In this article, the higher order asymptotic expansions of cumulative distribution function and probability density function of extremes for generalized Maxwell distribution are established under nonlinear normalizati...In this article, the higher order asymptotic expansions of cumulative distribution function and probability density function of extremes for generalized Maxwell distribution are established under nonlinear normalization. As corollaries, the convergence rates of the distribu- tion and density of maximum are obtained under nonlinear normalization.展开更多
The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonanc...The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.展开更多
Within the linear framework,the Modal Electromechanical Coupling Factor(MEMCF)is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures.It is a...Within the linear framework,the Modal Electromechanical Coupling Factor(MEMCF)is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures.It is also an important tool to guide the piezoelectric damping design of linear structures.Advanced aircraft often fly in maneuvers,and the variable working conditions induce drastic changes in the load level on structures.Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated.To achieve a good vibration reduction effect covering all working conditions,one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures.Therefore,this paper defines the Nonlinear Modal Electromechanical Coupling Factor(NMEMCF)and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures.Three candidate definitions of the NMEMCF are given,including two frequency definitions and one energy definition.The energy definition is the most promising one.It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF.In addition,based on the energy formula,the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state.The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities.A strong correlation among the NMEMCF,geometric parameters,and energy dissipation is observed.The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping,especially for variable working conditions.展开更多
Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation t...Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation technique. Emphasis is placed on singular characteristics as the linear coupling between subsystems degenerated. For nonresonances, it is analytically presented that a single-mode motion and localization of vibrations occur in the system, and the degree of localization relates not only to the coupling stiffness between oscillators, but also to the asymmetric parameter. The parametric threshold value of localization is analytically given. For 1 : 1 resonance, there exist bifurcations of normal modes with nonlinearly coupling stiffness and asymmetric parameter varying. The bifurcating set on the parameter and bifurcating curves of normal modes are obtained.展开更多
The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in te...The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.展开更多
In this paper,an asymmetric vibroacoustic system that can passively realize nonreciprocal transmission of acoustic energy is reported.This experimental system consists of a waveguide,a strongly nonlinear membrane,and ...In this paper,an asymmetric vibroacoustic system that can passively realize nonreciprocal transmission of acoustic energy is reported.This experimental system consists of a waveguide,a strongly nonlinear membrane,and three acoustic cavities with different sizes.The theoretical modeling of the system is verified by experiments,and parametric analysis is also carried out.These intensive studies reveal the nonreciprocal transmission of acoustic energy in this prototype system.Under forward excitation,internal resonance between the two nonlinear normal modes of the vibroacoustic system occurs,and acoustic energy is irreversibly transferred from the waveguide to the nonlinear membrane.However,under backward excitation,there is no internal resonance in the system.Energy spectra and wavelet analysis are used to highlight the mechanism of nonreciprocal transfer of acoustic energy.Consequently,nearly unidirectional(preferential)transmission of acoustic energy transfer is shown by this system.The nonreciprocal acoustic energy transfer method illustrated in this paper provides a new way to design the odd acoustic element.展开更多
Nonlinear normal modes and a numerical iterative approach are applied to study the parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic continua.The nonlinear non-autonomous governing e...Nonlinear normal modes and a numerical iterative approach are applied to study the parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic continua.The nonlinear non-autonomous governing equations are transformed into a set of pseudo-autonomous ones by employing the harmonic balance method.The nonlinear normal modes are constructed by the invariant manifold method on the state space and a numerical iterative approach is adopted to obtain numerical solutions,in which two types of initial conditions for the modal coefficients are employed.The results show that both initial conditions can lead to fast convergence.The frequency-amplitude responses with some modal motions in phase space are obtained by the present iterative method.Quadrature phase difference and traveling waves are found in the time-domain complex modal analysis.展开更多
In this paper the concept of absolute observability of nonlinear control systems is advanced.Different from the linear time-invariant version, there are different definitions of absolute observability for nonlinear co...In this paper the concept of absolute observability of nonlinear control systems is advanced.Different from the linear time-invariant version, there are different definitions of absolute observability for nonlinear control systems.Two algorithms for maximal absolutely observable subsystems are given.Correspondingly,there are two relevant normal forms.The relations with the largest controlled invariant distribution contained in kerdh,zero dynamics etc.,are discussed from the view point of maximal absolute observabilities.展开更多
A beam combination setup for a dual-frequency laser with orthogonal linear polarization is proposed. It consists of two polarizing beam splitters（PBSs） whose polarization axes are orthogonal to each other. A theoret...A beam combination setup for a dual-frequency laser with orthogonal linear polarization is proposed. It consists of two polarizing beam splitters（PBSs） whose polarization axes are orthogonal to each other. A theoretical analysis demonstrates that a combined dual-frequency laser beam with this setup strictly meets orthogonal linear relation. The experimental results show that compared with the conventional setup, the ellipticity and nonorthogonality of the combined dual-frequency laser beam are significantly reduced.展开更多
基金Supported by the Natural Science Foundation of China(61673015,61273020)the Fundamental Research Funds for the Central Universities(XDJK2015A007,SWU1809002)+3 种基金the Science Computing and Intelligent Information Processing of Guangxi Higher Education Key Laboratory(GXSCIIP201702)the Science and Technology Plan Project of Guizhou Province(LH[2015]7053,LH[2015]7055)Science and Technology Foundation of Guizhou Province(Qian Ke He Ji Chu[2016]1161)Guizhou Province Natural Science Foundation in China(Qian Jiao He KY[2016]255)
文摘In this article, the higher order asymptotic expansions of cumulative distribution function and probability density function of extremes for generalized Maxwell distribution are established under nonlinear normalization. As corollaries, the convergence rates of the distribu- tion and density of maximum are obtained under nonlinear normalization.
文摘The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.
基金funded by Major Projects of Aero-Engines and Gas Turbines(J2019-Ⅳ-0023-0091 and J2019-Ⅳ-0005-0073)Aeronautical Science Foundation of China(2019ZB051002)+1 种基金China Postdoctoral Science Foundation(2021M700326)Advanced Jet Propulsion Creativity Center(Projects HKCX2020-02-013,HKCX2020-02-016 and HKCX2022-01009)。
文摘Within the linear framework,the Modal Electromechanical Coupling Factor(MEMCF)is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures.It is also an important tool to guide the piezoelectric damping design of linear structures.Advanced aircraft often fly in maneuvers,and the variable working conditions induce drastic changes in the load level on structures.Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated.To achieve a good vibration reduction effect covering all working conditions,one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures.Therefore,this paper defines the Nonlinear Modal Electromechanical Coupling Factor(NMEMCF)and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures.Three candidate definitions of the NMEMCF are given,including two frequency definitions and one energy definition.The energy definition is the most promising one.It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF.In addition,based on the energy formula,the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state.The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities.A strong correlation among the NMEMCF,geometric parameters,and energy dissipation is observed.The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping,especially for variable working conditions.
文摘Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation technique. Emphasis is placed on singular characteristics as the linear coupling between subsystems degenerated. For nonresonances, it is analytically presented that a single-mode motion and localization of vibrations occur in the system, and the degree of localization relates not only to the coupling stiffness between oscillators, but also to the asymmetric parameter. The parametric threshold value of localization is analytically given. For 1 : 1 resonance, there exist bifurcations of normal modes with nonlinearly coupling stiffness and asymmetric parameter varying. The bifurcating set on the parameter and bifurcating curves of normal modes are obtained.
基金Supported by National Natural Science Foundation of China(No. 10372068).
文摘The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.
基金supported by the National Natural Science Foundation of China(No.51875522)the“One Belt One Road”Program through Zhejiang Province,and the Zhejiang University of Technology-Institute of Applied Physics,Russian Academy of Sciences Joint Research Laboratory of Innovative Technology of Acoustics and Vibration(No.2018C04018).
文摘In this paper,an asymmetric vibroacoustic system that can passively realize nonreciprocal transmission of acoustic energy is reported.This experimental system consists of a waveguide,a strongly nonlinear membrane,and three acoustic cavities with different sizes.The theoretical modeling of the system is verified by experiments,and parametric analysis is also carried out.These intensive studies reveal the nonreciprocal transmission of acoustic energy in this prototype system.Under forward excitation,internal resonance between the two nonlinear normal modes of the vibroacoustic system occurs,and acoustic energy is irreversibly transferred from the waveguide to the nonlinear membrane.However,under backward excitation,there is no internal resonance in the system.Energy spectra and wavelet analysis are used to highlight the mechanism of nonreciprocal transfer of acoustic energy.Consequently,nearly unidirectional(preferential)transmission of acoustic energy transfer is shown by this system.The nonreciprocal acoustic energy transfer method illustrated in this paper provides a new way to design the odd acoustic element.
基金This study was partially funded by the National Natural Science Foundation of China(Grant Nos.11672189,11672007)the postdoctoral fund of Beijing Chaoyang District(Grant No.Q5001015201602)+3 种基金the Program Funded by Liaoning Province Education Administration(Grant No.L2016010)Prof.X.-D.Yang was founded by the Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education,Northeastern University(VCAME201601)Prof.Melnik was funded by the Natural Sciences and Engineering Research Council(NSERC)of Canada,the Canada Research Chair(CRC)program,and the Bizkaia Talent Grant under the Basque Government through the BERC 2014-2017 programas well as Spanish Ministry of Economy and Competitiveness MINECO:BCAM Severo Ochoa excellence accreditation SEV-2013-0323.
文摘Nonlinear normal modes and a numerical iterative approach are applied to study the parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic continua.The nonlinear non-autonomous governing equations are transformed into a set of pseudo-autonomous ones by employing the harmonic balance method.The nonlinear normal modes are constructed by the invariant manifold method on the state space and a numerical iterative approach is adopted to obtain numerical solutions,in which two types of initial conditions for the modal coefficients are employed.The results show that both initial conditions can lead to fast convergence.The frequency-amplitude responses with some modal motions in phase space are obtained by the present iterative method.Quadrature phase difference and traveling waves are found in the time-domain complex modal analysis.
文摘In this paper the concept of absolute observability of nonlinear control systems is advanced.Different from the linear time-invariant version, there are different definitions of absolute observability for nonlinear control systems.Two algorithms for maximal absolutely observable subsystems are given.Correspondingly,there are two relevant normal forms.The relations with the largest controlled invariant distribution contained in kerdh,zero dynamics etc.,are discussed from the view point of maximal absolute observabilities.
基金supported by the National Natural Science Foundation of China (No. 51305105)the China Postdoctoral Science Foundation (No. 2013M531024)the Fundamental Research Funds for the Central Universities (No. HIT. NSRIF. 2014008)
文摘A beam combination setup for a dual-frequency laser with orthogonal linear polarization is proposed. It consists of two polarizing beam splitters（PBSs） whose polarization axes are orthogonal to each other. A theoretical analysis demonstrates that a combined dual-frequency laser beam with this setup strictly meets orthogonal linear relation. The experimental results show that compared with the conventional setup, the ellipticity and nonorthogonality of the combined dual-frequency laser beam are significantly reduced.
