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
The modal method is applied to analyze coupled vibration of belt drive systems. A belt drive system is a hybrid system consisting of continuous belts modeled as strings as well as discrete pulleys and a tensioner arm....The modal method is applied to analyze coupled vibration of belt drive systems. A belt drive system is a hybrid system consisting of continuous belts modeled as strings as well as discrete pulleys and a tensioner arm. The characteristic equation of the system is derived from the governing equation. Numerical results demenstrate the effects of the transport speed and the initial tension on natural frequencies.展开更多
The transmission of transverse vibrational energy of a vertically rigid beam plate coupled structure is analyzed to get the theoretical results of coupling loss factor(CLF), a very important parameter in statistical ...The transmission of transverse vibrational energy of a vertically rigid beam plate coupled structure is analyzed to get the theoretical results of coupling loss factor(CLF), a very important parameter in statistical energy analysis(SEA). The modal analysis method is used to discuss the vibration energy of the typical model, as well as the power flow between the two subsystems. Furthermore, the resolution to the coupling loss factor is also derived and compared with the measured values. The analytical results of the coupling loss factor agree with the measured ones fully, this new resolution is significant for the application of SEA.展开更多
In rotor dynamics,blades are normally modelled as a slender beam,in which elastic deformations are coupled with each other.To identify these coupling effects,new rigid-flexible structural model for helicopter rotor sy...In rotor dynamics,blades are normally modelled as a slender beam,in which elastic deformations are coupled with each other.To identify these coupling effects,new rigid-flexible structural model for helicopter rotor system is proposed in this paper.Finite rotations of the whole blade(on flapwise,lagwise,and torsional)are described as three global rigid degrees of freedom.The nonlinear deformation geometrics of the beam is built on geometrically exact beam theory.New expressions for blade strain energy,kinetic energy,and virtual work of various kinds of external forces are derived as functions of finite rotations and elastic deformations.To quantify the coupling characteristics,following the definition of coupling factor in electromagnetics,a new coupling factor between two modal components on each mode is introduced in modal analysis.Simulations show that the new structural model is highly capable of solving static and dynamic problems in rotor system and the maximum deformation that moderate deformation beam theory can predict might be 15%of beam length.After the new coupling factor is applied to study structurally coupled characteristics of rotor blade,it can be concluded that closeness of natural frequencies likely indicates considerable coupling between corresponding DOFs in structure.展开更多
Based on the modal coupling theory,the rotor and stator contact stiffness and axial relative velocity are considered to build an electric aircraft brake dynamic system model in this study.Both the complex modal analys...Based on the modal coupling theory,the rotor and stator contact stiffness and axial relative velocity are considered to build an electric aircraft brake dynamic system model in this study.Both the complex modal analysis and transient dynamic analysis methods are used to study the aircraft brake squeal performance and vibratory mechanism.The unstable vibration modes indicate that the out-of-plane vibration plays an important role and the feed-in energy is larger than the output energy in the brake rotor–stator module so that brake squeal takes place.Then the influences of the contact stiffness,friction damping and frictional coefficient on the brake squeal system are carried out,laying the foundation for the three proposed vibration suppression methods.Results show that the coefficient negative-slope condition will intensify the vibration.Also,a linear relationship between the squeal factor and the frictional coefficient is obtained to provide a guidance to predict squeal stability under more conditions.Vibration reduction design shows that adding a damping layer to the brake mechanism and chamfering the edge of braking stators both can reduce brake squeal effectively,while slotting braking stators is invalid in aircraft braking system.展开更多
In order to test the bending-torsional coupled vibration characteristics of the multi-shafts gear transmission system of large power vehicles,a torsional vibration exciter was used to apply torsional excitation on the...In order to test the bending-torsional coupled vibration characteristics of the multi-shafts gear transmission system of large power vehicles,a torsional vibration exciter was used to apply torsional excitation on the gear transmission systems and thirty-two acceleration sensors were used to measure the tangential acceleration of each shaft.Torsional vibration signals and bending vibration signals of each measuring point were obtained by calculation of the four-point-response signal.The modal parameters of gear transmission systems including nature frequency,modal shape and modal damping ratio were obtained by identifying modal parameters of the torsional vibration signal and bending vibration signal.The characteristic of the bending vibration and torsional vibration of the gear systems were studied through the analysis of the nature frequency and modal shape.The nonlinearity characteristic of the gear transmission system was investigated through single frequency excitation test,which can be the foundation for further nonlinearity research.展开更多
Due to the influence of deep-sea environment,deep-sea sediments are usually heterogeneous,and their moduli of elasticity and density change as depth changes.Combined with the characteristics of deep-sea sediments,the ...Due to the influence of deep-sea environment,deep-sea sediments are usually heterogeneous,and their moduli of elasticity and density change as depth changes.Combined with the characteristics of deep-sea sediments,the thermo-hydro-mechanical coupling dynamic response model of heterogeneous saturated porous sediments can be established to study the influence of elastic modulus,density,frequency,and load amplitude changes on the model.Based on the Green-Lindsay generalized thermoelasticity theory and Darcy’s law,the thermo-hydro-mechanical coupled dynamic response model and governing equations of heterogeneous deep-sea sediments with nonlinear elastic modulus and density are established.The analytical solutions of dimensionless vertical displacement,vertical stress,excess pore water pressure,and temperature are obtained by means of normal modal analysis,which are depicted graphically.The results show that the changes of elastic modulus and density have few effects on vertical displacement,vertical stress,and temperature,but have great effects on excess pore water pressure.When the mining machine vibrates,the heterogeneity of deep-sea sediments has great influence on vertical displacement,vertical stress,and excess pore water pressure,but has few effects on temperature.In addition,the vertical displacement,vertical stress,and excess pore water pressure of heterogeneous deep-sea sediments change more gently.The variation trends of physical quantities for heterogeneous and homogeneous deep-sea sediments with frequency and load amplitude are basically the same.The results can provide theoretical guidance for deep-sea mining engineering construction.展开更多
This paper analyses the modal interactions in the nonlinear, size-dependent dynamics of geometrically imperfect microplates. Based on the modified couple stress theory,the equations of motion for the in-plane and out-...This paper analyses the modal interactions in the nonlinear, size-dependent dynamics of geometrically imperfect microplates. Based on the modified couple stress theory,the equations of motion for the in-plane and out-of-plane motions are obtained employing the von Kármán plate theory as well as Kirchhoff＇s hypotheses by means of the Lagrange equations. The equations of motions are solved using the pseudo-arclength continuation technique and direct timeintegration method. The system parameters are tuned to the values associated with modal interactions, and then nonlinear resonant responses and energy transfer are analysed.Nonlinear motion characteristics are shown in the form of frequency-response and force-response curves, time histories, phase-plane portraits, and fast Fourier transforms.展开更多
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.
基金Project supported by the National Natural Science Foundation of China(Nos.10672092 and 10725209)Scientific Research Project of Shanghai Municipal Education Commission(No.07ZZ07)Shanghai Leading Academic Discipline Project(No.Y0103)
文摘The modal method is applied to analyze coupled vibration of belt drive systems. A belt drive system is a hybrid system consisting of continuous belts modeled as strings as well as discrete pulleys and a tensioner arm. The characteristic equation of the system is derived from the governing equation. Numerical results demenstrate the effects of the transport speed and the initial tension on natural frequencies.
文摘The transmission of transverse vibrational energy of a vertically rigid beam plate coupled structure is analyzed to get the theoretical results of coupling loss factor(CLF), a very important parameter in statistical energy analysis(SEA). The modal analysis method is used to discuss the vibration energy of the typical model, as well as the power flow between the two subsystems. Furthermore, the resolution to the coupling loss factor is also derived and compared with the measured values. The analytical results of the coupling loss factor agree with the measured ones fully, this new resolution is significant for the application of SEA.
文摘In rotor dynamics,blades are normally modelled as a slender beam,in which elastic deformations are coupled with each other.To identify these coupling effects,new rigid-flexible structural model for helicopter rotor system is proposed in this paper.Finite rotations of the whole blade(on flapwise,lagwise,and torsional)are described as three global rigid degrees of freedom.The nonlinear deformation geometrics of the beam is built on geometrically exact beam theory.New expressions for blade strain energy,kinetic energy,and virtual work of various kinds of external forces are derived as functions of finite rotations and elastic deformations.To quantify the coupling characteristics,following the definition of coupling factor in electromagnetics,a new coupling factor between two modal components on each mode is introduced in modal analysis.Simulations show that the new structural model is highly capable of solving static and dynamic problems in rotor system and the maximum deformation that moderate deformation beam theory can predict might be 15%of beam length.After the new coupling factor is applied to study structurally coupled characteristics of rotor blade,it can be concluded that closeness of natural frequencies likely indicates considerable coupling between corresponding DOFs in structure.
基金This study was funded by the National Natural Science Foundation of China(Grant 51905264)the China Postdoctoral Science Foundation Funded Project(Grants 2019M650115,2019M661818 and 2020T130298)+1 种基金the National Defense Outstanding Youth Science Foundation(Grant 2018-JCJQ-ZQ-053)the Fundamental Research Funds for the Central Universities(Grant NF2O18OO1)and the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘Based on the modal coupling theory,the rotor and stator contact stiffness and axial relative velocity are considered to build an electric aircraft brake dynamic system model in this study.Both the complex modal analysis and transient dynamic analysis methods are used to study the aircraft brake squeal performance and vibratory mechanism.The unstable vibration modes indicate that the out-of-plane vibration plays an important role and the feed-in energy is larger than the output energy in the brake rotor–stator module so that brake squeal takes place.Then the influences of the contact stiffness,friction damping and frictional coefficient on the brake squeal system are carried out,laying the foundation for the three proposed vibration suppression methods.Results show that the coefficient negative-slope condition will intensify the vibration.Also,a linear relationship between the squeal factor and the frictional coefficient is obtained to provide a guidance to predict squeal stability under more conditions.Vibration reduction design shows that adding a damping layer to the brake mechanism and chamfering the edge of braking stators both can reduce brake squeal effectively,while slotting braking stators is invalid in aircraft braking system.
基金Sponsored by the Ministerial Level Advanced Research Foundation(40402060103)
文摘In order to test the bending-torsional coupled vibration characteristics of the multi-shafts gear transmission system of large power vehicles,a torsional vibration exciter was used to apply torsional excitation on the gear transmission systems and thirty-two acceleration sensors were used to measure the tangential acceleration of each shaft.Torsional vibration signals and bending vibration signals of each measuring point were obtained by calculation of the four-point-response signal.The modal parameters of gear transmission systems including nature frequency,modal shape and modal damping ratio were obtained by identifying modal parameters of the torsional vibration signal and bending vibration signal.The characteristic of the bending vibration and torsional vibration of the gear systems were studied through the analysis of the nature frequency and modal shape.The nonlinearity characteristic of the gear transmission system was investigated through single frequency excitation test,which can be the foundation for further nonlinearity research.
基金Project supported by the National Natural Science Foundation of China(Nos.12072309,61603322)。
文摘Due to the influence of deep-sea environment,deep-sea sediments are usually heterogeneous,and their moduli of elasticity and density change as depth changes.Combined with the characteristics of deep-sea sediments,the thermo-hydro-mechanical coupling dynamic response model of heterogeneous saturated porous sediments can be established to study the influence of elastic modulus,density,frequency,and load amplitude changes on the model.Based on the Green-Lindsay generalized thermoelasticity theory and Darcy’s law,the thermo-hydro-mechanical coupled dynamic response model and governing equations of heterogeneous deep-sea sediments with nonlinear elastic modulus and density are established.The analytical solutions of dimensionless vertical displacement,vertical stress,excess pore water pressure,and temperature are obtained by means of normal modal analysis,which are depicted graphically.The results show that the changes of elastic modulus and density have few effects on vertical displacement,vertical stress,and temperature,but have great effects on excess pore water pressure.When the mining machine vibrates,the heterogeneity of deep-sea sediments has great influence on vertical displacement,vertical stress,and excess pore water pressure,but has few effects on temperature.In addition,the vertical displacement,vertical stress,and excess pore water pressure of heterogeneous deep-sea sediments change more gently.The variation trends of physical quantities for heterogeneous and homogeneous deep-sea sediments with frequency and load amplitude are basically the same.The results can provide theoretical guidance for deep-sea mining engineering construction.
文摘This paper analyses the modal interactions in the nonlinear, size-dependent dynamics of geometrically imperfect microplates. Based on the modified couple stress theory,the equations of motion for the in-plane and out-of-plane motions are obtained employing the von Kármán plate theory as well as Kirchhoff＇s hypotheses by means of the Lagrange equations. The equations of motions are solved using the pseudo-arclength continuation technique and direct timeintegration method. The system parameters are tuned to the values associated with modal interactions, and then nonlinear resonant responses and energy transfer are analysed.Nonlinear motion characteristics are shown in the form of frequency-response and force-response curves, time histories, phase-plane portraits, and fast Fourier transforms.
