In view of engineering application, it is practicable to decompose the aerodynamics into three components： the static aerodynamics, the aerodynamic increment due to steady rotations, and the aerodynamic increment due...In view of engineering application, it is practicable to decompose the aerodynamics into three components： the static aerodynamics, the aerodynamic increment due to steady rotations, and the aerodynamic increment due to unsteady separated and vortical flow. The first and the second components can be presented in conventional forms, while the third is described using a one-order differential equation and a radial-basis-function （RBF） network. For an aircraft configuration, the mathematical models of 6- component aerodynamic coefficients are set up from the wind tunnel test data of pitch, yaw, roll, and coupled yawroll large-amplitude oscillations. The flight dynamics of an aircraft is studied by the bifurcation analysis technique in the case of quasi-steady aerodynamics and unsteady aerodynam- ics, respectively. The results show that： （1） unsteady aerodynamics has no effect upon the existence of trim points, but affects their stability; （2） unsteady aerodynamics has great effects upon the existence, stability, and amplitudes of periodic solutions; and （3） unsteady aerodynamics changes the stable regions of trim points obviously. Furthermore, the dynamic responses of the aircraft to elevator deflections are inspected. It is shown that the unsteady aerodynamics is beneficial to dynamic stability for the present aircraft. Finally, the effects of unsteady aerodynamics on the post-stall maneuverability展开更多
In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are...In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are also considered.in particular,the conditions for the existence of Hopf bifurcation can be given in terms of the coefficients of the characteristic equation.The method extends the application of the Hopf bifurcation theorem to higher differential equations which occur in biological models,chemical models,and epidemiological models etc.展开更多
Grinding force is an essential metric for determining whether a material is grindable.It can directly affect surface integrity,machining efficiency,and tool life.Therefore,the mechanical behavior of grinding has long ...Grinding force is an essential metric for determining whether a material is grindable.It can directly affect surface integrity,machining efficiency,and tool life.Therefore,the mechanical behavior of grinding has long been a topic of research.A large number of studies have demonstrated that ultrasonic vibration-assisted grinding(UVAG)reduces grinding force and improves surface quality after grinding.However,these studies have many gaps,and the mechanism underlying UVAG force has not been explored.First,the study investigates the influence of grinding and ultrasonic vibration parameters on grinding force with an empirical model based on statistical theory.Second,the material removal mechanism of UVAG is investigated using a finite element model,and the mechanical properties and grinding force evolution mechanism of various materials(difficult-to-cut alloys,brittle materials,and composite materials)for UVAG are reviewed.Simultaneously,a mathematical analysis model of ultrasonic-assisted grinding force based on kinematics and separation characteristics is presented.The error comparison and source analysis of the grinding force model are performed.Finally,based on the current difficulties and research gaps in the UVAG force model,various future research directions are proposed.展开更多
Liquid-solid fluidized beds are used in mineral processing industries to separate particles based on parti- cle size, density, and shape. Understanding the expanded fluidized bed is vital for accurately assessing its ...Liquid-solid fluidized beds are used in mineral processing industries to separate particles based on parti- cle size, density, and shape. Understanding the expanded fluidized bed is vital for accurately assessing its performance. Expansion characteristics of the fluidized bed were studied by performing several experi- ments with iron ore, chromite, quartz, and coal samples. Using water as liquid medium, experiments were conducted to study the effects of particle size, particle density, and superficial velocity on fluidized bed expansion. The experimental data were utilized to develop an empirical mathematical model based on dimensional analysis to estimate the expansion ratio of the fluidized bed in terms of particle character- istics, operating and design parameters. The predicted expansion ratio obtained from the mathematical model is in good agreement with the experimental data.展开更多
文摘In view of engineering application, it is practicable to decompose the aerodynamics into three components： the static aerodynamics, the aerodynamic increment due to steady rotations, and the aerodynamic increment due to unsteady separated and vortical flow. The first and the second components can be presented in conventional forms, while the third is described using a one-order differential equation and a radial-basis-function （RBF） network. For an aircraft configuration, the mathematical models of 6- component aerodynamic coefficients are set up from the wind tunnel test data of pitch, yaw, roll, and coupled yawroll large-amplitude oscillations. The flight dynamics of an aircraft is studied by the bifurcation analysis technique in the case of quasi-steady aerodynamics and unsteady aerodynam- ics, respectively. The results show that： （1） unsteady aerodynamics has no effect upon the existence of trim points, but affects their stability; （2） unsteady aerodynamics has great effects upon the existence, stability, and amplitudes of periodic solutions; and （3） unsteady aerodynamics changes the stable regions of trim points obviously. Furthermore, the dynamic responses of the aircraft to elevator deflections are inspected. It is shown that the unsteady aerodynamics is beneficial to dynamic stability for the present aircraft. Finally, the effects of unsteady aerodynamics on the post-stall maneuverability
基金This project is supported by the National Science Foundation "Tian Yuan" Terms and LNM Institute of Mechanics Academy of ScienceThis project is supported by the NationalYunnan Province Natural Science Foundation of China
文摘In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are also considered.in particular,the conditions for the existence of Hopf bifurcation can be given in terms of the coefficients of the characteristic equation.The method extends the application of the Hopf bifurcation theorem to higher differential equations which occur in biological models,chemical models,and epidemiological models etc.
基金supported by the National Natural Science Foundation of China(Grant Nos.52375447,52205481,and 52105457)the Shandong Natural Science Foundation of China(Grant Nos.ZR2023QE057 and ZR2022QE028)the Science and Technology SMEs Innovation Capacity Improvement Project of Shandong Province,China(Grant No.2022TSGC1115).
文摘Grinding force is an essential metric for determining whether a material is grindable.It can directly affect surface integrity,machining efficiency,and tool life.Therefore,the mechanical behavior of grinding has long been a topic of research.A large number of studies have demonstrated that ultrasonic vibration-assisted grinding(UVAG)reduces grinding force and improves surface quality after grinding.However,these studies have many gaps,and the mechanism underlying UVAG force has not been explored.First,the study investigates the influence of grinding and ultrasonic vibration parameters on grinding force with an empirical model based on statistical theory.Second,the material removal mechanism of UVAG is investigated using a finite element model,and the mechanical properties and grinding force evolution mechanism of various materials(difficult-to-cut alloys,brittle materials,and composite materials)for UVAG are reviewed.Simultaneously,a mathematical analysis model of ultrasonic-assisted grinding force based on kinematics and separation characteristics is presented.The error comparison and source analysis of the grinding force model are performed.Finally,based on the current difficulties and research gaps in the UVAG force model,various future research directions are proposed.
基金the financial support given by CSIRthrough a network project(NWP-31)to carry out this study
文摘Liquid-solid fluidized beds are used in mineral processing industries to separate particles based on parti- cle size, density, and shape. Understanding the expanded fluidized bed is vital for accurately assessing its performance. Expansion characteristics of the fluidized bed were studied by performing several experi- ments with iron ore, chromite, quartz, and coal samples. Using water as liquid medium, experiments were conducted to study the effects of particle size, particle density, and superficial velocity on fluidized bed expansion. The experimental data were utilized to develop an empirical mathematical model based on dimensional analysis to estimate the expansion ratio of the fluidized bed in terms of particle character- istics, operating and design parameters. The predicted expansion ratio obtained from the mathematical model is in good agreement with the experimental data.
