Amplitude Limit Research Articles

Deep learning-based automated identification on vortex-induced vibration of long suspenders for the suspension bridge

Large amplitude vortex-induced vibration (VIV) of long suspenders, caused by vortex-shedding and wake flow, will decrease the service life of high-strength wires and its anchorage systems, hence listed as an essential monitoring indicator of the structural health monitoring system in the suspension bridges. Traditionally, a static vibration amplitude limitation is usually predefined and used to identify VIV from continuously monitored acceleration data of bridge suspenders. Due to the complexity of the starting vibration of the suspenders, it may not be able to flexibly adapt to the suspenders VIV under different conditions. In addition, transient but significant vibration events may not be captured since it relies only on static vibration amplitude limits without considering the temporal information of vibration. To address the above-mentioned issues, a novel framework to autonomously identify the suspenders VIV is proposed using the multimodal fusion techniques with deep neural networks. The main contributions of the methodology are: i) by calculating the wind field and vibration characteristic, two vibration response parameters are identified as indexes for the identification of suspenders VIV based on the significant difference method of big data analysis; ii) Two different modal information of time history images and power spectral density (PSD) sequences are used as inputs to the convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM) to extract the suspenders vibration response features from the time and frequency domain perspectives, respectively; and iii) The multimodal information is concentrated and enhanced by the multi-head attention (MHA) mechanism to achieve automated identification of the suspenders VIV. The proposed framework is validated with data collected from a full-scale long-span suspension bridge in comparison with the base model. The results show that the proposed framework can efficiently identify the full-cycle development process of the suspenders VIV. This study provides a convenient strategy for suspenders VIV identification, which can be used for bridge management and vibration mitigation device design.

Current-controlled periodic double-polarity reversals in a spin-torque vortex oscillator

Micromagnetic simulations are used to study a spin-torque vortex oscillator excited by an out-of-plane dc current. The vortex core gyration amplitude is confined between two orbits due to periodical vortex core polarity reversals. The upper limit corresponds to the orbit where the vortex core reaches its critical velocity triggering the first polarity reversal which is immediately followed by a second one. After this double polarity reversal, the vortex core is on a smaller orbit that defines the lower limit of the vortex core gyration amplitude. This double reversal process is a periodic phenomenon and its frequency, as well as the upper and lower limit of the vortex core gyration, is controlled by the input current density while the vortex chirality determines the apparition of this confinement regime. In this non-linear regime, the vortex core never reaches a stable orbit and thus, it can be of interest for neuromorphic application as a leaky integrate-and-fire neuron for example.

Study on radial deviation amplitude of out-of-roundness of resilient wheel installed on a subway vehicle based on vehicle operation safety regulation

Following the extensive use of resilient wheels on trams, several subways in China have also started to pre-launch testing of resilient wheels, while it remains to be at a beginning stage, the wheel maintenance during its long-term service has become a great concern by subway operators and wheel suppliers. An effort is presented in this paper, trying to provide an invaluable reference. Firstly, a metro vehicle-track dynamic system model fitted with the resilient wheels is built. Then, based on the operation safety index and current wheel re-profiling regulations, the influence of wheel axial and radial stiffness combination on radial deviation maximum of resilient wheel polygonization wear is analyzed. The equivalent stiffnesses of the resilient wheel involve the radial stiffness within 600 kN/mm and the axial stiffness within 100 kN/mm. The amplitude of polygonization below the 10th order on the resilient wheel is within 1 mm. A contour chart is drawn to present how the wheel weight reduction rate varies with wheel polygonization order and amplitude under different combinations of resilient wheel equivalent axial and radial stiffnesses. A series of contours is abstracted to query the amplitude limits of the polygonization of different orders on resilient wheels with different equivalent stiffnesses.

Supergluon scattering in AdS: constructibility, spinning amplitudes, and new structures

We elaborate on a new recursive method proposed in [1] for computing tree-level n-point supergluon amplitudes as well as those with one gluon, i.e. spinning amplitudes, in AdS5 × S3. We present an improved proof for the so-called “constructibility” of supergluon and spinning amplitudes based on their factorizations and flat-space limit, which allows us to determine these amplitudes in Mellin space to all n. We present explicit and remarkably simple expressions for up to n = 7 supergluon amplitudes and n = 6 spinning amplitudes, which can be viewed as AdS generalizations of the scalar-scaffolded gluon amplitudes proposed recently. We then reveal a series of hidden structures of these AdS amplitudes including (1). an understanding of general pole structures especially the precise truncation on descendent poles (2). a derivation of simple “Feynman rules” for the all-n amplitudes with the simplest R-symmetry structures, and (3). certain universal behavior analogous to the soft/collinear limit of flat-space amplitudes.

The Baker-Coon-Romans N-point amplitude and an exact field theory limit of the Coon amplitude

We study the N-point Coon amplitude discovered first by Baker and Coon in the 1970s and then again independently by Romans in the 1980s. This Baker-Coon-Romans (BCR) amplitude retains several properties of tree-level string amplitudes, namely duality and factorization, with a q-deformed version of the string spectrum. Although the formula for the N-point BCR amplitude is only valid for q > 1, the four-point case admits a straightforward extension to all q ≥ 0 which reproduces the usual expression for the four-point Coon amplitude. At five points, there are inconsistencies with factorization when pushing q < 1. Despite these issues, we find a new relation between the five-point BCR amplitude and Cheung and Remmen’s four-point basic hypergeometric amplitude, placing the latter within the broader family of Coon amplitudes. Finally, we compute the q → ∞ limit of the N-point BCR amplitudes and discover an exact correspondence between these amplitudes and the field theory amplitudes of a scalar transforming in the adjoint representation of a global symmetry group with an infinite set of non-derivative single-trace interaction terms. This correspondence at q = ∞ is the first definitive realization of the Coon amplitude (in any limit) from a field theory described by an explicit Lagrangian.

Synchronization and limit cycles in a simple contagion model with time delays

We examine a system of N=2 coupled non-linear delay-differential equations representing financial market dynamics. In such time delay systems, coupled oscillations have been derived. We linearize the system for small time delays and study its collective dynamics. Using analytical and numerical solutions, we obtain the bifurcation diagrams and analyze the corresponding regions of amplitude death, phase locking, limit cycles and market synchronization in terms of the system frequency-like parameters and time delays. We further numerically explore higher order systems with N>2, and demonstrate that limit cycles can be maintained for coupled N−asset models with appropriate parameterization.

Maximal canards in a slow–fast Rosenzweig–MacArthur model with intraspecific competition among predators

Using geometric singular perturbation theory, this paper investigates the canard phenomenon of a slow–fast Rosenzweig–MacArthur model. The model incorporates intraspecific competition among predators, assuming predator reproduction occurs much slower than prey. We demonstrate the occurrence of maximal canards between attracting and repelling slow manifolds as a bifurcation parameter varies. Additionally, we derive an analytic expression to approximate the bifurcation parameter value at which a maximal canard occurs. The method employed for this analysis relies on the blowup method. This involves finding a quasihomogeneous blowup map to desingularize the nonnormally hyperbolic point. Subsequently, charts are utilized to express the blowup in local coordinates, calculate local data, investigate the dynamics of the blown-up vector fields, and establish connections across charts. Furthermore, we provide numerical simulations to illustrate the canard explosion phenomenon in the model. Through parameter variation, we observe that the model transitions from a small amplitude limit cycle to small amplitude canard cycles (canards without a head), then to large amplitude canard cycles (canards with a head), and finally to a large amplitude relaxation cycle.

Obliquely Propagating Self-Gravitational Shock Waves in Non-Relativistic Degenerate Quantum Plasmas

A rigorous theoretical investigation has been carried out on the propagation of non-linear self-gravitational shock waves (SGSHWs) in a magnetized super dense degenerate quantum plasma system (DQPS) composed of inertia-less non-relativistic degenerate electrons and inertial non-degenerate extremely heavy nuclei/element. The nonlinear propagation of these SGSHWs in the plasma system under consideration is studied by the standard reductive perturbation technique, which is valid for a small finite amplitude limit. The nonlinear dynamics of the SGSHWs are found to be governed by the Burgers equation. The Burgers equation is derived analytically and solved numerically. It has been found that the considered plasma model supports positive potential shock waves only. The fundamental properties (amplitude, steepness, etc.) of these SGSHWs are significantly modified by the variation of kinematic viscosity, obliqueness and number density of the plasma species. The results of our present investigation can be applied to astrophysical compact objects like neutron stars. Journal of Engineering Science 15(1), 2024, 21-29

Experimental investigation on the hydrodynamic performance of a bioinspired manta-ray underwater vehicle in various forward propulsion modes

Bionic propulsion technology is revolutionizing underwater exploration by enabling underwater vehicles to navigate the oceans more efficiently. This research developed a scaled-down (10:1) experimental prototype of bionic manta-ray underwater vehicle, which has two degrees of freedom (2-DOF) pectoral fins: flapping and rotating. The impact of four different pectoral fin motion patterns (sinusoidal flapping and rotating, flapping frequency asymmetric, flapping amplitude offset, and rotating amplitude limitation) on the forward propulsion performance was investigated experimentally in a static water tunnel using a force/torque sensor and power analyzer. The results revealed that introducing asymmetry into the fin's flapping motion (asymmetric frequency or amplitude) significantly improved both average thrust and propulsive efficiency (the average thrust can be increased by more than 30%). Flapping with amplitude offset can effectively adjust its pitching moment without sacrificing much thrust. While the rotating motion of the pectoral fins contributes minimally to thrust generation compared to flapping, it plays an important role in enhancing both longitudinal stability and propulsive efficiency. Understanding the hydrodynamic performance of these various forward propulsion modes provides valuable insights for optimizing control strategies of bionic manta-ray underwater vehicles.

Study on the allowed maximum amplitudes of low-order polygonal wear on resilient wheels based on operational safety

Following the extensive use of resilient wheels on trams, several subways in China have started pre-launch testing of resilient wheels. While it remains at an early stage, the long-term behavior of the wheel has become a great concern for subway operators and wheel suppliers. To address the concern, this study focuses on derailment risk by evaluating the allowed maximum amplitudes of low-order polygonal wear on resilient wheels. Firstly, a metro vehicle-track dynamic system model equipped with resilient wheels is built. Then, based on the operation safety index and current re-profiling regulations for conventional wheels, the influence of wheel axial and radial stiffness on the radial amplitude limits of resilient wheel polygonal wear is analyzed. To perform the analysis, firstly the commonly-used stiffness for a resilient wheel (300 kN/mm in radial direction and 50 kN/mm in axial direction) is adopted to study the effect of resilient wheel polygonization on wheel load reduction ratio. Then, wheel load reduction ratio is predicted for different radial (up to 600 kN/mm) and axial (up to 100 kN/mm) stiffnesses of the resilient wheel and different orders (up to 10) of wheel polygonization of 1 mm amplitude. A contour plot is provided to illustrate how the wheel load reduction ratio varies with the harmonic order and amplitude of wheel polygonization under different combinations of resilient wheel’s equivalent axial and radial stiffnesses. It is found that, with the increase of the amplitude of the polygonal wear of a certain harmonic order on resilient wheel, the number of the available combinations of the equivalent stiffnesses adopted by the resilient wheel becomes less by considering the operation safety indexed with wheel load reduction ratio. Besides, depending on the stiffness of the resilient wheel, the allowed amplitude corresponding to the polygonization of each order has been suggested with the contour plots.

One-loop five-parton amplitudes in the NMRK limit

We analyse the real part of one-loop five-parton amplitudes in the next-to-multi-Regge kinematic (NMRK) limit, to leading power, and to finite order in the dimensional regularisation parameter. To leading logarithmic (LL) accuracy, it is known that five-parton amplitudes in this limit are given to all-orders by a single factorised expression, in which the pair of partons which are not well-separated in rapidity are described by a two-parton emission vertex. In this study, we investigate the one-loop amplitudes at next-to-leading logarithmic (NLL) accuracy, and find that is has a more complex structure. In particular, it is found that the purely gluonic amplitudes are compatible with an analogous factorisation of individual colour structures. From the one-loop amplitudes we extract one-loop two-parton emission vertices, which are functions of a subset of the momenta of the amplitude. In the multi-Regge kinematic (MRK) limit, the vertices themselves factorise into the known one-loop single-parton emission vertices and Lipatov vertex, with rapidity dependence governed by the one-loop gluon Regge trajectory, as required by compatibility with the known MRK limit of amplitudes. The one-loop two-parton emission vertices are necessary ingredients for the construction of the next-to-next-to leading order (NNLO) jet impact factors in the BFKL framework.

ATEP: an advanced transport model for energetic particles

In this paper we report on the implementation and verification of a phase-space resolved energetic particle (EP) transport model. It is based on a first-principle theoretical framework, i.e. the system of non-linear gyrokinetic equations and the related transport equations. Its focus is primarily directed toward understanding the meso-scale character of EPs and its consequences. Compared to the conventional description of thermal radial transport via a one-dimensional radial diffusion equation, the newly developed model is three-dimensional using canonical constants-of-motion (CoM) variables. The model does not assume diffusive processes to be dominant a priori, instead the EP fluxes are self-consistently calculated and directly evolved in CoM space. We use the EP-Stability workflow and the HAGIS code to determine the phase space fluxes explicitly either in the limit of constant mode amplitudes or an energy-conserving quasi-linear model. As an application of the model the transport of neutral-beam-generated EPs due to a toroidal Alfvén eigenmode in an ITER plasma is investigated. As there are no sources and collisions taken into account so far (for an extension of the model see the companion paper (Meng et al 2024 Nucl. Fusion accepted)), the results cannot be considered as an exhaustive study, but rather as a practical demonstration of the conceptual framework on the way to a comprehensive reduced description of burning plasmas.

A Polynomial System of Degree Four with an Invariant Square Containing At Least Five Limit Cycles

We consider a class of polynomial systems of degree four with four real invariant straight lines that form a square, called this an invariant square, and also that contains in its interior at least five small amplitude limit cycles for a certain choice of the parameters. Moreover, we will obtain the necessary and sufficient conditions for the critical point inside the square to be a center.

Soft algebras for leaf amplitudes

Celestial MHV amplitudes are comprised of non-distributional leaf amplitudes associated to an AdS3 leaf of a foliation of flat spacetime. It is shown here that the leaf amplitudes are governed by the same infinite-dimensional soft ‘S-algebra’ as their celestial counterparts. Moreover, taking the soft limit of the smooth three-point MHV leaf amplitude yields a nondegenerate minus-minus two-point leaf amplitude. The two- and three-point MHV leaf amplitudes are used to compute the plus-minus-minus leaf operator product coefficients.

Active Flutter Suppression: Quantification of Performance Loss Due to Actuator Saturation

Active flutter suppression technologies have the potential to lead to major weight savings while keeping the envisaged flight envelope for the future generation of commercial aircraft. Since the stabilization of aeroelastic systems undergoing flutter instabilities is strongly affected by actuators’ characteristics and delays in the closed loop, the degradation of closed-loop performance due to actuators’ nonlinearities must be thoroughly understood. Comparisons between the region of attraction and the controllable region can support the quantification of performance loss due to common actuators’ nonlinearities, such as amplitude and rate limits. At first, this paper illustrates a numerically robust algorithm for the full characterization of the controllable region of a generic unstable system under input amplitude and rate constraints. Secondly, the concept of region of attraction is expanded to assess the boundedness of the closed-loop response in the presence of input saturation and atmospheric disturbances. These concepts are here employed to define two nonlinear performance measures that quantify the performance loss due to actuators’ saturation in an unstable aeroelastic system stabilized by a flutter suppression controller. The approach is demonstrated on a realistic aeroelastic system for which different H2 and H∞ output feedback controllers are synthesized to augment the damping of the critical flutter mode.

Effect of Moisture Content and Wet–Dry Cycles on the Strength Properties of Unsaturated Clayey Sand

Based on the actual situation of the project on the Weihai–Yanhai Expressway section of Rongwu Expressway, the effects of water content change and the dry–wet cycle on the mechanical behavior of unsaturated clayey sandy soil were analyzed in this study. In this study, ventilated undrained triaxial shear tests were carried out on unsaturated clayey sandy soils with different water contents (6%, 8%, 10%, 12%, 14% and 16%). Concurrently, the soil samples were subjected to three distinct wet and dry cycle pathways (2~22%, 2~12%, and 12~22%) to gain an understanding of how the mechanical features of the soil changed under the different conditions. The test findings demonstrate that when the water content increases, the unsaturated clayey sandy soil’s cohesiveness and shear strength diminish. The strength of shear decline exhibits a pattern of first being quick, followed by sluggish. The strength of shear and cohesiveness of clayey sandy soil declined under the influence of the dry and wet cycles, with the first cycle primarily affecting variations in cohesiveness and strength of shear. Furthermore, the strength of shear and cohesiveness of clayey sandy soil diminish more with increasing wet and dry cycle amplitude and upper water content limits. Lastly, the drying shrinkage and hygroscopic expansion of clay particles in clayey sandy soils during wet and dry cycles are not significant, resulting in less structural damage and deterioration of the mechanical properties of the soils. The study’s findings have a significant impact on the durability of roadbeds made of unsaturated clayey sandy soil in both wet and dry situations.

Control of large amplitude limit cycle of a multi-dimensional nonlinear dynamic system of a composite cantilever beam

For the first time, a control strategy based on Fuzzy Sliding Mode Control is implemented in the control of a large amplitude limit cycle of a composite cantilever beam in a multi-dimensional nonlinear form. In the dynamic model establishment of the investigated structure, the higher-order shearing effect is applied, as well as the second-order discretization. Numerical simulation demonstrates that a multi-dimensional nonlinear dynamic system of the investigated structure is demanded for accurate estimation of large amplitude limit cycle responses. Therefore, a control strategy is employed to effectively suppress such responses of the beam in multi-dimensional nonlinear form.

Modelling surface waves on shear current with quadratic depth-dependence

The currents in the ocean have a serious impact on ocean dynamics, since they affect the transport of mass and thus the distribution of salinity, nutrients and pollutants. In many physically important situations the current depends quadratic-ally on the depth. We consider a single layer of fluid and study the propagation of the surface waves in the presence of depth-dependent current with quadratic profile. We select the scale of parameters and quantities, which are typical for the Boussinesq propagation regime (long wave and small amplitude limit) and we also derive the well known KdV model for the surface waves interacting with current.

Hybrid finite-amplitude periodic modes for two uniformly magnetized spheres.

We analyze a system of two uniformly magnetized spheres, one fixed and the other free to slide in frictionless contact with the surface of the first. The centers of the two magnets, and their magnetic moments, are restricted to a plane. We search for sets of initial conditions that yield finite-amplitude oscillatory periodic solutions. We extend two small-amplitude base modes, one with orbital and spin motions that are in phase and the other out of phase, to finite amplitudes and show that the motion for arbitrary oscillatory solutions can be considered to be a nonlinear superposition of these base modes. Some solutions are pure periodic finite-amplitude extensions of one base mode, while others are hybrid finite-amplitude superpositions of the two modes. Hybrid modes with rational frequency ratios are periodic and come in families defined by their frequency ratios. We further characterize hybrid periodic modes by identifying two symmetry classes that describe their relative phases. We see continuous transitions between one finite-amplitude base mode and the other, with one mode gradually transforming into the other. We also calculate frequency spectra of nonperiodic modes, show that the two base modes have well-defined frequencies even for nonperiodic states, and show that periodic solutions can give clues about the behavior of nearby nonperiodic solutions. In the limit of small amplitudes, we confirm that the computed frequencies of these modes agree with small-amplitude analytical results. We also generate a Lyapunov exponent heatmap that reflects periodic and nonperiodic regions of state space.

Wronskian solutions, bilinear Bäcklund transformation, quasi-periodic waves and asymptotic behaviors for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

In this paper, we investigate the integrability of a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation, which is widely used in fluid mechanics and theoretical physics. The N-soliton solution is obtained via the Hirota’s bilinear method. The Wronskian solution is derived by using the Wronskian technique for the bilinear form. Through the exchange formula, we deduce the bilinear Bäcklund transformation consisting of four equations and six parameters. In order to consider the quasi-periodic wave having complex structure, one-, two- and three-periodic waves are investigated systemically by combining the Hirota’s bilinear method with Riemann theta function. Furthermore, the corresponding graphs of periodic wave are presented by considering the geometric properties between the characteristic lines. The propagation characteristics of periodic waves are investigated by virtue of the characteristic lines. Finally, the asymptotic relationships between quasi-periodic wave solutions and soliton solutions are established theoretically under a condition of the small amplitude limit. The analytical method used in this paper can be applied in other integrable systems.