• International journal of advanced smart convergence
• /
• 제2권1호
• /
• pp.18-20
• /
• 2013

The significance, is to introduce a novel way to employ the improved Runge-Kutta fifth order five stage method, here after called as Modified IRK(5,5) method, for system of second order robot arm problem and variations in angles at the joints in which parameters governing with two degrees of freedom which requires lesser number of function evaluations per time step as compared to the existing ones, in order to save time and spaceAn ultimate aim of this present paper is to solve application problem such as robot arm and initial value problems by applying Runge-Kutta fifth order five stage numerical techniques. The calculated output for robot arm coincides with exact solution which is found to be better, suitable and feasible for solving real time problems.

• Mass Spectrometry Letters
• /
• 제6권3호
• /
• pp.59-64
• /
• 2015

Quadrupole ion trap mass analyzer with a simplified geometry, namely, the cylindrical ion trap (CIT), has been shown to be well-suited using in miniature mass spectrometry and even in mass spectrometer arrays. Computation of stability regions is of particular importance in designing and assembling an ion trap. However, solving CIT equations are rather more difficult and complex than QIT equations, so, analytical and matrix methods have been widely used to calculate the stability regions. In this article we present the results of numerical simulations of the physical properties and the fractional mass resolutions m/Δm of the confined ions in the first stability region was analyzed by the fifth order Runge-Kutta method (RKM5) at the optimum radius size for both ion traps. Because of similarity the both results, having determining the optimum radius, we can make much easier to design CIT. Also, the simulated results has been performed a high precision in the resolution of trapped ions at the optimum radius size.

• 한국전산유체공학회지
• /
• 제13권3호
• /
• pp.69-78
• /
• 2008

The high-order numerical method based on the adaptive mesh refinement(AMR) on the quadrilateral unstructured grids has been developed in this paper. This adaptive-grid method, originally developed with MUSCL-TVD scheme, is now extended to the WENO (weighted essentially no-oscillatory) scheme with the Runge-Kutta time integration of fifth order in spatial and temporal accuracy. The multidimensional interpolation was studied in the preliminary research, which allows us to maintain the same order of accuracy for the computation of numerical flux between two adjacent cells of different levels. Some standard benchmark tests are done to validate this method for checking the overall capacity and efficiency of the present adaptive-grid technique.

• 멤브레인
• /
• 제16권3호
• /
• pp.204-212
• /
• 2006

이산화탄소에 대한 가소화 안정성 및 이산화탄소/질소의 분리특성이 탁월한 폴리이서술폰(PES)중공사 분리막에 의한 이산화탄소 분리특성을 수치해석으로 알아보고자 하였다. 공정변수에 따른 이산화탄소 분리 거동을 예측하기 위하여 공급 기체와 투과기체가 같은 방향으로 흐르는 병류 흐름에 대한 분리막 공정 지배 방정식을 5차 Runge-Kutta-Verner 방법을 사용하여 Compaq Visual Fortran 6.6 소프트웨어를 이용 공정모사 프로그램을 개발하였다. 개발된 프로그램을 사용하여 수치해석을 수행한 결과, 이산화탄소 투과특성에 영향을 주는 가장 중요한 인자로서 공급 이산화탄소 분압, 투과측과 분리막 내부의 압력비 그리고 공급 기체가 분리막 내부에 머무르는 체류 시간임을 알 수 있었다.

• Advances in aircraft and spacecraft science
• /
• 제8권4호
• /
• pp.345-372
• /
• 2021

The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.