The frequency veering of a metal porous rotating cantilever twisted plate with twist angle and stagger angle is investigated.Metal porous materials may have the characteristics of gradient or uniform distribution alon...The frequency veering of a metal porous rotating cantilever twisted plate with twist angle and stagger angle is investigated.Metal porous materials may have the characteristics of gradient or uniform distribution along the thickness direction.Based on the classical shell theory,considering the influence of centrifugal force produced by high-speed rotation,the free vibration equations of a rotating cantilever twisted plate are derived.Through the polynomial function and Rayleigh-Ritz method,the natural frequencies and mode shapes of the metal porous cantilever twisted plate in both static and rotating states are derived.The accuracy of the present theory and calculation results is confirmed by a comparison between them and the results available from the literature and those obtained from Abaqus.The influences of the thickness ratio,porosity,twist angle,stagger angle and rotational velocity on the frequency veering and mode shape shift of the rotating cantilever twisted plate with porous material under three different distributions are analyzed.It should be mentioned that the frequency veering accompanied by mode shape shift occurs in both static and dynamic states.展开更多
In this paper,the blade is assumed to be a rotating variable thickness cantilever twisted plate structure,and the natural vibrations of variable thickness cantilever twisted plate made of metal porous material are stu...In this paper,the blade is assumed to be a rotating variable thickness cantilever twisted plate structure,and the natural vibrations of variable thickness cantilever twisted plate made of metal porous material are studied.It is assumed that the thickness of the plate changes along spanwise direction and chordwise direction,respectively,and it changes in both directions.The classical thin shell theory,the first and second fundamental forms of surface and von Karman geometric relationship are employed to derive the total potential energy and kinetic energy of the cantilever twisted plate,in which the centrifugal force potential due to high rotational speed is included.Then,according to the Rayleigh-Ritz procedure and applying the polynomial functions which satisfy the cantilever boundary conditions,the dynamic system expressed by equations of motion is reduced to an eigenvalue problem.By numerical simulation,the frequency curves and the mode shapes of the twisted plate can be obtained to reveal the internal connection between natural vibration and the parameters.A series of comparison studies are performed to verify the accuracy of the present formulation and calculations,in which compared data come from experimental,finite element method and theoretical calculation,respectively.The influence of pre-twist angle,three different forms of thickness taper ratio and rotational speed on natural vibration,mode exchange and frequency veering phenomenon of the system is discussed in detail.In addition,the approach proposed here can efficiently extract analytical expressions of mode functions for rotating variable thickness cantilever twisted plate structures.展开更多
Dynamic transient responses of rotating twisted plate under the air-blast loading and step loading respectively considering the geometric nonlinear relationships are investigated using classical shallow shell theory.B...Dynamic transient responses of rotating twisted plate under the air-blast loading and step loading respectively considering the geometric nonlinear relationships are investigated using classical shallow shell theory.By applying energy principle,a novel high dimensional nonlinear dynamic system of the rotating cantilever twisted plate is derived for the first time.The use of variable mode functions by polynomial functions according to the twist angles and geometric of the plate makes it more accurate to describe the dynamic system than that using the classic cantilever beam functions and the free-free beam functions.The comparison researches are carried out between the present results and other literatures to validate present model,formulation and computer process.Equations of motion describing the transient high dimensional nonlinear dynamic response are reduced to a four degree of freedom dynamic system which expressed by out-plane displacement.The effects of twisted angle,stagger angle,rotation speed,load intensity and viscous damping on nonlinear dynamic transient responses of the twisted plate have been investigated.It’s important to note that although the homogeneous and isotropic material is applied here,it might be helpful for laminated composite,functionally graded material as long as the equivalent material parameters are obtained.展开更多
基金The authors acknowledge the financial support of National Natural Science Foundation of China(grant nos.11872127,11832002,and 11732005)the Qin Xin Talents Cultivation Program,Beijing Information Science&Technology University(QXTCP A201901)the Project of High-level Innovative Team Building Plan for Beijing Municipal Colleges and Universities(No.IDHT20180513).
文摘The frequency veering of a metal porous rotating cantilever twisted plate with twist angle and stagger angle is investigated.Metal porous materials may have the characteristics of gradient or uniform distribution along the thickness direction.Based on the classical shell theory,considering the influence of centrifugal force produced by high-speed rotation,the free vibration equations of a rotating cantilever twisted plate are derived.Through the polynomial function and Rayleigh-Ritz method,the natural frequencies and mode shapes of the metal porous cantilever twisted plate in both static and rotating states are derived.The accuracy of the present theory and calculation results is confirmed by a comparison between them and the results available from the literature and those obtained from Abaqus.The influences of the thickness ratio,porosity,twist angle,stagger angle and rotational velocity on the frequency veering and mode shape shift of the rotating cantilever twisted plate with porous material under three different distributions are analyzed.It should be mentioned that the frequency veering accompanied by mode shape shift occurs in both static and dynamic states.
基金the financial support of National Natural Science Foundation of China through grant nos.11872127,11832002,11732005Qin Xin Talents Cultivation ProgramBeijing Information Science&Technology University QXTCP A201901。
文摘In this paper,the blade is assumed to be a rotating variable thickness cantilever twisted plate structure,and the natural vibrations of variable thickness cantilever twisted plate made of metal porous material are studied.It is assumed that the thickness of the plate changes along spanwise direction and chordwise direction,respectively,and it changes in both directions.The classical thin shell theory,the first and second fundamental forms of surface and von Karman geometric relationship are employed to derive the total potential energy and kinetic energy of the cantilever twisted plate,in which the centrifugal force potential due to high rotational speed is included.Then,according to the Rayleigh-Ritz procedure and applying the polynomial functions which satisfy the cantilever boundary conditions,the dynamic system expressed by equations of motion is reduced to an eigenvalue problem.By numerical simulation,the frequency curves and the mode shapes of the twisted plate can be obtained to reveal the internal connection between natural vibration and the parameters.A series of comparison studies are performed to verify the accuracy of the present formulation and calculations,in which compared data come from experimental,finite element method and theoretical calculation,respectively.The influence of pre-twist angle,three different forms of thickness taper ratio and rotational speed on natural vibration,mode exchange and frequency veering phenomenon of the system is discussed in detail.In addition,the approach proposed here can efficiently extract analytical expressions of mode functions for rotating variable thickness cantilever twisted plate structures.
基金support of National Natural Science Foundation of China through grant Nos.11872127,11832002 and 11732005,Fundamental Research Program of Shenzhen Municipality No.JCYJ20160608153749600 and the Project of Highlevel Innovative Team Building Plan for Beijing Municipal Colleges and Universities No.IDHT20180513 and the project of Qin Xin Talents Cultivation Program,Beijing Information Science&Technology University QXTCP A201901.
文摘Dynamic transient responses of rotating twisted plate under the air-blast loading and step loading respectively considering the geometric nonlinear relationships are investigated using classical shallow shell theory.By applying energy principle,a novel high dimensional nonlinear dynamic system of the rotating cantilever twisted plate is derived for the first time.The use of variable mode functions by polynomial functions according to the twist angles and geometric of the plate makes it more accurate to describe the dynamic system than that using the classic cantilever beam functions and the free-free beam functions.The comparison researches are carried out between the present results and other literatures to validate present model,formulation and computer process.Equations of motion describing the transient high dimensional nonlinear dynamic response are reduced to a four degree of freedom dynamic system which expressed by out-plane displacement.The effects of twisted angle,stagger angle,rotation speed,load intensity and viscous damping on nonlinear dynamic transient responses of the twisted plate have been investigated.It’s important to note that although the homogeneous and isotropic material is applied here,it might be helpful for laminated composite,functionally graded material as long as the equivalent material parameters are obtained.
