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Numerical simulation method is a powerful technique for chaos analysis. The traditional analytic method can't predict the behavior of the piecewise linear system (PLS) exactly because of the non-smoothness of the system, if the system is strong nonlinearity. The piecewise linear vibration isolation system with single degree of freedom (SDOF) was studied in this paper. The “inverse” integral method...
The second-order explicit Runge-Kutta-Chebyshev method(RKC) is an s-stage Runge-Kutta method designed for explicit integration of modestly stiff systems of ordinary differential equations. The method possesses extended real stability interval with a length β proportional to s2. Remarkable properties of the RKC method make it possible to select at each size the most efficient stable formula as well...
A new integrated measuring system with eight force-balance accelerometers was proposed to obtain a direct measurement of six degree-of-freedom (DOF) strong ground motions, including three rotational and three actual translational acceleration components without gyroscopes. In the proposed measuring system, the relationship between the outputs from eight accelerometers and the six DOF motions of the...
This paper proposes a convolution quadrature method based on implicit Runge-Kutta schemes for the temporal discretization, resulting in a higher-order convergence. Specifically, A-stable Radau IIA methods are employed for the mapping from the Laplace domain to Z-domain. The proposed method, with two and three stages, has thirdand fifth-order convergence respectively. The inverse Z-transform is computed...
In the path following motion control system, the reference tool path of the machine tool is geometric curves predetermined by applications. The reference motion command for servo control system is generated based on the geometric tool path and the feedrate. The command generation module is called path interpolation. It is a classical problem in the motion control system. However, a clear formula is...
This paper improves FDDM by using an implicit RungeKutta scheme [4] for the temporal discretization and applies the approach to dielectric scattering problems. Specifically, A-stable Radau ΠA methods are employed for the approximation, and the methods with two and three stages have the thirdand fifth-order convergence respectively. The inverse Z-transform is computed numerically using the discrete...
This paper propose a hybrid spectralelement / finite-element method (SEM/FEM) combined with the implicit-explicit Runge-Kutta (IMEX-RK) scheme for multiscale electromagnetic computation. This method is flexible in spatial discretization and efficient in time stepping. The basic idea and numerical results are presented in following sections.
The paper presents a thermodynamic model for a scroll compressor used for Compressed Air Energy Storage. The model includes energy conservation equation, instantaneous volume equation and gas leakage equation. The numerical simulation results are achieved by means of the 4th order Runge-Kutta method under Matlab and are compared with the experimental values. Different performance parameters of the...
A steady-state dynamic model for a cable in air is put forward by using some tensor relations. For the dynamic motion of a long-span Cable Driven Parallel Robot (CDPR) system, a driven cable deployment and retrieval mathematical model of CDPR is developed by employing lumped mass method. The boundary condition of cable and initial values of equations is founded, The partial differential governing...
Flutter, a dynamic instability of aircrafts, may degrade the safety of the structures. Active flutter suppression (AFS) is a considerable solution to this issue. Sliding mode control (SMC) method, a nonlinear control strategy, is applied to AFS of a typical two-dimensional airfoil in this work. The airfoil has a trailing-edge flap utilized for flutter control. The system involves a two-DOF (degree-of-freedom)...
The dimensionless control equations of three dimensional flow in single screw extruders is developed in terms of velocity and vertorcity, and then a new method for solving the Non-newtionian flow is presented without solving pressure equation. The simulation concerns the incompressible fluid obeying power law properties and the application of finite volume method to the geometrical configuration of...
The problem of flutter and limit cycle oscillation (LCO) for two-degrees-of freedom airfoil with structural and aerodynamic nonlinearities is addressed in this paper. The model which includes freeplay in pitching is established using the Lagrange equation. The aerodynamic lift and moment are derived in terms of the 3rd-order piston theory. The forth order Runge-Kutta method is employed to solve the...
Numerical models are an important tool to simulate dam-break flows. A high-resolution relaxed scheme is proposed for simulating one-dimensional dam-break problems. The scheme is based on combining relaxation approximation with an improved fifth-order weighted essentially nonoscillatory (WENO) reconstruction and third-order strong stability preserving (SSP) Runge-Kutta scheme. The new method enjoy...
Diesel traction Locomotives are widely used in railway tunnels in the plateau of China. Harmful gases given out by internal combustion engines must be excluded from the tunnel for human safety on railway. In the present study, nitrogen dioxide (NO2) was taken into account as a representative harmful pollutant of the investigation object. Natural ventilation of diluting the concentration of NO2 pollutant...
In this paper the order conditions for Runge-Kutta methods are presented based on Butcher's rooted tree theory. A new Runge-Kutta method of order four (MINRK4) is obtained by means of minimizing the error constant. The results of numerical experiments show the competence of the new method in accuracy and efficiency compared with some highly efficient codes in the literature.
This paper presents a family of the improved ARKN (IARKN) methods which are enhancement of the ARKN methods for perturbed oscillators proposed by J. M. Franco. Order conditions are given, and a two-stage method of order three and a three-stage method of order four are constructed specifically. They are analyzed to have good stability and phase properties. Numerical experiments show the superiority...
The central idea in this paper is to examine the attributes that binary gas mixtures having helium (He) as the principal gas and xenon (Xe), nitrogen (N2), oxygen (O2), carbon dioxide (CO2), methane (CH4), tetrafluoromethane (CF4) and sulfur hexafluoride (SF6) as secondary gases may bring forward. From fluid physics, it is known that the thermophysical properties affecting free convection with binary...
Research on the high-intensity laser frequency doubling in KDP crystal with a temperature distribution for typeIangle-phase matching has been carried out by the use of a split-step fast Fourier transform algorithm and a fourth-order Runge-Kutta(R-K) integrator method. Special attention has been paid on the influences of the temperature distribution in the crystal owing to laser energy's absorption...
This paper is concerned with a mathematical model for simulating hydrodynamics of 2D river flow with groins based on the WENO scheme and the Finite Volume Method on unstructured grids. The time discretization uses the Runge-Kutta TVD scheme. By using the proposed model, we calculated the flow property with a groin, and obtained the flow velocity field distributions. The comparisons of the calculated...
The Reynolds equation with oil rupture boundary is solved based on database method. Nonlinear oil film force of combination journal bearing is obtained by retrieval, interpolation, and assembly techniques. As for symmetrical Jeffcott rigid rotor system supported by combination journal bearings, the nonlinear motion of the system is calculated by Poincaré map and self-adaptive Runge-Kutta method....
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