The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical ...The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.展开更多
By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed....By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.展开更多
We consider the problem of trying to send a single classical bit through an amplitude-damping channel when two transmissions through the channel are available as a resource. It is demonstrated that two entangled trans...We consider the problem of trying to send a single classical bit through an amplitude-damping channel when two transmissions through the channel are available as a resource. It is demonstrated that two entangled transmissions can enhance the receiver＇s capability of making a correct inference under certain conditions compared with two product-state transmissions.展开更多
The problem of sending a single classical bit through a generalized amplitude damping channel is considered. When two transmissions through the channel arc available as a resource, we find that two entangled transmiss...The problem of sending a single classical bit through a generalized amplitude damping channel is considered. When two transmissions through the channel arc available as a resource, we find that two entangled transmissions can enhance the capability of receiver＇s judging information correctly under certain conditions compared with two productstate transmissions. In addition, we find a special case in which the two entangled transmissions can always make a classical bit more effectively disable the noise influence.展开更多
A fractional nonlinear system with power damping term is introduced to study the forced vibration system in order to solve the resonance and bifurcation problems between grinding wheel and steel bar during robot grind...A fractional nonlinear system with power damping term is introduced to study the forced vibration system in order to solve the resonance and bifurcation problems between grinding wheel and steel bar during robot grinding.The robot,grinding wheel and steel bar are reduced to a spring-damping second-order system model.The implicit function equations of vibration amplitude of the dynamic system with coulomb friction damping,linear damping,square damping and cubic damping are obtained by average method.The stability of the system is analyzed and explained,and the stability condition of the system is proposed.Then,the amplitude-frequency characteristic curves of the system under different fractional differential orders,nonlinear stiffness parameters,fractional differential term coefficients and external excitation amplitude are analyzed.It is shown that the fractional differential term in the dynamic system is the damping characteristic.Then the influence of four kinds of damping on the vibration amplitude of the system under the same parameter is investigated and it is proved that the cubic damping suppresses the vibration of the system to the maximum extent.Finally,based on the idea that the equilibrium point of the system is the constant part of the Fourier series expansion term,the bifurcation behavior caused by the change of damping parameters in linear damping,square damping and cubic damping systems with different values of fractional differential order is investigated.展开更多
In this paper, we are concerned with a class of second-order nonlinear differential equations with damping term. By using the generalized Riccati technique and the integral averaging technique of Philos-type, two new ...In this paper, we are concerned with a class of second-order nonlinear differential equations with damping term. By using the generalized Riccati technique and the integral averaging technique of Philos-type, two new oscillation criteria are obtained for every solution of the equations to be oscillatory, which extend and improve some known results in the literature recently.展开更多
基金National Natural Science Foundation of ChinaUnder Grant No. 50578047, 50338020 China Ministry ofEducation (Program for New Century Excellent Talents inUniversity) China Ministry of Science and Technology UnderGrant No.2003AA602150
文摘The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.
文摘By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
基金Project supported by the National Natural Science Foundation of China （Grant No 10374025）, and the Natural Science Foundation of Hunan Normal University （Grant No 22040640）.
文摘We consider the problem of trying to send a single classical bit through an amplitude-damping channel when two transmissions through the channel are available as a resource. It is demonstrated that two entangled transmissions can enhance the receiver＇s capability of making a correct inference under certain conditions compared with two product-state transmissions.
基金Project supported by the National Natural Science Foundation of China （Grant No 10374025）, the Natural Science Foundation of Hunan Normal University （Grant No 22040640） and the Natural Science Foundation of Hunan Province （Grant No 03jjy3012）.
文摘The problem of sending a single classical bit through a generalized amplitude damping channel is considered. When two transmissions through the channel arc available as a resource, we find that two entangled transmissions can enhance the capability of receiver＇s judging information correctly under certain conditions compared with two productstate transmissions. In addition, we find a special case in which the two entangled transmissions can always make a classical bit more effectively disable the noise influence.
基金supported by the National Key Research and Development Program of China(No.2018YFB1308702)the Graduate Education Innovation Program of Shanxi Provence(No.2020BY142)+1 种基金the National Natural Science Foundation of China(Nos.51905367,51905372,52105557)the Specipal Funding for Guiding Local Scientific and Technological Development of the Central(No.YDZX20191400002149).
文摘A fractional nonlinear system with power damping term is introduced to study the forced vibration system in order to solve the resonance and bifurcation problems between grinding wheel and steel bar during robot grinding.The robot,grinding wheel and steel bar are reduced to a spring-damping second-order system model.The implicit function equations of vibration amplitude of the dynamic system with coulomb friction damping,linear damping,square damping and cubic damping are obtained by average method.The stability of the system is analyzed and explained,and the stability condition of the system is proposed.Then,the amplitude-frequency characteristic curves of the system under different fractional differential orders,nonlinear stiffness parameters,fractional differential term coefficients and external excitation amplitude are analyzed.It is shown that the fractional differential term in the dynamic system is the damping characteristic.Then the influence of four kinds of damping on the vibration amplitude of the system under the same parameter is investigated and it is proved that the cubic damping suppresses the vibration of the system to the maximum extent.Finally,based on the idea that the equilibrium point of the system is the constant part of the Fourier series expansion term,the bifurcation behavior caused by the change of damping parameters in linear damping,square damping and cubic damping systems with different values of fractional differential order is investigated.
文摘In this paper, we are concerned with a class of second-order nonlinear differential equations with damping term. By using the generalized Riccati technique and the integral averaging technique of Philos-type, two new oscillation criteria are obtained for every solution of the equations to be oscillatory, which extend and improve some known results in the literature recently.
