Nonlinear Simulation Results Research Articles

On Optimal Truncated Biharmonic Current Waveforms for Class-F and Inverse Class-F Power Amplifiers

In this paper, two-parameter families of periodic current waveforms for class-F and inverse class-F power amplifiers (PAs) are considered. These waveforms are obtained by truncating cosine waveforms composed of dc component and fundamental and either second(k=2)or third(k=3)harmonic. In each period, waveforms are truncated to become zero outside of a prescribed interval (so-called conduction angle). The considered families of waveforms include both discontinuous and continuous waveforms. Fourier series expansion of truncated waveform contains an infinite number of harmonics, although a number of harmonics may be missing. Taking into account common assumptions that for class-F PA the third(n=3)harmonic is missing in current waveform and for inverse class-F PA the second(n=2)harmonic is missing in current waveform, we consider the following four cases: (i)n=k=3,(ii)n=3,k=2,(iii)n=k=2,and (iv)n=2,k=3.We show that, in each of these cases, current waveform enabling maximal efficiency (optimal waveform) of class-F and inverse class-F PA is continuous for all conduction angles of practical interest. Furthermore, we provide closed-form expressions for parameters of optimal current waveforms and maximal efficiency of class-F (inverse class-F) PA in terms of conduction angle only. Two case studies of practical interest for PA design, involving suboptimal current waveforms, along with the results of nonlinear simulation of inverse class-F PA, are also presented.

Stability analysis of dissolution-driven convection in porous media

We study the stability of dissolution-driven convection in the presence of a capillary transition zone and hydrodynamic dispersion in a saturated anisotropic porous medium, where the solute concentration is assumed to decay via a first-order chemical reaction. While the reaction enhances stability by consuming the solute, porous media anisotropy, hydrodynamic dispersion, and capillary transition zone destabilize the diffusive boundary layer that is unstably formed in a gravitational field. We perform linear stability analysis, based on the quasi-steady-state approximation, to assess critical times, critical wavenumbers, and neutral stability curves as a function of anisotropy ratio, dispersivity ratio, dispersion strength, material parameter, Bond number, Damköhler number, and Rayleigh number. The results show that the diffusive boundary layer becomes unstable in anisotropic porous media where both the capillary transition zone and dispersion are considered, even if the geochemical reaction is significantly large. Using direct numerical simulations, based on the finite difference method, we study the nonlinear dynamics of the system by examining dissolution flux, interaction of convective fingers, and flow topology. The results of nonlinear simulations confirm the predictions from the linear stability analysis and reveal that the fingering pattern is significantly influenced by combined effects of reaction, anisotropy, dispersion, and capillarity. Finally, we draw conclusions on implications of our results on carbon dioxide sequestration in deep saline aquifers.

Reduced-Order Modeling of Gust Responses

This paper describes two approaches to the construction of reduced-order models from computational fluid dynamics to predict the gust response of airfoils and wings. The first is a linear reduced-order model constructed using the eigensystem realization algorithm from pulse responses, and the second approach modifies the linear reduced-order model using steady-state data to introduce some nonlinearity into the reduced-order model. Results are presented for the Future Fast Aeroelastic Simulation Technologies wing and the Future Fast Aeroelastic Simulation Technologies crank airfoil. These show that for gusts of large amplitude in the transonic regime the response exhibits nonlinearity due to shock motion. This nonlinearity is not captured well by linear reduced-order models; however, the nonlinear reduced-order model shows better agreement with the full nonlinear simulation results.

Size dependent dynamic behavior of electrostatically actuated microbridges

In this paper, based on the size dependent theories, an accurate investigation for nonlinear dynamic analysis of electrostatically actuated microbridges is presented by using the nonlinear finite element formulation, analytical method and numerical approach. The microbridge used as a microresonator, is driven by simultaneously applied DC and AC voltages. In the framework of modified couple stress theory (MCST), the nonlinear equation of dynamic motion for this system is derived using extended Hamilton's principle. Thereupon, the nonlinear partial differential equation is converted to the nonlinear ordinary equation by Galerkin's method and solved by analytical and numerical techniques. The analytical solution for nonlinear vibration of the microresonators is obtained by perturbation theory. Findings show that the numerical and analytical results are in good agreement with each other. In order to make further verification of the analytical expression, a nonlinear nonclassical finite element formulation for dynamic deformation of the system is presented to calculate the time history results. The good agreement observed between the results of analytical method and nonlinear finite element simulation demonstrates that the procedures used in the analytical method such as Taylor expansion, one mode analysis and perturbation expansion in multiple scale approach are appropriate. By determining the frequency-response curves, the effects of size dependency on the amplitude of vibration and frequency position of the peak response are studied. Results show that considering the size dependent theory leads to notable decreasing of the amplitude of nonlinear vibration and approaching the frequency value of peak response to linear resonance frequency.

Fluid theory and simulations of instabilities, turbulent transport and coherent structures in partially-magnetized plasmas of discharges

Partially-magnetized plasmas with magnetized electrons and non-magnetized ions are common in Hall thrusters for electric propulsion and magnetron material processing devices. These plasmas are usually in strongly non-equilibrium state due to presence of crossed electric and magnetic fields, inhomogeneities of plasma density, temperature, magnetic field and beams of accelerated ions. Free energy from these sources make such plasmas prone to various instabilities resulting in turbulence, anomalous transport, and appearance of coherent structures as found in experiments. This paper provides an overview of instabilities that exist in such plasmas. A nonlinear fluid model has been developed for description of the Simon-Hoh, lower-hybrid and ion-sound instabilities. The model also incorporates electron gyroviscosity describing the effects of finite electron temperature. The nonlinear fluid model has been implemented in the BOUT++ framework. The results of nonlinear simulations are presented demonstrating turbulence, anomalous current and tendency toward the formation of coherent structures.

The Seismic Behaviour of Stone Masonry Greek Orthodox Churches

The seismic behaviour of structural systems representing Greek Orthodox churches is examined. All these churches are made of stone masonry in various architectural forms. During the years such churches developed damage to their stone masonry structural elements due to the amplitude of the gravitational forces acting together with the seismic forces. In certain cases such damage was amplified due to the deformability of the foundation. The behaviour of structural systems representing Greek Orthodox churches was simulated through linear and non-linear numerical models. The numerical results together with assumed strength values or failure criteria were utilized to predict the behaviour of the various masonry parts in in-plane shear and flexure as well as out-of-plane flexure. The deformability of the foundation partly explains the appearance of structural damage as can be seen both from observations and the numerical predictions. A limit-state methodology is presented whereby the demands obtained from linear elastic numerical models combined with limit-state in-plane behaviour of unreinforced stone masonry walls in shear/flexure or diagonal tension can yield reasonably good predictions of observed behaviour. Furthermore, the possibilities offered by non-linear inelastic numerical analyses as alternative means for examining the performance of unreinforced stone masonry walls is also briefly presented. Towards this objective, non-linear inelastic numerical simulation results are presented that yield reasonably good agreement with the relevant measured behaviour of stone masonry wall specimens of prototype dimensions that were subjected to simultaneous vertical compression and horizontal cyclic seismic-type loading in the laboratory. The obtained results from these specimens were utilized to also validate an expert system based on this limit-state methodology. Again, the observed behaviour was predicted with reasonable accuracy in terms of bearing capacity and mode of failure by this expert system.

Robust spot-poled membrane hydrophones for measurement of large amplitude pressure waveforms generated by high intensity therapeutic ultrasonic transducers.

The output characterization of medical high intensity therapeutic ultrasonic devices poses several challenges for the hydrophones to be used for pressure measurements. For measurements at clinical levels in the focal region, extreme robustness, broad bandwidth, large dynamic range, and small receiving element size are all needed. Conventional spot-poled membrane hydrophones, in principle, meet some of these features and were used to detect large amplitude ultrasonic fields to investigate their applicability. Cavitation in water was the limiting effect causing damage to the electrodes and membrane. A new hydrophone design comprising a steel foil front protection layer has been developed, manufactured, characterized, tested, and optimized. The latest prototypes additionally incorporate a low absorption and acoustic impedance matched backing, and could be used for maximum peak rarefactional and peak compressional pressure measurements of 15 and 75 MPa, respectively, at 1.06 MHz driving frequency. Axial and lateral beam profiles were measured also for a higher driving frequency of 3.32 MHz to demonstrate the applicability for output beam characterization at the focal region at clinical levels. The experimental results were compared with results of numerical nonlinear sound field simulations and good agreement was found if detection bandwidth and spatial averaging were taken into account.

Robust ESS-Based Stabilizer Design for Damping Inter-Area Oscillations in Multimachine Power Systems

In this paper, a robust approach to the energy storage system (ESS)-based stabilizer is proposed to select its installation location, feedback signals, and damping control loop, and to tune the stabilizer parameters. Based on the linearized model of the power system with ESS and application of damping torque analysis (DTA), the maximum of all minimum damping torque indices (DTIs) under multi-operational conditions is used as the index for selecting ESS installation locations, feedback signals and damping control loops. The operational condition for the minimum DTI provides the condition for tuning the ESS-based stabilizer parameters for robust operation. And a proper compensation angle is selected by a robust method to design the ESS-based stabilizer parameters. The eigenvalue analysis and non-linear simulation results of a four-machine power system and New England ten-machine power system with ESS show that power system oscillations are suppressed effectively and robustly by the ESS-based stabilizer.

Wide-area power system stabilizer design based on Grey Wolf Optimization algorithm considering the time delay

This paper proposes a method for designing wide-area power system stabilizer (WAPSS) based on the Grey Wolf Optimization (GWO) algorithm. The stabilizer is used to damp the inter-area oscillations by considering the communication latency which is related to the remote feedback signals. For this reason, a new multi-objective function is proposed for the design of the WAPSS. In this function, in addition to improving the stability of the system by displacing the critical modes, the stabilizer is designed in the minimum-phase with a less control gain. In this method, the maximum delay margin in which the closed-loop power system can remain stable can also be optimally identified.The proposed approach is tested in a small and a large multi-machine power system. The nonlinear simulation results and eigenvalues analysis have demonstrated that the approach which has been proposed in this article is highly effective in damping the inter-area oscillations as well as compensating for the destructive effects of the communication delay on the remote feedback signals.

電磁比例弁内のクーロン摩擦力に起因した自励振動の解析

This paper describes self-excited oscillation caused by coulomb friction of electromagnetic proportion valve. Especially, we focus on a hydraulic system in which electromagnetic proportion and pressure proportion valves are located tandemly. In the system, the coulomb frictional force effects on the displacement direction of the spool of the former valve and the piston is established in the downstream region of the latter valve. Each valve is stable, but, the connection of them causes instability. In this study, we analyze the mechanism of this unstable vibration and then investigate an anti-vibration design method. In analysis, this paper clarifies that the vibration is caused by an elastic deformation delay of the oil in the piston. This delay increases the phase delay of the spool due to the coulomb frictional force. In the design method, we use the describing function method to express phase delay phenomenon due to the coulomb frictional force. The effectiveness of this design method is demonstrated via practical experiment and non-linear simulation results.

Exploring New Boundaries to Mitigate Structural Vibrations of Bridges in Seismic Regions: A Smart Passive Strategy

The combined use of two emerging technologies in the field of seismic engineering is investigated. The first is a semiactive control, to reduce smartly the effects induced by earthquakes on structures. The second is the Seismic Early Warning System which allows an estimate of the Peak Ground Accelerations of an incoming earthquake. This paper proposes the exploitation of this information in the framework of a semiactive control strategy based on the use of magnetorheological (MR) dampers. The main idea consists of changing the MR dampers’ behaviour by the PGA estimated by the SEWS, to obtain the optimal seismic response of the structure. The control algorithm needed to drive the variable devices, according to the PGA estimate, is the core issue of the proposed strategy. It has been found that different characteristics of earthquakes that occur at different sites play a significant role in the definition of a control algorithm. Therefore, a design procedure for “regional” control algorithms has been performed. It is based on the results of several nonlinear dynamic simulations performed using natural earthquakes and on the use of a multicriteria decision-making procedure. The effectiveness of the proposed control strategy has been verified with reference to a highway bridge and to two specific worldwide seismic regions.

Vertical Track Irregularity Influence on the Wheel High-Frequency Vibration in Wheel-Rail System

A three-dimensional deformable finite element model of wheel-rail system is established. The vertical vibration natural frequencies are calculated by modal analysis. The improved central difference method by ABAQUS explicit nonlinear dynamics module is chosen to calculate the vertical vibration of wheel axle. Through the vibration measurement experiment ofLMAwheel by China Academy of Railway Sciences, the contact parameter is optimized and the model is modified. According to the nonlinear simulation results, the important influence of vertical track irregularity on the wheel set high-frequency vibration is discovered. The advantage frequencies through spectrum are close to the vertical vibration natural frequencies of seventh, eighth, ninth, and tenth mode. When the velocity is 350 km/h, system’s nonlinear dynamic characteristic is higher than the results at 200 km/h. The critical wavelength of vertical track irregularity on the wheel vertical vibration is about 0.8 m. In addition, a particular attention should be paid to one situation that the main dominant frequency amplitude is more than 50% of the acceleration amplitude even if the peak acceleration is low.

Numerical simulation of the Rayleigh–Taylor instability of a miscible slice in a porous medium

Convective instability in miscible slices is important in understanding the contaminant spreading in groundwater and sample dispersion in a chromatographic column. In the present study, the temporal evolution of the Rayleigh–Taylor instability of a miscible high-density slice in a porous medium is analyzed theoretically using nonlinear numerical simulations. Nonlinear governing equations are derived and solved with the Fourier spectral method. To connect the previous linear stability analysis and the present nonlinear simulation, the most unstable disturbance which was identified in the linear analysis is employed as an initial condition for the nonlinear study. In contrast to the fingering between two semi-infinite regions, the nonlinear fingering of a finite slice is influenced by the depth of the high-density region. The present nonlinear analysis shows that there exists a critical depth below which the system is linearly unstable, but nonlinear phenomena cannot be expected. The nonlinear simulation results show that nonlinear competition yields a series of cells of slightly different widths and amplitudes. Also, it is found that the upper stable region hinders the development of instability motions and stabilizes the system.

A coordinated genetic based type-2 fuzzy stabilizer for conventional and superconducting generators

This paper presents a new coordinated genetic interval type-2 fuzzy stabilizer for enhancing stability of a single machine infinite-bus (SMIB) power system including conventional or superconducting generators. Its principle is based on a coordination done by implementing simultaneously, interval type-2 fuzzy controllers, into excitation and turbine governor systems. Optimal adjustment of scaling factors has been carried out using genetic algorithms (GAs). Type-2 fuzzy controller provides improvement in comparison with type-1 controller in terms of modeling and minimizing the effect of uncertainties. Furthermore, governor control helps in damping oscillations enhancement especially in case of superconducting machine when excitation control alone is not sufficient. Non-linear simulation results of a SMIB power system, under different operating conditions, prove the effectiveness and the robustness of the proposed optimized type-2 fuzzy stabilizer (GFLC2EG) for both conventional and superconducting generators. In order to validate the robust performance of the proposed stabilizer, a comparative study is presented showing its superiority over other types of stabilizers.

Eigenvalue Assignments in Multimachine Power Systems using Multi-Objective PSO Algorithm

Applying multi-objective particle swarm optimization (MOPSO) algorithm to multi-objective design of multimachine power system stabilizers (PSSs) is presented in this paper. The proposed approach is based on MOPSO algorithm to search for optimal parameter settings of PSS for a wide range of operating conditions. Moreover, a fuzzy set theory is developed to extract the best compromise solution. The stabilizers are selected using MOPSO to shift the lightly damped and undamped electromechanical modes to a prescribed zone in the s-plane. The problem of tuning the stabilizer parameters is converted to an optimization problem with eigenvalue-based multi-objective function. The performance of the proposed approach is investigated for a three-machine nine-bus system under different operating conditions. The effectiveness of the proposed approach in damping the electromechanical modes and enhancing greatly the dynamic stability is confirmed through eigenvalue analysis, nonlinear simulation results and some performance indices over a wide range of loading conditions.

Nonlinear Theory for a Compact Radial Extended Interaction Oscillator

In this paper, a nonlinear theoretical simulation method based on a 1-D electron ring model for a new extended interaction structure—the radial extended interaction oscillator (R-EIO)—working in the fundamental mode is presented. The R-EIO has a compact structure and good heat dissipation characteristics. Furthermore, because of a significant increase in the electron injection channel area, the R-EIO has the potential for higher power operation using the same current density condition as a traditional EIO structure, giving it great research value. This paper presents an example of predicted R-EIO performance based on the results of nonlinear theoretical simulation and particle-in-cell (PIC) code simulation. At a voltage and current of 3 kV and 8.48 A, respectively, the theoretical simulations predict that the as designed R-EIO could generate 1.8 kW at 12.2104 GHz, while the PIC simulation predict 1.7 kW at 12.5 GHz. Similar results could be obtained from the nonlinear theoretical simulation, which cost less than 5 min, while about 50 h for PIC code simulation in the same computer condition.

Three-dimensional dynamic liquid slosh in partially-filled horizontal tanks subject to simultaneous longitudinal and lateral excitations

Three-dimensional liquid slosh in a horizontal cylindrical tank is analyzed assuming inviscid, incompressible and irrotational flows under simultaneous application of longitudinal and lateral accelerations, idealizing a braking-in-a-turn maneuver in a road tanker. The spectral problem of liquid slosh within the partially-filled tank of arbitrary cross-section and finite length is initially formulated using the higher order boundary element method (BEM). The three-dimensional Laplace equation is subsequently reduced to a two-dimensional Helmholtz equation using the separation of variables, which significantly reduces the computing demand. The computing time is further reduced by reducing the generalized eigenvalue problem to a standard one considering only the velocity potential on the half free-surface length. The resulting natural slosh frequencies and modes are implemented in a linear multimodal method to obtain generalized coordinates of the free-surface in a partly-filled circular cross-section tank. The slosh forces and moments are subsequently formulated in terms of generalized coordinates and hydrodynamic coefficients considering the damping due to liquid viscosity in the boundary layer. It is shown that the proposed BEM integrating the multimodal method yields computationally efficient solution of the three-dimensional liquid slosh within moving horizontal tanks. The validity of the model is demonstrated using reported analytical and experimental results. The range of applicability of the linear theory for predicting three-dimensional transient slosh is further discussed through comparisons with nonlinear simulation results obtained from a commercial CFD code. The results suggest that the linear theory can predict the slosh forces and moments with reasonably good accuracy when the steady-magnitudes of the lateral and longitudinal accelerations are less than 0.3 g and 0.2 g, respectively, for a tank with aspect ratio in the order of 2.4.

Numerical evaluation of absorbing boundary layers for the transient Khokhlov–Zabolotskaya–Kuznetsov Equation

FOCUS, the “Fast Object-Oriented C + + Ultrasound Simulator” (http://www.egr.msu.edu/~fultras-web), simulates nonlinear ultrasound propagation in the time-domain by numerically evaluating the transient Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation. KZK simulations in FOCUS previously required a computational grid with a large radial distance relative to the aperture radius to reduce the effect of reflections from the boundary. To decrease the size of the grid required for these calculations, an absorbing boundary layer derived from the power law wave equation provides an alternative to the stretched coordinate system in a perfectly matched layer. Simulations of the linear pressure fields generated by a spherically focused transducer with an aperture radius of 1.5 cm and a radius of curvature of 6 cm are evaluated for a short pulse with a center frequency of 1 MHz and a peak surface pressure of 0.5 MPa. Numerical results for linear KZK simulations with and without the absorbing boundary layer are compared to an on-axis analytical solution. Results of nonlinear KZK simulations with and without the PML are also evaluated, and all of these show that the absorbing layer effectively attenuates the wavefronts that reach the boundary of the computational grid. [This work was supported in part by NIH Grant R01 EB012079.]

Monitoring Data Filter and Deformation Information Extraction Based on Wavelet Filter and Empirical Mode Decomposition

Analyses of GPS signals by wavelet algorithms and empirical mode decomposition (EMD) have demonstrated the strength of these techniques in discriminating signals from noise. However, the denoising precision seriously affects the final EMD error, especially for signals containing incremental developments in information. We present a new noise filter and trend extraction model based on the orthogonal wavelet transform and EMD. Simulated and real data are used to evaluate the proposed method. The results suggest that: 1) The orthogonal wavelet transform and EMD method can better mitigate the random errors hidden in periodic signals; 2) For signals with a linear trend, the orthogonal wavelet transform filtering method is superior to EMD. We suggest a method of trend extraction by EMD after noise filtering using the wavelet; 3) For signals with a nonlinear trend, theoretical analysis and simulation results show that the new noise filter and trend extraction model is superior to EMD and the simple combination of wavelets with EMD. The proposed approach not only extracts instantaneous features, but also reduces the number of decomposition layers of the signals and the cumulative errors in later decomposition. This method significantly improves the accuracy of the extracted deformation; 4) After mitigating the influence of multipath and other error effects with the new model, we attain millimeter accuracy for the vertical component position in GPS dynamic deformation.

Switching robust control for a nanosatellite launch vehicle

The attitude control of a launch vehicle is a challenging task due to the dramatically varying vehicle dynamics along a flight path. The objective of this paper is to design a switching robust control strategy for launch vehicles, applied here to a notional nanosat launch vehicle. In order to control the rocket along a trajectory ascending through the Earth's atmosphere, a set of operating points at different times along the flight path are selected, the corresponding dynamics models of the rocket are obtained via linearization, and a robust H∞ controller is designed for each operating point using the linear matrix inequality approach. These controllers are applied to the nonlinear plant model via a switching strategy when the rocket flies along the flight path. Both linear and nonlinear simulation results are given to show the performance of the closed-loop system.