In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependen...In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, a Maxwellian initial condition pulse is then studied. The L<sub>2</sub> and L<sub>∞</sub> error norms are computed to study the accuracy and the simplicity of the presented method.展开更多
In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement...In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.展开更多
Based on the volume constancy with equal flow-per-second and elastic sheet stability theory, a coupling relationship among lateral thickness difference, width-to-thickness ratio of cold rolling strip steel under ideal...Based on the volume constancy with equal flow-per-second and elastic sheet stability theory, a coupling relationship among lateral thickness difference, width-to-thickness ratio of cold rolling strip steel under ideal and actual working conditions, and shape is concluded according to the comprehensive influence principle of various factors on the critical instable shape analyzed in-depth. Firstly, the influence model under actual working condition is developed by referring to the basic relationship between lateral thickness difference and shape under ideal condition. The test results prove that for thin strips with thickness below 0.3 mm, their lateral thickness differences have significant effect on the shape. After then, the combined influence of lateral thickness difference and width-to-thickness ratio on the critical instable shape is concluded according to the elastic sheet stability model, with the synthetic effect of these three factors analyzed. Test data indicate that for cold rolling strip steel with width-to-thickness ratio above 3 000, the critical instability stress difference decreases significantly. Actual measurements are conducted on the lateral thickness differences of two rolls of typical strip manufactured by a sixhigh cold mill, with the influence law of lateral thickness variation and width-to-thickness ratio comprehensively investigated. It is demonstrated that during the production of ultrathin strip steel with different width-to-thickness ratios, the loading roll shapes should be fine adjusted according to the lateral thickness difference of input strips.Therefore, the variation of lateral thickness difference of output strips can meet the requirement of shape stability,so as to obtain fine shape.展开更多
文摘In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, a Maxwellian initial condition pulse is then studied. The L<sub>2</sub> and L<sub>∞</sub> error norms are computed to study the accuracy and the simplicity of the presented method.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China (Grant No. Y6110007)
文摘In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.
基金the Special Research Fund for the National Major Science and Technology Achievement Transformation Project(No.2012GG01)the National Natural Science Foundation of China(No.51305387)the Provincial Natural Science Foundation of Hebei of China(No.E2015203103)
文摘Based on the volume constancy with equal flow-per-second and elastic sheet stability theory, a coupling relationship among lateral thickness difference, width-to-thickness ratio of cold rolling strip steel under ideal and actual working conditions, and shape is concluded according to the comprehensive influence principle of various factors on the critical instable shape analyzed in-depth. Firstly, the influence model under actual working condition is developed by referring to the basic relationship between lateral thickness difference and shape under ideal condition. The test results prove that for thin strips with thickness below 0.3 mm, their lateral thickness differences have significant effect on the shape. After then, the combined influence of lateral thickness difference and width-to-thickness ratio on the critical instable shape is concluded according to the elastic sheet stability model, with the synthetic effect of these three factors analyzed. Test data indicate that for cold rolling strip steel with width-to-thickness ratio above 3 000, the critical instability stress difference decreases significantly. Actual measurements are conducted on the lateral thickness differences of two rolls of typical strip manufactured by a sixhigh cold mill, with the influence law of lateral thickness variation and width-to-thickness ratio comprehensively investigated. It is demonstrated that during the production of ultrathin strip steel with different width-to-thickness ratios, the loading roll shapes should be fine adjusted according to the lateral thickness difference of input strips.Therefore, the variation of lateral thickness difference of output strips can meet the requirement of shape stability,so as to obtain fine shape.
