It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study ...It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study the sub-harmonic resonances of highly nonlinear parameter excited oscillating systems with absolute value terms. The non-smoothness of absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach. The square residuals of the homotopy-approximations of the two examples decrease to 10-6and 10-5,respectively. Thus,the HAM combining with other methods gives hope to solve complex singular oscillating systems analytically.展开更多
To improve the slab quality, a kind of non-sinusoidal oscillation technique of mold driven by elliptic gears was developed. The waveform functions of non-sinusoidal oscillation were determined, and the calculation met...To improve the slab quality, a kind of non-sinusoidal oscillation technique of mold driven by elliptic gears was developed. The waveform functions of non-sinusoidal oscillation were determined, and the calculation method and curves of technological parameters for non-sinusoidal oscillation were given. At the case of waveform deviation factor a equal to 0.31 and oscillation amplitude h equal to ±2.7 mm, the relationship between oscillation frequency and casting speed is determined, and the technological parameters for non-sinusoidal oscillation are calculated. The testing results of industrial application indicated that this technique could not only improve the Slab surface quality, but also reduce the steel breakout.展开更多
A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of th...A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are obtained using the concepts of supersymmetric quantum mechanics and the property of shape invariance. In order to exemplify the general results and to analyze the properties of the coherent states, several examples have been considered.展开更多
基金Sponsored by the National Natural Science Foundation of China(Grant No.11272209)the State Key Laboratory of Ocean Engineering(Grant No.GKZD010059)
文摘It is difficult to obtain analytic approximations of nonlinear problems such as parameter excited system with strong nonlinearity. An analytic approach based on the homotopy analysis method( HAM) is proposed to study the sub-harmonic resonances of highly nonlinear parameter excited oscillating systems with absolute value terms. The non-smoothness of absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach. The square residuals of the homotopy-approximations of the two examples decrease to 10-6and 10-5,respectively. Thus,the HAM combining with other methods gives hope to solve complex singular oscillating systems analytically.
基金Item Sponsored by National Natural Science Foundation of China(51275446)National Natural Science Foundation of China and Baosteel Group Co.,Ltd.(U1260203)Natural Science Foundation of Hebei Province of China(E2012203080)
文摘To improve the slab quality, a kind of non-sinusoidal oscillation technique of mold driven by elliptic gears was developed. The waveform functions of non-sinusoidal oscillation were determined, and the calculation method and curves of technological parameters for non-sinusoidal oscillation were given. At the case of waveform deviation factor a equal to 0.31 and oscillation amplitude h equal to ±2.7 mm, the relationship between oscillation frequency and casting speed is determined, and the technological parameters for non-sinusoidal oscillation are calculated. The testing results of industrial application indicated that this technique could not only improve the Slab surface quality, but also reduce the steel breakout.
文摘A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are obtained using the concepts of supersymmetric quantum mechanics and the property of shape invariance. In order to exemplify the general results and to analyze the properties of the coherent states, several examples have been considered.
