Time-domain Solution Method Research Articles

Research on the Time-Domain Explicit and Implicit Solution Methods of the Shallow Water Seismic Wavefield Equations

The current time-domain solution methods for the wavefield equations of a single medium do not apply to the wavefield equations of shallow water seismic with a fluid–elastomer coupling. To solve this problem, based on the explicit central difference method and implicit Newmark method, the explicit–explicit method, implicit–implicit method, and explicit–implicit method time-domain expressions for the local solution are derived, and the time-domain expressions for the explicit and implicit methods in the global solution are derived.The stability and computational efficiency of different time-domain solving methods for the shallow water seismic wavefield equations are theoretically analyzed. The numerical results are compared with the simulation data from the multiphysics field simulation software COMSOL 6.0, and the numerical stability, computational efficiency and accuracy of the different solving methods are also analyzed theoretically. The results show that the implicit method in the global solution is relatively optimal among the methods proposed in this paper, which ensures numerical stability at the larger step size for improving the computational efficiency and considers the higher computational efficiency and accuracy.

Active vibration control of fluid-conveying pipelines: Theoretical and experimental studies

For the fluid-conveying pipeline with macro-fiber composites (MFC), relevant dynamic modeling and experimental testing studies are rarely found in previous papers. Therefore, this paper has carried out related research work. Firstly, considering the fluid-structure interaction and piezoelectric effects, a semi-analytical modeling method for the fluid-conveying pipeline with MFC attaching to any position is proposed. A new Runge-Kutta-Gear (RKG) time-domain solution method is presented for solving state-space equations with the characteristics of rigid equations, and the design methods of Linear-Quadratic Regulator (LQR) controller and Proportional-Integral-Derivative (PID) controller are introduced, respectively. Secondly, an experimental system for active control and vibration test is built, and the dynamic model and control method are verified by experiments and simulations. Finally, the influence of relevant control parameters in the controller on the active control effect is discussed, and the influence law of fluid parameters such as fluid velocity and fluid pressure on the active control is also clarified. The novelty of this work is that the active vibration control and solution methods for the fluid-conveying pipeline with MFC are proposed, and the feasibility of MFC for pipeline vibration suppression is verified by experiments, which provides a new technical idea for the vibration reduction design of the fluid-conveying pipeline.

Time Domain Analysis of Ride Comfort and Energy Dissipation Characteristics of Automotive Vibration Proportional–Integral–Derivative Control

<div>A time domain analysis method of ride comfort and energy dissipation characteristics is proposed for automotive vibration proportional–integral–derivative (PID) control. A two-degrees-of-freedom single wheel model for automotive vibration control is established, and the conventional vibration response variables for ride comfort evaluation and the energy consumption vibration response variables for energy dissipation characteristics evaluation are determined, and the Routh stability criterion method was introduced to assess the impact of PID control on vehicle stability. The PID control parameters are tuned using the differential evolution algorithm, and to improve the algorithm’s adaptive ability, an adaptive operator is introduced, so that the mutation factor of differential evolution algorithm can change with the number of iterations. The PID control parameter optimization method presented in this article is versatile and can be used to optimize PID control parameters under different conditions. This article provides the results of PID control parameter optimization under different conditions. Based on PID control and its parameter tuning, a time domain solution method for two types of vibration response variables, their root mean square values, and the average power of energy consumption vibration of automotive vibration PID control is proposed. Two kinds of simulation test schemes are designed under urban driving conditions, which are commonly used Class B road and pulse road, with a commonly used vehicle speed of 60 km/h. The ride comfort and energy dissipation characteristics of passive suspension and PID control are compared. The results show that introducing energy consumption vibration response variables as a supplement to the conventional vibration response variables is beneficial for expanding the research and application scope of the automotive vibration and its control; with the sprung mass acceleration deviation as the control input, PID control can effectively improve the vehicle ride comfort, but it makes the vibration energy dissipation characteristics worse.</div>

Numerical analysis of the performance of a composite marine propeller blade subject to structural blade oscillations

High-fidelity Large Eddy Simulations (LES) are conducted over the oscillating marine propeller blades to investigate the effects of blade oscillation on the unsteady flow behaviour as well as to analyse the performance of the composite marine propeller blades. The accuracy of the results is first verified against the reference experimental results. A nonlinear frequency-domain solution or harmonic solution method is also applied to this study, based on a high-fidelity LES model, in addition to the traditional time-domain solution method to investigate the capabilities of the frequency-domain method in predicting the unsteady flow parameters, vortex generation, and hydrodynamic damping to determine the stability of the propeller blades. Results obtained reveal that the oscillation of the blade has a great impact on the vortex generation process which could impose implications on the performance and structural integrity of the composite marine propeller blades.

Stability Analysis of an Industrial Blade Accounting for a Blade-Tip/Casing Nonlinear Interface

Abstract This paper investigates the local stability analysis of periodic solutions corresponding to the nonlinear vibration response of an industrial compressor blade, NASA rotor 37, on which are applied different types of nonlinearities. These solutions are obtained using a harmonic balance method-based approach presented in a previous paper. It accounts for unilateral contact and dry friction of the rotating blade against a rigid casing through a regularized penalty law. A Lanczos filtering technique is also employed to mitigate spurious oscillations related to the Gibbs phenomenon thus enhancing the robustness of the solver. In addition, a component mode synthesis technique is used to reduce the dimension of the numerical model. Stability assessment of the computed solutions relies on Floquet theory. It is performed through the computation of the monodromy matrix as well as Hill's method. Both methodologies are applied and thoroughly compared as the severity of the nonlinearity is gradually increased from a cubic spring to three-dimensional contact conditions on a deformed casing. While the presented results underline the applicability of both stability assessment methodologies for all types of nonlinearities, they also put forward the much higher computational effort required when computing the monodromy matrix. Indeed, it is shown that Hill's method yields converged results for significantly lower values of both the number of retained harmonics and the considered number of time steps thus making it a far more efficient method when dealing with industrial models. It is also underlined that the presented results are in excellent agreement with reference solution points obtained with time domain solution methods. Specific implementation tweaks that were found to be of critical importance in order to efficiently assess the stability of computed solutions are also detailed in order to provide a comprehensive view of the challenges inherent to such numerical developments.

An Experimental and Numerical Study on the Aerodynamic Performance of Vibrating Wind Turbine Blade with Frequency-Domain Method

A highly efficient nonlinear frequency-domain solution method is proposed and employed to investigate the aerodynamic and aeromechanical performances of an oscillating wind turbine blade aerofoil in this study. Extensive validations of a frequency-domain method against an experiment as well as a typical time-domain solution method are provided in this paper. An experiment is also designed and conducted to measure pressure distributions over an aerofoil as well as to validate the numerical model. Unsteady pressure distributions and aeroelasticity parameters of the oscillating NACA0012 aerofoil are computed at various angles of attack and Reynolds numbers. Results indicate that the difference of unsteady pressure distributions between the two surfaces of the aerofoil becomes larger as the angle of attack is increased, whereas the flow separation on the suction surface is reduced by raising the Reynolds number. The turbulent flow develops in the downstream region due to the laminar vortex shedding at lower Reynolds numbers. It is also revealed that the Reynolds number has an impact on the aeroelasticity, and the aerodynamic damping value is larger at higher Reynolds numbers. The comparison between the frequency-domain method and the time-domain method shows that the frequency-domain method is not only accurate but also computationally very efficient as the computation time is reduced by 90%.

High-fidelity CFD simulations of two wind turbines in arrays using nonlinear frequency domain solution method

Aerodynamics of a wind turbine within windfarms is strongly influenced by the wake of neighbouring turbines. In particular, the performance of a wind turbine can be dramatically reduced depending on its location in the wake region of an upstream turbine. A detailed investigation of the effect of the upstream turbine on the downstream turbine with respect to their distances is essential for the design and optimisation of wind farm layouts. Conventional time domain solution methods, such as Unsteady Reynolds Averaged Navier Stokes (URANS) based Computational Fluid Dynamics (CFD) model of wind turbines in arrays, can provide a detailed analysis of this interaction effect. These methods are, however, impractical due to a high computational cost required for modelling turbines in array configurations. In this paper, a novel modelling and computational method is proposed to simulate two wind turbines in arrays by considering them as a multi-stage turbine. A nonlinear frequency domain solution method is then employed to model flow nonlinearities due to their interactions. The distances between the turbines are varied, and the effects of the upstream wind turbine on the downstream one are thoroughly investigated. Extensive validations of the nonlinear frequency domain solution method against the conventional time domain solution method reveal that the proposed frequency domain solution method provides accurate results while reducing the computational cost by one to two orders of magnitude.

Aeromechanical Analysis of a Complete Wind Turbine Using Nonlinear Frequency Domain Solution Method

Abstract The high-fidelity computational fluid dynamics (CFD) simulations of a complete wind turbine model usually require significant computational resources. It will require much more resources if the fluid–structure interactions (FSIs) between the blade and the flow are considered, and it has been the major challenge in the industry. The aeromechanical analysis of a complete wind turbine model using a high-fidelity CFD method is discussed in this paper. The distinctiveness of this paper is the application of the nonlinear frequency domain solution method to analyze the forced response and flutter instability of the blade as well as to investigate the unsteady flow field across the wind turbine rotor and the tower. This method also enables the aeromechanical simulations of wind turbines for various interblade phase angles in a combination with a phase shift solution method. Extensive validations of the nonlinear frequency domain solution method against the conventional time domain solution method reveal that the proposed frequency domain solution method can reduce the computational cost by one to two orders of magnitude.

Vibrational dynamics of hydrogen molecules under intense THz waves

The physical properties and dynamics of molecules can be studied by the interaction between electromagnetic field and molecular system. The continuous development of terahertz technology provides a terahertz source capable of generating a sub-picosecond directional intense electric field. The generated intense-field terahertz wave has the same electric field intensity as the molecular local electric field environment, and on a sub-picosecond time scale of the directional electric field there can happen many ultrafast physical and chemical reactions. At present, the interaction between terahertz waves and molecules is limited mainly to the resonance interaction, that is, the molecules transition at different vibrational levels, caused through dipole interaction. In this work, based on the density functional theory calculation and the finite difference time domain solution method of Schrödinger equation, the intense non-resonance effect of intense terahertz wave electric field on hydrogen molecules is studied. The results show that under the action of intense terahertz wave sub-picosecond directional intense electric field, hydrogen molecule will produce an induced dipole moment. This dipole interacts with the external terahertz field, resulting in the fluctuation of proton probability density distribution and the change of vibration energy level population. Based on the non-resonant interaction between non-polar diatomic molecule hydrogen and intense terahertz wave, a unique way of producing the interaction between electromagnetic waves and molecules is displayed in this work, which is a method of studying the dynamics of non-polar molecules and molecules with weak polarity in intense terahertz field.

Nonlinear frequency domain solution method for aerodynamic and aeromechanical analysis of wind turbines

The aerodynamic simulations of wind turbines are typically carried out using a steady inflow condition. However, the aerodynamics and aeroelasticity of wind turbine blades can be significantly affected by inflow wakes due to the environmental conditions or the presence of neighbouring wind turbines. In this paper, the effects of flow unsteadiness on the aerodynamics and aeroelasticity of the wind turbine rotor are investigated. It is found that the unsteadiness of the wake can have an impact on the aerodynamic flow field around the wind turbine rotor and it could also influence the aeroelasticity of the wind turbine. One of the distinctive features of this paper is the application of the highly efficient nonlinear frequency domain solution method for modelling harmonic disturbances for the aerodynamic and aeromechanical analysis of wind turbines. A test case wind turbine is selected for the aerodynamic and aeromechanical analysis as well as for the validation of the method used. The effects of different material properties along with a large vibration amplitude on the aeroelasticity parameter known as aerodynamic damping of the wind turbine blade are also investigated in the present work. Compared to the conventional time domain solution methods, which require prohibitively large computational cost for modelling and solving aerodynamics and aeroelasticity of wind turbines, the proposed frequency domain solution method can reduce the computational cost by one to two orders of magnitude.

A time domain solution of the Modified Temperature Vegetation Dryness Index (MTVDI) for continuous soil moisture monitoring

This study presents indexes developed from remote sensing observations for continuous soil surface moisture monitoring. The Modified Temperature Vegetation Dryness Index (MTVDI) proposed in our earlier work is developed using a time domain solution method rather than the traditional spatial domain solution method, because of limitations arising from a traditional temperature-vegetation index (TVX) method. In the procedure herein proposed, the MTVDI parameterization scheme is transformed from regional scale to pixel scale, and the boundary conditions defining maximum water stress are determined pixel by pixel using the surface energy balance principle. All the parameters required for the retrieval of MTVDI are pixel specific, thereby avoiding the limitations of the traditional spatial domain solution method. Previous studies demonstrate the applicability of the TVX method with data from only a few days of clear sky conditions. In contrast, our proposed MTVDI is demonstrated using Moderate Resolution Imaging Spectroradiometer (MODIS) products over the course of a full year, and the soil moisture status over the Southern Great Plains (SGP) region is monitored continuously. Finally, the volumetric surface soil water content (θv) is estimated using a calibration procedure from the MTVDI retrievals. The results show that the accuracy of both MTVDI retrievals and θv estimates obtained in this work has reached a level comparable with those produced in previous studies. Across all sites, the correlation coefficient (r) between the MTVDI and θv measurements is 0.60. The values of r, mean absolute error (MAE) and root mean square error (RMSE) for θv estimates are 0.75, 0.019m3m−3 and 0.025m3m−3, respectively.

Time domain simulation of side-by-side floating bodies using a 3D numerical wave tank approach

The coupled system of two side-by-side fixed and/or floating bodies interacting with a large amplitude nonlinear wave is studied using a direct time domain solution method. The numerical model is based on a three-dimensional mixed Eulerian–Lagrangian (MEL) method under certain simplifying approximations permitting Rankine panel scheme to be implemented over a time-invariant boundary surface to solve the boundary value problem for the unknown velocity potentials. A 4th order Adams–Bashforth–Moulton scheme is used for time marching of rigid-body motion histories of the individual bodies and evolution of the free-surface including the gap region in which large resonant fluid motions occur. A systematic study has been carried out to evaluate the performance of the developed time domain method in simulating the forces and motions as well as the fluid motion in the gap region for the two body system under various arrangements and in different wave-headings. At first, the computed numerical results have been validated and verified with computational and experimental results available in literature for standard geometries such as vertical truncated cylinders and rectangular boxes. Secondly, effectiveness of the damping lid model which is introduced to suppress wave resonance in the gap region is investigated including its influence on maximum sway forces on fixed and floating rectangular barges in side-by-side configurations. Thirdly, comparative studies on absolute and relative motion response for two cases (two rectangular barges, and a FLNG-FPSO+shuttle tanker) in side-by-side arrangement are detailed to bring out the importance of nonlinearities arising due to steep nonlinear incident waves. Finally, coupled motions of the two-body system of an FPSO and a shuttle tanker floating in side-by-side configuration in a steep nonlinear wave field are studied in which the two bodies are connected through hawsers, and also the FPSO is moored to the ground. Additionally there is a fender between the two bodies.

Comparison of Frequency Domain and Time-Domain Methods for Aeromechanical Analysis

Unsteady flow around an oscillating plate cascade and that through a single compressor rotor subject to vibration have been computationally studied, aimed at examining the predictive ability of two low fidelity frequency methods compared with a high fidelity time-domain solution method for aeroelasticity. The computational solutions demonstrate the capabilities of the frequency domain methods compared with the nonlinear time-domain solution method in capturing small perturbations in the unsteady flow. They also show the great advantage of significant CPU time saving by the frequency methods over the nonlinear time method. Comparisons of two different frequency methods, nonlinear harmonic and phase solution method, show that these methods can produce different results due to the differences in numeric and physical conditioning. The results obtained using phase solutions method are in better agreement with the nonlinear time-domain solution. This is because the same numeric and physical conditioning are used in both the nonlinear time-domain method and phase solution frequency domain method.

Nonlinear Simulation Methods for Active Microwave Circuits: A Review of the Art and Novel Trends

This paper discusses in detail, two techniques for the analysis of non-linearelectronic circuit. The first technique is an automated version of thetraditional time domain solution method (Transient Analysis). For a givencircuit topology the state equations are generated by computer and solvednumerically. The second technique involves the use of a hybrid timefrequencydomain approach and is known as harmonic balance (Steady StateAnalysis). The formulation and solution methods adopted for both methodsare outlined in detail. Emphasis is placed throughout an application tomicrowave circuits. In order to illustrate the properties of each method,sample analyses for two main circuits are given. The first circuit is that of alinear amplifier operating at 12 GHz and driven into saturation. The secondcircuit is that of a nonlinear frequency doubler, doubling from 7-14 GHz.Some advanced applications are discussed in order to further highlight therelative advantages and disadvantages of each technique. Finally it is shownhow a non-linear CAD package can be produced which allows circuitoptimization in a similar way to that allowed by linear CAD programs.Some remaining problems which need more investigations and possiblefuture work are highlighted.

Dynamic train–turnout interaction in an extended frequency range using a detailed model of track dynamics

A time domain solution method for general three-dimensional dynamic interaction of train and turnout (switch and crossing) that accounts for excitation in an extended frequency range (up to several hundred Hz) is proposed. Based on a finite element (FE) model of a standard turnout design, a complex-valued modal superposition of track dynamics is applied using the first 500 eigenmodes of the turnout model. The three-dimensional model includes the distribution of structural flexibility along the turnout, such as bending and torsion of rails and sleepers, and the variations in rail cross-section and sleeper length. Convergence of simulation results is studied while using an increasing number of eigenmodes. It is shown that modes with eigenfrequencies up to at least 200 Hz have a significant influence on the magnitudes of the wheel–rail contact forces. Results from using a simplified track model with a commercial computer program for low-frequency vehicle dynamics are compared with the results from using the detailed FE model in conjunction with the proposed method.

Discrete Huygens’ modeling for the characterization of a sound absorbing medium

Based on the equivalence between the wave propagation in the electrical transmission-lines and acoustic tubes, the authors proposed the use of the transmission-line matrix modeling (TLM) for time-domain solution method of the sound field. TLM is known in electromagnetic engineering community, which is equivalent to the discrete Huygens’ modeling. The wave propagation is simulated by tracing the sequences of the transmission and scattering of impulses. The theory and the demonstrated examples are presented in the references, in which a sound absorbing field was preliminarily considered to be a medium with simple acoustic resistance independent of frequency and the angle of incidence for the absorbing layer placed on the room wall surface. The present work is concerned with the time-domain response for the characterization of the sound absorbing materials. A lossy component with variable propagation velocity is introduced for sound absorbing materials to facilitate the energy consumption. The frequency characteristics of the absorption coefficient are also considered for the normal, oblique and random incidence. Some numerical demonstrations show that the present modeling provide a reasonable modeling of the homogeneous sound absorbing materials in time domain.

Time-linearised transonic computations including entropy, vorticity and shock wave motion effects

AbstractThe effect of small perturbations on steady nonlinear transonic small disturbance flowfields, in the context of two-dimensional flows governed by the general-frequency transonic small disturbance equation with nonreflecting far-field boundary conditions, is investigated. This paper presents a time-linearised time-domain solution method that includes effects due to the shock-generated entropy and vorticity and shock wave motions. The solution procedure correctly accounts for the small-amplitude shock wave motion due to small unsteady changes in the aerofoil boundary conditions, and correctly models a flowfield with embedded strong shock waves. Steady and first harmonic pressure distributions for the NACA 0003 aerofoil with a harmonically oscillating flap, and NACA 0012 aerofoil undergoing a sinusoidal pitching oscillation, are predicted and compared with the Euler results.

Efficient transient solution of linear circuits to sinusoidal inputs

In this paper, an efficient method for time domain solution of linear circuits to sinusoidal inputs is given. If the transient response of the circuit at frequency /spl omegasub 1/ is known, the method efficiently computes the response at another frequency /spl omegasub 2/. The results are obtained by one frequency solution of the circuit for each additional frequency of interest. Applications include simulation of periodically switched linear circuits; examples include switched capacitor, switched current, and sigma-delta modulators.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modal truncation vectors and periodic time domain analysis applied to a cyclic symmetry structure

A finite element analysis was performed to assess the vibration response of a cyclic symmetric rotating turbopump impeller to a periodic time domain triangular pressure pulse loading. A summary of the cyclic symmetry methodology and cyclic symmetry boundary conditions used in the analysis is given. Two new analysis algorithms that were applied for the response analysis are detailed. The first algorithm involves appending ‘modal truncation’ vectors to the eigenvector set which, with the retained eigenvectors, will completely represent the spatial portion of the dynamic loading. This algorithm is applicable to any type of modal response analysis such as time domain, random, harmonic or shock spectrum. The second algorithm is a time domain response analysis method as opposed to the frequency domain analysis method for the solution to an arbitrary periodic time domain loading. The modal truncation vectors with the time domain solution method results in a complete representation of the applied dynamic loading in both the spatial and time domains for the dynamic response analysis.

Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method

A multi-harmonic, frequency domain analysis of dry friction damped systems is presented which uses an incremental harmonic balance method. When compared with time domain solution methods, it is found that the incremental harmonic balance method can yield very accurate results with some advantages over the time domain methods. Both one and two degree-of-freedom systems are studied.