Nonlinear Amplitude Research Articles

Resistive wall tearing mode disruptions in DIII-D and ITER tokamaks

Disruptions are a serious problem in tokamaks, in which thermal and magnetic energy confinement is lost. This paper uses data from the DIII-D experiment, theory, and simulations to demonstrate that resistive wall tearing modes (RWTMs) produce the thermal quench (TQ) in a typical locked mode shot. Analysis of the linear RWTM dispersion relation shows the parameter dependence of the growth rate, particularly on the resistive wall time. Linear simulations of the locked mode equilibrium show that it is unstable with a resistive wall and stable with an ideally conducting wall. Nonlinear simulations demonstrate that the RWTM grows to sufficient amplitude to cause a complete thermal quench. The RWTM growth time is proportional to the thermal quench time. The nonlinearly saturated RWTM magnetic perturbation amplitude agrees with experimental measurements. The onset condition is that the q = 2 rational surface is sufficiently close to the resistive wall. Collectively, this identifies the RWTM as the cause of the TQ. In ITER, RWTMs will produce long TQ times compared to present-day experiments. ITER disruptions may be significantly more benign than previously predicted.

Chaotic Dynamics of a Periodically Forced Duffing Oscillator with Cubic Quintic Septic Power Nonlinearities

In this paper, we investigate the chaotic dynamics of Cubic Quintic Septic Duffing oscillator. The conditions of the system parameters for the existence of fixed points and the stability of the undamped free Cubic Quintic Septic Duffing oscillator are obtained. Multiple scales method is employed to determine the various resonance states of the system through frequency-amplitude response curves. Using linear damping, septic coefficient, excitation amplitude and excitation frequency as control parameters, the bifurcation diagrams are drawn numerically and the results are confirmed using phase space trajectories and their corresponding Poincaré sections. The influence of septic nonlinearity, linear damping and excitation amplitude in controlling the chaotic behavior of the system is also investigated.

Absolute displacement transmissibility of vibration isolator with the quasi-zero stiffness

A vibration isolator with quasi-zero stiffness (QZS) is proposed, which is composed of positive stiffness mechanism and negative stiffness mechanism in parallel. Considering the nonlinear stiffness and nonlinear damping, the equation of motion is derived and further solved by the average method. Subsequently, the amplitude-frequency equation relationship and the expression of absolute displacement transmissibility (ADT) are deduced. Then, the effects of nonlinear coefficient, excitation amplitude, horizontal and vertical damping on dynamic response characteristics and ADT are analyzed. The results indicate that there are many ways to reduce the peak value of ADT, such as increasing vertical and horizontal damping, reducing the nonlinear coefficient or excitation amplitude. In addition, by decreasing the nonlinear coefficient or excitation amplitude can minish initial vibration isolation frequency. The higher vertical and horizontal damping may expand the isolation frequency bandwidth. The low frequency vibration isolation performance of the vibration isolation system of the horizontal spring with decreasing stiffness is better than that with increasing stiffness. Contrasted by the equivalent linear system, the QZS isolation system possesses the advantages of smaller transmissibility peak, lower initial frequency of vibration isolation and larger isolation frequency bandwidth.

Fully Nonlinear Small Amplitude Dynamical Waves for Multicomponent Complex Plasma with Kappa Distributed Electrons and Ions

Multicomponent plasmas are ubiquitous in astrophysics and space plasma environments. In the present manuscript, we assumed a dusty plasma system consisting of negative and positive dust species and kappa-distributed electrons and ions. The analysis is based on the fluid model of plasmas, and the reductive perturbation method was used to study the behavior of propagating waves. New arbitrary parameters were obtained to measure the strength of nonlinearity, dispersion, and dissipation in the plasma system. We investigated the effects of the arbitrary parameters on the appearance of the different nonlinear waves as soliton, shock, and solitary waves. Furthermore, we studied the effects of the kappa parameter, the viscosity of dust species, and the ratio between the temperature of positive and negative dust species in the type of wave, i.e., compressive or rarefactive.

Design of Gas Turbine Cooling System Based on Improved Jumping Spider Optimization Algorithm

The gas turbine cooling system is a complex MIMO system with a strong coupling, nonlinear, time-varying and large disturbance amplitude. In order to automatically control the target flow, target temperature and pipeline pressure, in this paper, the decoupler and regulator of a gas turbine cooling system are designed. Firstly, the working principle of a gas turbine cooling system and the coupling between the controlled variables of the system are analyzed. The decoupler of the system is designed by using the diagonal matrix decoupling method. The transfer function models of the coupling system are built through system identification, and the decoupling matrix of the system is calculated according to the diagonal matrix decoupling method and transfer function models. Then, the engine cooling control system simulation model is constructed and an improved jumping spider optimization algorithm is proposed. The parameters of the controller are optimized by the improved jumping spider optimization algorithm. Finally, the control system simulation is done and compared with the jumping spider optimization algorithm and the particle swarm optimization algorithm. The simulation results show that the improved jumping spider optimization algorithm is more suitable for the multivariable strong coupling nonlinear engine cooling system. For the flow and pressure control, the transient time and overshoot are reduced, and the steady-state error is less than 1%. For the temperature control, the result of the improved jumping spider optimization algorithm is more smooth, without overshoot, and almost does not exceed the set inlet water temperature. The overshoot, steady-state errors and transient time of the system have been improved, which proves the feasibility and significance of the improved jumping spider optimization algorithm by comparing the control performance and optimization time.

Cnoidal waves and dark solitons with linear third-order dispersion and self-steepening effect

The present paper investigates the conditions needed for the generation and propagation of cnoidal waves in the form of dark solitons under the influence of self-steepening effect and linear third-order dispersion. This kind of optical pulses could be obtained in single-mode waveguides due to the precise balance between higher orders of nonlinear and dispersive phenomena. As a basic equation, it is used the nonlinear amplitude equation (NAE). It is found a new analytical solution of this equation in the form of a cnoidal wave (Jacobi elliptic sine function). In the article it is presented that the solution can be reduced to dark soliton at specific values of the modulus of ellipticity κ.

The association of myocardial infarction hospitalizations and weather conditions in a private hospital in Brazil

Abstract Background The relationship between seasonal temperature peaks and the incidence of hospitalization for myocardial infarction has been reported in different countries. Despite increased interest in assessing the impact of temperature on hospitalization, few studies have used case-crossover designs to study non-linear and distributed delay effects temperature and thermal amplitude. In addition, is not clear how myocardial hospitalization is affected by temperature in subtropical climate cities. Objective We investigated the effects of climatic variables on the number of hospitalizations for myocardial infarctions at a private hospital at a city with a subtropical climate from 2017 to 2019. Methods Myocardial hospitalization records were extracted from database obtained through the Brazilian Information System on Hospitalization according to the municipality of residence and the CID-10 classification in elderly people. The temporal analysis of this study aimed at verifying the relationship between hospitalizations, climatic attributes, and the standard deviation of other descriptive statistics. To estimate the non-linear and time-interval effects, we used Distributed Lag Non-Linear Models (DLNM), which allowed us to observe their distributed delay effects. This model is suitable for studying the impact of environmental conditions on health, as it usually occurs a few days after exposure. The data were analyzed using the R software. Results In Figure 1, five descriptive graphs illustrate the study's primary data.Distribution of hospitalizations by gender (A), showing the predominance of males (65.81%), age group of 60 to 69 years (44.63%), followed by the group of 70 to 79 years (33.61%). Chart D shows that the medians representing hospitalization rates are higher in different bimesters throughout the year. Moreover, in chart E, the monthly averages of hospitalization rates per 100,000 elderly inhabitants, segmented by gender, show a prevalence of the male gender in all months.Based on the Poisson model for the variables combined, some lags were shown to be significant (17 and 20) at an α= 5% significance level, both for minimum temperature (p=0.00768) and relative humidity (p=0.03263). In addition to the other factors such as gender (p=4.14e-09) and all age levels (p=0.000), they can influence the number of hospitalizations. From the results shown in Table 1, we can interpret that when the Odds Ratio has a value between 0 and 1, the chance of hospitalization is reduced as the variable increases, or when the estimated value of the Odds Ratio is greater than 1, there is an increase in the chance of hospitalization as the respective variable increases. No significant results were found for maximum temperature and mean temperature. Conclusion Understanding the effects of temperature on cardiovascular risk factors over time in the elderly may help optimize prevention strategies and better organize care for elderly patients throughout the year. Funding Acknowledgement Type of funding sources: Private hospital(s). Main funding source(s): Constantini Cardiology Hospital

Softening-spring nonlinearity in large amplitude vibration of unsymmetric double-layer lattice truss core sandwich beams

In recent years, many novel sandwich structures with multilayer or graded lattice truss cores that exhibited superior structural performance have been proposed. However, only limited works have studied the nonlinear behavior of sandwich structures with unsymmetric lattice truss cores. This paper aims to provide an analytical study on the nonlinear vibration of the unsymmetric double-layer lattice truss core sandwich beams (LTCSBs). The double-layer LTCSB is designed to be unsymmetric and possesses varying material property and structural geometry in each layer. In this study, six unsymmetric cases of LTCSB classified as two categories according to the midplane locations are considered. Subsequently, an analytical model for the unsymmetric double-layer LTCSB is developed based on the Allen’s model and von Kármán nonlinear theory. The axial displacement of the midplane of LTCSB is considered in the analytical model, therefore the proposed model is more generalized compared with previous models for the symmetric double-layer LTCSB. The Ritz method with a direct iterative procedure is applied to solve the nonlinear governing equations and determine the nonlinear frequencies for the unsymmetric double-layer LTCSB. Finally, the effects of six unsymmetric cases of LTCSBs on the nonlinear frequency ratio versus amplitude curve under three different types of boundary conditions are discussed detailly. An interesting phenomenon of softening-spring nonlinearity is found for hinged–hinged and clamped–hinged sandwich beams with large bending–extension coupling.

Modeling nonlinear acoustic damping due to flow separation

Nonlinear acoustic damping has been observed in many high-amplitude acoustic systems as a result of flow separation and shear layer vortical motion, eventually transforming some of the acoustical energy into heat. The amount of nonlinear acoustic damping helps determine the nonlinear limit cycle amplitude, e.g., damping caused by baffle blades in a liquid rocket engine to reduce combustion instabilities. The damping mechanism is dependent on both the location and phase of flow separation. Identifying the flow separation is a function of both the boundary layer growth and the acoustically imposed pressure gradient. When the acoustic pressure gradient is adverse, the boundary layer is more prone to separation. Using this as a basis, a model can be created that is applicable to general geometry, which will then be used to approximate the nonlinear acoustic damping in various situations. The constructed model will be compared to established cases, such as an orifice in a duct, to validate the model.

An efficient analytical approach to assess root cause of nonlinear electric vehicle gear whine

Noise, vibration, and harshness (NVH) issues pose considerable challenges for electric vehicle powertrain engineers. Gear vibrations generate an intrusive gear whine noise, with significant impact on the sound quality of electric powertrains. Dynamic transmission error (DTE) is the most quantitative indicator for gear NVH. Backlash, time variable meshing stiffness and damping contribute to DTE. Hence, a better understanding of these excitation sources is essential. A gear tribodynamics model is developed using potential energy method to estimate time variable meshing stiffness (TVMS). A fully analytical time-efficient model is proposed for lubricated contact stiffness based on transitions in the regimes of lubrication. The model accounts for the combined effects of surface elasticity and lubricant stiffness. Film thickness and damping coefficients are transiently updated at each instant during meshing cycle. The predictions from this model are compared with measured results from the literature and predicted results from Hertz contact model. The lubricated contact model successfully shows the contribution of the lubricant stiffness to TVMS and its variations with elasticity and viscosity parameters during meshing cycle. Gear harmonic and super-harmonic resonances are accurately estimated in terms of amplitude, frequencies and stiffness softening nonlinearities. Time history responses and phase-displacement diagrams show good agreement with the gear dynamics response at the main harmonic and second super-harmonic frequencies. The proposed model has a reasonable accuracy, significantly better than those from Hertzian contact models, and is considerably time efficient in comparison to numerical EHL solvers.

Effects of compressibility and guiding field on the Kelvin–Helmholtz instability in weakly reversed magnetic shear configurations

The effects of compressibility and guiding field on the Kelvin–Helmholtz (KH) instability in a double resonant surface system are numerically investigated by using a compressible magnetohydrodynamics model. The linear growth rate and the nonlinear saturation amplitude are analyzed for different parameters. A transition from double tearing modes to the KH instability occurs depending on the compressibility and guiding field with a weak magnetic shear. These results may deepen our understanding of the properties of the KH instability with double resonant surfaces in both space and laboratory plasmas.

Neutron star stability with equations of state breaking the conformal QCD limit

We explore the structural stability of neutron stars against radial pulsations obtained by a set of equations of state calculated from successive interpolations between perturbative QCD at high densities and chiral effective field theory at low densities being constrained also by observational data at intermediate densities. In order to do this, we solve a pair of first-order coupled differential equations equivalent to the original Sturm-Liouville problem to obtain the zero-mode frequencies characterizing stable stars. Besides, we study the effects of mild and large breakings of the conformal limit put for the speed of sound, , in stars that can possibly contain cold quark matter at their cores. We find that some neutron-star families display an unusual humps in the mass-radius diagram which are associated to large non-linear oscillation amplitudes near the core.

Nonlinear steady state vibrations of beams made of the fractional Zener material using an exponential version of the harmonic balance method

This paper presents the application of an exponential version of the harmonic balance method to the analysis of steady state vibration of geometrically nonlinear systems. A detailed description of the method and of the corresponding numerical procedure is provided. The von Karman theory is used to describe the effects of geometric nonlinearity. The material of the beams is modelled with the help of the Zener model using the fractional calculus. The problem is solved using an exponential version of the harmonic balance method. In the above-mentioned version, the complex calculus is used in contrast to the ordinary harmonic balance method, where the steady state vibrations are described with the help of the trigonometric functions. It significantly simplifies derivation of the amplitude equations. Moreover, the exponential version of the harmonic balance method is more elegant in comparison with the ordinary one. A detailed derivation of the amplitude equations is presented. The modified continuation method is proposed to solve the nonlinear amplitude equations and to determine the response curves. Moreover, the results of the exemplary calculation are presented and compared with known results in order to justify the efficiency and the correctness of the proposed approach.

The dynamical motion of a rolling cylinder and its stability analysis: analytical and numerical investigation

The present paper addresses the dynamical motion of two degrees-of-freedom (DOF) auto-parametric system consisting of a connected rolling cylinder with a damped spring. This motion has been considered under the action of an excitation force. Lagrange's equations from second kind are utilized to obtain the governing system of motion. The uniform approximate solutions of this system are acquired up to higher order of approximation using the technique of multiple scales in view of the abolition of emerging secular terms. All resonance cases are characterized, and the primary and internal resonances are examined simultaneously to set up the corresponding modulation equations and the solvability conditions. The time histories of the amplitudes, modified phases, and the obtained solutions are graphed to illustrate the system's motion at any given time. The nonlinear stability approach of Routh–Hurwitz is used to examine the stability of the system, and the different zones of stability and instability are drawn and discussed. The characteristics of the nonlinear amplitude for the modulation equations are investigated and described, as well as their stabilities. The gained results can be considered novel and original, where the methodology was applied to a specific dynamical system.

Nonlinear Modes in Shear Horizontal Wave Propagation–Analytical and Numerical Analysis

Nonlinear shear horizontal guided wavefield is investigated analytically in plates. The major focus is on the effect of nonlinear material parameters, excitation frequency, wave number and wave amplitude on nonlinear mode generation. The analytical solution is based on the multiple-scale perturbation method and modal decomposition approach. The approximate analytical solution is validated using the Local Interaction Simulation Approach, implemented for nonlinear shear wave propagation. The results show that the analysed shear horizontal wavefield is distorted by material nonlinearity. The resulting displacement field can be interpreted in a form of nonlinear modes.

Aerodynamic stability of typical sea-crossing bridge with streamlined box girder under wave-interfered complex wind fields

Tropical cyclones landing on the coast are usually associated with both strong winds and waves, posing a major threat to sea-crossing bridges. Strong waves riding on the elevated storm surge squeeze the narrow gap between the sea surface and bottom of the bridge deck, thus complicating the wind field and leading to different bridge nonlinear flutter responses as compared with the steady flow field. In this study, to evaluate the bridge safety under such circumstances, wind tunnel test was carried out for a typical sea-crossing bridge with streamlined box girder based on a developed dynamic response test system for simulating the coupling effect of wind, wave, and current on bridges, where the clearance, underneath the bridge deck, and wave speed can be systematically adjusted to investigate the wind field characteristics and bridge nonlinear flutter response. Numerical simulation with the LES (large eddy simulation) scheme was employed to successfully visualize the wind field around the bridge and the mechanism of the nonlinear flutter response was analyzed in detail. The results of this preliminary investigation show that: (a) In the wind tunnel tests, when the wave crest passes under the bridge, the acceleration effect due to the narrow gap can lead to an increase for the nonlinear flutter amplitude of the bridge, which threatens the structural safety; (b) The measured wind speed at the bridge site exhibits strong turbulence intensity and non-Gaussian distribution tendency; and (c) Based on the numerical simulation, the airflow between the wave crest and the main structure features a large vertical velocity component, leading to a large AOA (angle of attack) value of the incoming flow. Meanwhile, the air pressure around the girder is unevenly distributed, thus unavoidably weakening the aerodynamic stability of the bridge.

Weakly nonlinear incompressible Kelvin–Helmholtz instability in plane geometry

A weakly nonlinear (WN) theoretical model for the two-dimensional incompressible Kelvin–Helmholtz instability (KHI) is proposed. Its solution form is the complete expansion in real space. The transition from linear to nonlinear growth is analytically studied via third-order solutions of plane KHI initiated by a single-mode surface perturbation. The difference between the WN growth of the Rayleigh–Taylor instability (RTI) in plane geometry and the WN growth of the KHI in plane geometry is discussed. It is found that there are resonance solutions in the higher harmonics of KHI but not in RTI. The vertex of spikes and bubbles is deflected because of the shearing effect in KHI compared with that in RTI. The spike velocity increases with the Atwood number before a particular time and then inversely after that time. There is no such reversal in RTI. However, the bubble velocity with the Atwood number of KHI has the same evolution rule as that of RTI. In addition to the influence of initial perturbation on the nonlinear saturation amplitude, the influence of Atwood number on the nonlinear saturation amplitude of the fundamental mode is obtained. Finally, compared with the numerical simulations, at the same initial conditions, the analytical solutions up to the third harmonics are well consistent with the simulated datum in the linear and weakly nonlinear stages for a widely varied Atwood number.

Kronecker Product Based Modeling of Darlington Amplifier and State Estimation using Unscented Kalman Filter

ABSTRACT This paper presents the application of unscented Kalman filter (UKF) for output voltage estimation of the Darlington amplifier (DA). Implementation of UKF requires the state-space model of DA circuit, which has been obtained using Kirchhoff’s voltage law (KVL), Kirchhoff’s current law (KCL) and the Gummel–Poon model of the bipolar junction transistor (BJT). This work uses Kronecker product for vector multiplication. The mathematical representation of nonlinear system in terms of Kronecker product helps to reduce the computational burden involved in the vector multiplication. The proposed method has the advantage that it can be used for the nonlinear region and large amplitude input signal. As the maximal precision of estimation requires modelling in terms of circuit elements and device parameters, the proposed method is able to provide an accurate estimation. We compared the UKF estimation results with the extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF). The UKF presents smaller mean square error (MSE) as compared to EKF and IEKF as UKF is accurate to the third order for any nonlinearity. In addition, IEKF presents smaller MSE as compared to EKF because the linearisation error is taken into account by IEKF.

A nonlinear metamaterial plate for suppressing vibration and sound radiation

Nonlinear acoustic metamaterials (NAMs) exhibit extraordinary properties for low-frequency and broadband vibration mitigation. Despite the increasing attention received, exotic properties and the physical mechanisms underpinning NAM-enabled functionalities have not been fully understood. Moreover, investigations on the sound radiation of NAM structures have not been reported. Here we systematically investigate the vibration of a NAM plate and its sound radiation using experimental and theoretical methods. We experimentally demonstrate that the NAM plate can entail significant vibration and sound radiation reduction in an ultra- low and broad frequency band, typically from 20 to 1800 Hz, without any artificial damping element. This is attributed to the nonlinear coupling among multiple local resonances, and the nonlinear collision-friction damping. This understanding allows the proposal of two design strategies to achieve ultra- low and broadband vibration and sound radiation suppression with NAMs. Moreover, we clarify the mechanisms governing the ultra- low and broadband features, including bandgaps, output saturation of nonlinear resonances, efficient energy pumping due to high-order harmonics and chaos, and modulation of nonlinear resonance modal amplitudes and shapes. These mechanisms and diverse wave behaviors are inter-related and occur concurrently. The reported study provides answers to several key questions of paramount importance in designs, mechanics and applications of nonlinear metamaterials.

Influence of End-Capped Modifications in the Nonlinear Optical Amplitude of Nonfullerene-Based Chromophores with a D-π-A Architecture: A DFT/TDDFT Study.

Nonlinear optical (NLO) materials have several uses in many fields such as solid physics, biology, medicine, nuclear physics, and material research. Therefore, a series of nonfullerene-based derivatives (CC10D1–CC10D8) with a D−π–A configuration was planned for the NLO investigation using CC10R as the reference molecule with structural alternations at acceptor moieties. Natural bonding orbital (NBO), UV–vis spectra, frontier molecular orbitals (FMOs), global reactivity parameters (GRPs), transition density matrix (TDM), and density of states (DOS) were analyzed using the M06/6-311G(d,p) functional in chloroform solvent to understand the NLO responses of CC10R and CC10D1–CC10D8. The highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) band gaps of CC10D1–CC10D6 were illustrated to be lower than that of CC10R, with the larger bathochromic shift (726.408–782.674 nm) resulting in a significant NLO response. Along with the band gap, the FMO method also identified an efficient interfacial charge transfer from D to A moieties via a π-bridge, which was further supported by the DOS and TDM map. Moreover, NBO calculations demonstrated that extended hyperconjugation and strong internal molecular interactions were important in their stabilization. The dipole moment (μ), linear polarizability ⟨α⟩, hyperpolarizability (βtotal), and second-order hyperpolarizability (γtotal.) were studied for CC10R and CC10D1–CC10D8. Among all of the derivatives, CC10D2 was proven to be the most appropriate candidate because of its suitable NLO behavior such as being well-supported by a reduced band gap (2.093 eV) and having a suitable maximum absorption wavelength (782.674 nm). Therefore, CC10D2 was reported to have a greater value of first hyperpolarizability (208 659.330 a.u.) compared with other derivatives and CC10R. For the second hyperpolarizability, a greater value was obtained for CC10R (5.855 × 107 a.u.), and its derivatives showed results comparable to that of the parent chromophore for γtotal. This theoretical framework reveals that structural customization with different acceptor units plays a significant role in obtaining attractive NLO materials for optoelectronic applications.