As one of the most important steps in the design of bearing-less rotor systems,the design of flexible beam has received much research attention.Because of the very complex working environment of helicopter,the flexibl...As one of the most important steps in the design of bearing-less rotor systems,the design of flexible beam has received much research attention.Because of the very complex working environment of helicopter,the flexible beam should satisfy both the strength and dynamic requirements.However,traditional optimization research focused only on either the strength or dynamical characteristics.To sufficiently improve the performance of the flexible beam,both aspects must be considered.This paper proposes a two-stage optimization method based on the Hamilton variational principle:Variational asymptotic beam section analysis(VABS)program and genetic algorithm(GA).Consequently,a two-part analysis model based on the Hamilton variational principle and VABS is established to calculate section characteristics and structural dynamics characteristics,respectively.Subsequently,the two parts are combined to establish a two-stage optimization process and search with GA to obtain the best dynamic characteristics combinations.Based on the primary optimization results,the section characteristics of the flexible beam are further optimized using GA.The optimization results show that the torsional stiffness decreases by 36.1%compared with the full 0°laying scheme without optimization and the dynamic requirements are achieved.The natural frequencies of flapping and torsion meet the requirements(0.5 away from the passing frequencies of the blade,0.25 away from the excitation force frequency,and the flapping and torsion frequencies keep a corresponding distance).The results indicate that the optimization method can significantly improve the performance of the flexible beam.展开更多
Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic ...Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic boundary conditions and the method of separation of variables,the magnetic potential of the air-gap magnetic field is obtained.Based on the magnetization force model and Lorentz force of ferromagnetic thin-walled structures,and introducing the electromagnetic constitutive relations and boundary conditions,the calculation model of electromagnetic force of the soft ferromagnetic thin plate moving in air-gap magnetic field is established.Considering geometric nonlinearity,expressions of strain energy and kinetic energy of the elastic thin plate and the work of forces are given,respectively.The magnetic-structure coupling nonlinear vibration equations of ferromagnetic thin plate parallel moving in the air-gap magnetic field excited by armatures are obtained by using the Hamilton principle,which can be of the characterization of the system dynamics model with electro-magneto-velocity-mechanical interaction.Through numerical examples,primary resonance characteristics of the strip thin plate under the action of air-gap magnetic force are obtained.The results show that the two stable amplitude values will increase as amplitude of magnetic potential increases and thickness of air-gap decreases,and the amplitude’s multi-valued region will change due to the varieties of magnetic potential,air-gap and velocity.The model established in this paper is a theoretical reference for investigation on the multi-field coupling dynamic behaviors of structures moving in complex electromagnetic fields.展开更多
Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time...Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation.展开更多
基金supported by the Foundation of National Key Laboratory of Rotorcraft Aeromechanics,Nanjing University of Aeronautics and Astronautics(No.614222004030917)。
文摘As one of the most important steps in the design of bearing-less rotor systems,the design of flexible beam has received much research attention.Because of the very complex working environment of helicopter,the flexible beam should satisfy both the strength and dynamic requirements.However,traditional optimization research focused only on either the strength or dynamical characteristics.To sufficiently improve the performance of the flexible beam,both aspects must be considered.This paper proposes a two-stage optimization method based on the Hamilton variational principle:Variational asymptotic beam section analysis(VABS)program and genetic algorithm(GA).Consequently,a two-part analysis model based on the Hamilton variational principle and VABS is established to calculate section characteristics and structural dynamics characteristics,respectively.Subsequently,the two parts are combined to establish a two-stage optimization process and search with GA to obtain the best dynamic characteristics combinations.Based on the primary optimization results,the section characteristics of the flexible beam are further optimized using GA.The optimization results show that the torsional stiffness decreases by 36.1%compared with the full 0°laying scheme without optimization and the dynamic requirements are achieved.The natural frequencies of flapping and torsion meet the requirements(0.5 away from the passing frequencies of the blade,0.25 away from the excitation force frequency,and the flapping and torsion frequencies keep a corresponding distance).The results indicate that the optimization method can significantly improve the performance of the flexible beam.
基金the National Natural Science Foundation of China(Grant Nos.12172321 and 11472239)the Hebei Provincial Natural Science Foundation of China(Grant No.A2020203007).
文摘Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic boundary conditions and the method of separation of variables,the magnetic potential of the air-gap magnetic field is obtained.Based on the magnetization force model and Lorentz force of ferromagnetic thin-walled structures,and introducing the electromagnetic constitutive relations and boundary conditions,the calculation model of electromagnetic force of the soft ferromagnetic thin plate moving in air-gap magnetic field is established.Considering geometric nonlinearity,expressions of strain energy and kinetic energy of the elastic thin plate and the work of forces are given,respectively.The magnetic-structure coupling nonlinear vibration equations of ferromagnetic thin plate parallel moving in the air-gap magnetic field excited by armatures are obtained by using the Hamilton principle,which can be of the characterization of the system dynamics model with electro-magneto-velocity-mechanical interaction.Through numerical examples,primary resonance characteristics of the strip thin plate under the action of air-gap magnetic force are obtained.The results show that the two stable amplitude values will increase as amplitude of magnetic potential increases and thickness of air-gap decreases,and the amplitude’s multi-valued region will change due to the varieties of magnetic potential,air-gap and velocity.The model established in this paper is a theoretical reference for investigation on the multi-field coupling dynamic behaviors of structures moving in complex electromagnetic fields.
基金Supported by National Natural Science Foundation of China under Grant Nos.11271168 and 11671177by the Priority Academic Program Development of Jiangsu Higher Education Institutionsby Innovation Project of the Graduate Students in Jiangsu Normal University
文摘Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation.
