of amplitude of vibrations are obtained. They provide the background for interpretation of partially exposed time averaged moiré. Recommendations for the choice of background intensity are provided.

Effect of Mean Stress on 2A12-T4 Aluminum Alloy under Tension-Torsion Constant Amplitude Loading

Fatigue tests have been carried out to investigate the effects of mean-stress and phase-difference on the tension-torsion fatigue failure of 2A12-T4 aluminum alloy. The results show that for fully reversed tension-torsion loading, the fatigue life increases with the increase of phase angle, but the fatigue life decreases with the increase of phase angle, when mean-stress exists, both for shear mean-stress and normal mean-stress. Fracture appearance shows that the crack initiation is on the direction of maximum shear stress amplitude plane. Critical plane criteria based on the linear combination of the maximum shear stress amplitude and maximum normal stress are studied and further discussion on the drawbacks of this kind of criteria are performed.

Ion wave breaking acceleration

Laser driven ion wave breaking acceleration (IWBA) in plasma wakefields is investigated by means of a one-dimensional (1D) model and 1D/3D particle-in-cell (PIC) simulations. IWBA operates in relativistic transparent plasma for laser intensities in the range of ${10}^{20}--{10}^{23}\text{ }\text{ }\mathrm{W}/{\mathrm{cm}}^{2}$. The threshold for IWBA is identified in the plane of plasma density and laser amplitude. In the region just beyond the threshold, self-injection takes place only for a fraction of ions and in a limited time period. This leads to well collimated ion pulses with peaked energy spectra, in particular for 3D geometry.

An elasto-plastic approach to estimate lifetime of notched components under variable amplitude fatigue loading: a preliminary investigation

The present paper is concerned with the formulation of an elasto-plastic strain based approach suitable for assessing fatigue strength of notched components subjected to in-service variable amplitude cyclic loading. The hypothesis is formed that the crack initiation plane is closely aligned with the plane of maximum shear strain amplitude, its orientation and the associated stress/strain quantities being determined using the Maximum Variance Method. Fatigue damage is estimated by applying the Modified Manson-Coffin Curve Method (MMCCM) along with the Point Method (PM). In the proposed approach, the required critical distance is treated as a material property whose value is not affected either by the sharpness of the notch being assessed or by the profile of the load spectrum being applied. The detrimental effect of non-zero mean stresses and degree of multiaxiality of the local stress/strain histories is also considered. The accuracy and reliability of the proposed design methodology was checked against several experimental data taken from the literature and generated under different uniaxial variable amplitude load histories. In order to determine the required local stress/strain states, refined elasto-plastic finite element models were solved using commercial software ANSYS®. This preliminary validation exercise allowed us to prove that the proposed approach is capable of estimates laying within an error factor of about 2. These preliminary results are certainly promising, strongly supporting the idea that the proposed design strategy can successfully be used to assess the fatigue lifetime of notched metallic components subjected to in-service multiaxial variable amplitude loading sequences.

Dynamic instability analysis of sandwich plates with CNT reinforced facesheets

In this paper, the dynamic instability characteristics of sandwich panels with carbon nanotube (CNT) reinforced facesheets subjected to in-plane periodic load is investigated using a shear flexible QUAD-8 serendipity element. The formulation accounts for the realistic variation of the displacements through the thickness, possible discontinuity in slope at the interface and the thickness stretch affecting the transverse deflection. The influence of the aerodynamic force due to airflow over the plate, the in-plane and the rotary inertia effects are also included in the formulation. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to bring out the efficacy of the present higher-order plate theory over the first-order plate theory. The present study examines the influence of the volume fraction of the CNT, core-to-facesheet thickness, the plate thickness and aspect ratio, damping and temperature on the dynamic instability boundaries and its associated origin of instability forcing frequencies. The effect of airflow over such sandwich plate is also investigated. The boundaries of the principal instability region are represented in the non-dimensional excitation frequency-load amplitude plane.

Devil's staircase in an optomechanical cavity.

We study self-excited oscillations (SEOs) in an on-fiber optomechanical cavity. While the phase of SEOs randomly diffuses in time when the laser power injected into the cavity is kept constant, phase locking may occur when the laser power is periodically modulated in time. We investigate the dependence of phase locking on the amplitude and frequency of the laser-power modulation. We find that phase locking can be induced with a relatively low modulation amplitude provided that the ratio between the modulation frequency and the frequency of SEOs is tuned close to a rational number of relatively low hierarchy in the Farey tree. To account for the experimental results, a one-dimensional map, which allows evaluating the time evolution of the phase of SEOs, is theoretically derived. By calculating the winding number of the one-dimensional map, the regions of phase locking can be mapped in the plane of modulation amplitude and modulation frequency. Comparison between the theoretical predictions and the experimental findings yields a partial agreement.

Effect of Phase Angle on Fatigue Failure of 30CrMnSiA Steel under Tension-torsion Fatigue Loading

Tension-torsion high-cycle fatigue experiments with solid cylindrical bar specimens of 30CrMnSiA steel were carried out under different phase angles. And the experiment data, characteristics of stresses with plane orientation and fracture appearance under different loading conditions were analyzed and investigated. Experiment results show that fatigue life increases gradually with the increase of phase angle. The fatigue life is shortest for 0° phase angle, while the fatigue life is longest for 90° out-of-phase angle. It could be found from analysis of stress parameters that as the phase angle increases, the shear stress amplitude decreases and the maximum normal stress increases gradually, which are on the maximum shear stress amplitude plane close to the axial of specimen. Macro-analysis of the fracture appearances show that when the phase angle increases, the angel between crack initiation plane and specimen axial decreases, and cracks are inclined to initial and propagate on or near the maximum shear stress amplitude plane with larger maximum normal stress under proportional loading as well as non-proportional loading.

Crack initiation and early propagation plane orientation of 2A12-T4 aluminum alloy under tension-torsion fatigue loading including mean tensile stress

The specimen fractures appearances are analyzed to investigate the effects of mean tensile stress on the fatigue crack initiation and early propagation plane orientation under axial-torsion fatigue loading for 2A12T4 aluminum alloy. The fatigue crack initiation and early propagation plane orientations are measured by optical microscope, the results of macro-analysis show that both the maximum shear stress amplitude and normal mean stress have effects on the orientations of crack initiation and propagation plane orientation, which are close to the plane of the maximum shear stress amplitude plane. With increasing the mean tensile stress, more cracks are inclined to initial and propagate on or near the maximum shear stress amplitude plane with larger normal mean stress, and the angle of deviation from the plane of maximum shear stress amplitude increases. The predicted plane orientations based on critical plane methods are compared with experimental measured results.

Dynamic phase transitions and dynamic phase diagrams of the Ising model on the Shastry-Sutherland lattice

The dynamic phase transitions and dynamic phase diagrams are studied, within a mean-field approach, in the kinetic Ising model on the Shastry-Sutherland lattice under the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The time-dependence behavior of order parameters and the behavior of average order parameters in a period, which is also called the dynamic order parameters, as a function of temperature, are investigated. Temperature dependence of the dynamic magnetizations, hysteresis loop areas and correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic phase transitions as well as to obtain the dynamic phase transition temperatures. We present the dynamic phase diagrams in the magnetic field amplitude and temperature plane. The phase diagrams exhibit a dynamic tricritical point and reentrant phenomena. The phase diagrams also contain paramagnetic (P), Néel (N), Collinear (C) phases, two coexistence or mixed regions, (N+C) and (N+P), which strongly depend on interaction parameters.

Supertransmission channel for an intrinsic localized mode in a one-dimensional nonlinear physical lattice.

It is well known that a moving intrinsic localized mode (ILM) in a nonlinear physical lattice looses energy because of the resonance between it and the underlying small amplitude plane wave spectrum. By exploring the Fourier transform (FT) properties of the nonlinear force of a running ILM in a driven and damped 1D nonlinear lattice, as described by a 2D wavenumber and frequency map, we quantify the magnitude of the resonance where the small amplitude normal mode dispersion curve and the FT amplitude components of the ILM intersect. We show that for a traveling ILM characterized by a specific frequency and wavenumber, either inside or outside the plane wave spectrum, and for situations where both onsite and intersite nonlinearity occur, either of the hard or soft type, the strength of this resonance depends on the specific mix of the two nonlinearities. Examples are presented demonstrating that by engineering this mix the resonance can be greatly reduced. The end result is a supertransmission channel for either a driven or undriven ILM in a nonintegrable, nonlinear yet physical lattice.

Geometrically nonlinear free vibration analysis of axially functionally graded taper beams

Large amplitude free vibration analysis is carried out on axially functionally graded (AFG) tapered slender beams under different boundary conditions. The problem is addressed in two parts. First the static problem corresponding to a uniform transverse loading is solved through an iterative scheme using a relaxation parameter and later on the subsequent dynamic problem is solved as a standard eigenvalue problem on the basis of known static displacement field. The mathematical formulation of the static problem is based on the principle of minimum total potential energy, whereas Hamilton's principle has been applied for the dynamic analysis. To account for the geometric non-linearity arising due to large deflection, nonlinear strain displacement relations are considered. The dynamic behaviour has been presented in the form of backbone curves in a dimensionless frequency–amplitude plane. The results are successfully validated with the previously published results.

Hummingbird flight stability and control in freestream turbulent winds.

Airflow conditions close to the Earth's surface are often complex, posing challenges to flight stability and control for volant taxa. Relatively little is known about how well flying animals can contend with complex, adverse air flows, or about the flight control mechanisms used by animals to mitigate wind disturbances. Several recent studies have examined flight in the unsteady von Kármán vortex streets that form behind cylinders, generating flow disturbances that are predictable in space and time; these structures are relatively rare in nature, because they occur only the immediate, downstream vicinity of an object. In contrast, freestream turbulence is characterized by rapid, unpredictable flow disturbances across a wide range of spatial and temporal scales, and is nearly ubiquitous in natural habitats. Hummingbirds are ideal organisms for studying the influence of freestream turbulence on flight, as they forage in a variety of aerial conditions and are powerful flyers. We filmed ruby-throated hummingbirds (Archilochus colubris) maintaining position at a feeder in laminar and strongly turbulent (intensity ∼15%) airflow environments within a wind tunnel and compared their mean kinematics of the head, body, tail and wing, as well as variability in these parameters. Hummingbirds exhibited remarkably stable head position and orientation in both smooth and turbulent flow while maintaining position at the feeder. However, the hummingbird's body was less stable in turbulent flow and appeared to be most sensitive to disturbances along the mediolateral axis, displaying large lateral accelerations, translations and rolling motions during flight. The hummingbirds mitigated these disturbances by increasing mean wing stroke amplitude and stroke plane angle, and by varying these parameters asymmetrically between the wings and from one stroke to the next. They also actively varied the orientation and fan angle of the tail, maintaining a larger mean fan angle when flying in turbulent flow; this may improve their passive stability, but probably incurs an energetic cost as a result of increased drag. Overall, we observed many of the same kinematic changes noted previously for hummingbirds flying in a von Kármán vortex street, but we also observed kinematic changes associated with high force production, similar to those seen during load-lifting or high-speed flight. These findings suggest that flight may be particularly costly in fully mixed, freestream turbulence, which is the flow condition that hummingbirds are likely to encounter most frequently in natural habitats.

Vibration Dynamics of an Inclined Cable Excited Near Its Second Natural Frequency

Inclined cables are essential structural elements that are used most prominently in cable-stayed bridges. When the bridge deck oscillates due to an external force, such as passing traffic, cable vibrations can arise not only in the plane of excitation, but also in the perpendicular plane. This undesirable phenomenon can be modeled as an auto-parametric resonance between the in-plane and out-of-plane modes of vibration of the cable. In this paper, we consider a three-mode model, capturing the second in-plane, and first and second out-of-plane modes, and use it to study the response of an inclined cable that is vertically excited at its lower (deck) support at a frequency close to the second natural frequency of the cable. Averaging is applied to the model and then the solutions and bifurcations of the resulting averaged differential equations are investigated and mapped out with numerical continuation. In this way, we present a detailed bifurcation study of the different possible responses of the cable. We first consider the equilibria of the averaged model, of which there are four types that are distinguished by whether each of the two out-of-plane modes is present or not in the cable response. Each type of equilibrium is computed and represented as a surface over the plane of amplitude and frequency of the forcing. The stability of the equilibria changes and different surfaces meet along curves of bifurcations, which are continued directly. Overall, we present a comprehensive geometric picture of the two-parameter bifurcation diagram of the constant-amplitude coupled-mode response of the cable. We then focused on bifurcating periodic orbits, which correspond to cable dynamics with varying amplitudes of the participating second in-plane and second out-of-plane modes. The range of excitation amplitude and frequency is determined where such whirling cable motion can occur. Further bifurcations — period-doubling cascades and a Shilnikov homoclinic bifurcation — are found that lead to a chaotic cable response. Whirling and chaotic cable dynamics are confirmed by time-step simulations of the full three-mode model. The different cable responses are characterized, and can be distinguished clearly, by their motion at the quarter-span and by their frequency spectra.

Dynamic Stability Analysis of Functionally Graded Plates Subjected to Complex Loads

The paper investigates the dynamic stability of thick functionally graded plates subjected to aero-thermo-mechanical loads, using the moving least squares differential quadrature method. Temperature field is assumed to be a uniform distribution over the plate plane, and varied in the thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction in the simple power law manner. The equilibrium equations governing the dynamic stability of the plate are derived by the Hamilton’s principle, then these equations are discretized by the moving least squares differential quadrature method. The boundaries of the instability region are obtained using the principle of Bolotin’s method and are conveniently represented in the non-dimensional excitation frequency to load amplitude plane. The influence of various factors such as gradient index, temperature, mechanical and aerodynamic loads, thickness and aspect ratios, as well as the boundary conditions on the dynamic instability region are carefully studied.

Gravity perturbed Crapper waves

Crapper waves are a family of exact periodic travelling wave solutions of the free-surface irrotational incompressible Euler equations; these are pure capillary waves, meaning that surface tension is accounted for, but gravity is neglected. For certain parameter values, Crapper waves are known to have multi-valued height. Using the implicit function theorem, we prove that any of the Crapper waves can be perturbed by the effect of gravity, yielding the existence of gravity–capillary waves nearby to the Crapper waves. This result implies the existence of travelling gravity–capillary waves with multi-valued height. The solutions we prove to exist include waves with both positive and negative values of the gravity coefficient. We also compute these gravity perturbed Crapper waves by means of a quasi-Newton iterative scheme (again, using both positive and negative values of the gravity coefficient). A phase diagram is generated, which depicts the existence of single-valued and multi-valued travelling waves in the gravity–amplitude plane. A new largest water wave is computed, which is composed of a string of bubbles at the interface.

Comparative characteristics of the wing apparatus and flight of Syrphid flies (Diptera: Syrphidae)

Comparative analysis of the wing apparatus and flight in nine species of flower flies (Syrphidae) has been performed. Data on the flight velocity, aerodynamic force, wing-beat frequency, stroke amplitude and stroke plane angle, wing area, body mass and volume, as well as correlations between these parameters at the intraspecific and family levels, have been obtained. Based on the obtained data, the subfamilies Syrphinae and Eristalinae have been compared.