A virtual sieving experimental simulation system was built using physical simulation principles.The effects of vibration frequency and amplitude,the inclination angle of the screen-deck and the vibration direction ang...A virtual sieving experimental simulation system was built using physical simulation principles.The effects of vibration frequency and amplitude,the inclination angle of the screen-deck and the vibration direction angle of screen on single particle kinematics were predicted.Properties such as the average velocity and the average throw height were studied.The results show that the amplitude and the angle of vibration have a great effect on particle average velocity and average height.The vibration frequency and the screen-deck inclination angle appear to have little influence on these responses.For materials that are difficult to screen the vibration frequency and amplitude,the screen-deck inclination angle and the vibration angle should be set to 14 Hz,6.6 mm,6° and 40°,respectively,to obtain optimal particle kinematics.A screening process can be simulated reliably by means of a virtual experiment and these results provide references for both screening theory research and sieving practice.展开更多
A new concept of banana vibrating screen which has the same effect as traditional banana vibrating screen in a new way was put forward.The dynamic model of vibrating screen was established and its working principle wa...A new concept of banana vibrating screen which has the same effect as traditional banana vibrating screen in a new way was put forward.The dynamic model of vibrating screen was established and its working principle was analyzed when the action line of the exciting force did not act through the centroid of screen box.Moreover,the dynamic differential equations of centroid and screen surface were obtained.The motions of centroid and screen surface were simulated with actual parameters of the design example in Matlab/Simulink.The results show that not only the amplitude has a significant decrease from 9.38 to 4.10 mm,but also the throwing index and vibrating direction angle have a significant decrease from 10.49 to 4.59,and from 58.10° to 33.29°,respectively,along the screen surface,which indicates that motion characteristics of vibrating screen are consistent with those of traditional banana vibrating screen only by means of a single angle of screen surface.What's more,such banana vibrating screen of variable linear trajectory with greater processing capacity could be obtained by adjusting the relative position of force center and the centroid of screen box properly.展开更多
This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester ma...This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).展开更多
In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalize...In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.展开更多
In previous studies about the synchronization of vibrators,the restoring forces of springs are mainly treated as linear directly,whereas the nonlinear features are rarely considered in vibrating systems.To make up thi...In previous studies about the synchronization of vibrators,the restoring forces of springs are mainly treated as linear directly,whereas the nonlinear features are rarely considered in vibrating systems.To make up this drawback,a dynamical model of a nonlinear vibrating mechanical system with double rigid frames(RFs),driven by two vibrators,is proposed to explore the synchronization and stability of the system.In this paper,the nonlinearity is reflected in nonlinear restoring forces of springs characterized by asymmetrical piecewise linear,where the nonlinear stiffness of springs is linearized equivalently using the asymptotic method.Based on the average method and Hamilton’s principle,the theory conditions to achieve synchronization and stability of two vibrators are deduced.After the theory analyses,some numerical qualitative analyses are given to reveal the coupling dynamical characteristics of the system and the relative motion properties between two RFs.Besides,some experiments are carried out to examine the validity of the theoretical results and the correctness of the numerical analyses results.Based on the comparisons of the theory,numeric and experiment,the ideal working regions of the system are suggested.Based on the present work,some new types of vibrating equipment,such as vibrating discharging centrifugal dehydrators/conveyers/screens,can be designed.展开更多
A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure ass...A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.展开更多
The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory ...The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations.展开更多
The nonlinear vibrational model of a slightly curved single-walled carbon nanotube （SWCNT） resting on a Winkler-type elastic foundation is developed using nonlocal Euler- Bernoulli elastic theory. The SWCNT is assum...The nonlinear vibrational model of a slightly curved single-walled carbon nanotube （SWCNT） resting on a Winkler-type elastic foundation is developed using nonlocal Euler- Bernoulli elastic theory. The SWCNT is assumed to vibrate under an external harmonic electric force field and an analytical solution is proposed to obtain the nonlinear resonant frequencies. The results show good agreement with the numerical simulation and the obtained analytical frequency is com- pletely related to the curvature of the nanotube. Our model predicts that although the model is nonlinear in nature, the curved SWCNT could behave linearly in a certain amount of curvatures and this quasi-linear vibrational behavior of curved SWCNT is a function of aspect ratio, nonlocal parameter, and stiffness of the foundation.展开更多
The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for ...The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.展开更多
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ...Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.展开更多
Given a real finite-dimensional or infinite-dimensional Hilbert space H with a Jordan product, the second-order cone linear complementarity problem(SOCLCP)is considered. Some conditions are investigated, for which the...Given a real finite-dimensional or infinite-dimensional Hilbert space H with a Jordan product, the second-order cone linear complementarity problem(SOCLCP)is considered. Some conditions are investigated, for which the SOCLCP is feasible and solvable for any element q?H. The solution set of a monotone SOCLCP is also characterized. It is shown that the second-order cone and Jordan product are interconnected.展开更多
This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are ...This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented.展开更多
A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general para...A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.展开更多
In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the origi...In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.展开更多
A linear ultrasonic motor using longitudinal vibration of bar with varying section is proposed. The lin- ear ultrasonic motor has two varying section bars connected by semi-circumferential structure. Elliptical trajec...A linear ultrasonic motor using longitudinal vibration of bar with varying section is proposed. The lin- ear ultrasonic motor has two varying section bars connected by semi-circumferential structure. Elliptical trajecto- ries of particles are formed on top of the semi-circumferential structure outer surface where a driving foot is locat- ed. And a mover is pushed to move linearly when the driving foot is pressed onto it. Finite element model of sta- tor is built and results of harmonic analysis verify its principle. Moreover, design requirements of the motor are analyzed through finite element analysis and the results of sensitive analysis provide an efficient way to design the type of linear ultrasonic motor. Prototype test shows that the motor can afford load of 10 N at the speed of 100 mm/s.展开更多
This paper deals with the vertical vibration, the horizontal translatory and flexural vibrations of plate gate with a flat bottom under the action of unstable submerged underflow. Based on a non linear resonant oscil...This paper deals with the vertical vibration, the horizontal translatory and flexural vibrations of plate gate with a flat bottom under the action of unstable submerged underflow. Based on a non linear resonant oscillator model by which the coupled excitation mechanism between the unstable vortices and gate motion can be simulated, the differential equations for the three types of gate vibrations are established. The parameters in the equations are determined by model experiments. Then, the steady state non linear responses of the three types of gate vibrations are calculated. The calculation results are in good agreement with the experimental data of gate vibrations with different reduced velocity and gate parameters by previous researchers.展开更多
Due to low damping ratio, fiat permanent magnet linear synchronous motor＇s vibration is difficult to be damped and the accuracy is limited. The vibration suppressing results are not good enough in the existing resear...Due to low damping ratio, fiat permanent magnet linear synchronous motor＇s vibration is difficult to be damped and the accuracy is limited. The vibration suppressing results are not good enough in the existing research because only the longitudinal direction vibration is considered while the normal direction vibration is neglected. The parameters of the direct-axis current controller are set to be the same as those of the quadrature-axis current controller commonly. This causes contradiction between signal noise and response. To suppress the vibration, the electromagnetic force model of the flat permanent magnet synchronous linear motor is formulated first. Through the analysis of the effect that direct-axis current noise and quadrature-axis current noise have on both direction vibration, it can be declared that the conclusion that longitudinal direction vibration is only related to the quadrature-axis current noise while the normal direction vibration is related to both the quadrature-axis current noise and direct-axis current noise. Then, the simulation test on current loop with a low-pass filter is conducted and the results show that the low-pass filter can not suppress the vibration but makes the vibration more severe. So a vibration suppressing strategy that the proportional gain of direct-axis current controller adapted according to quadrature-axis reference current is proposed. This control strategy can suppress motor vibration by suppressing direct-axis current noise. The experiments results about the effect of Kp and Ti on normal direction vibration, longitudinal vibration and the position step response show that this strategy suppresses vibration effectively while the motor＇s motion performance is not affected. The maximum reduction of vibration can be up to 40%. In addition, current test under rated load condition is also conducted and the results show that the control strategy can avoid the conflict between the direct-axis current and the quadrature-axis current under typical load. Adaptive PI control strategy can effectively suppress the flat permanent magnet linear synchronous motor＇s vibration without affecting the motor＇s performance.展开更多
The hybrid vibration isolation, which takes advantages of both the passive and active approaches, has been an important solution for space missions. The objective of this paper is to design a vibration isolation platf...The hybrid vibration isolation, which takes advantages of both the passive and active approaches, has been an important solution for space missions. The objective of this paper is to design a vibration isolation platform for payloads on spacecrafts with the robust, wide bandwidth, and multi-degree-of-freedom(MDOF). The proposed solution is based on a parallel mechanism with six voice-coil motors(VCMs) as the actuators. The linear active disturbance resistance control(LADRC) algorithm is used for the active control. Numerical simulation results show that the vibration isolation platform performs effectively over a wide bandwidth, and the resonance introduced by the passive isolation is eliminated. The system robustness to the uncertainties of the structure is also verified by simulation.展开更多
Linear vibration table can provide harmonic accelerations to excite the nonlinear error terms of Pendulous Integrating Gyro Accelerometer(PIGA).Integral precession calibration method is proposed to calibrate PIGA on a...Linear vibration table can provide harmonic accelerations to excite the nonlinear error terms of Pendulous Integrating Gyro Accelerometer(PIGA).Integral precession calibration method is proposed to calibrate PIGA on a linear vibration table in this paper.Based on the precise expressions of PIGA’s inputs,the error calibration model of PIGA is established.Precession angular velocity errors of PIGA are suppressed by integer periodic precession and the errors caused by non-integer periods vibrating are compensated.The complete calibration process,including planning,preparation,PIGA testing,and coefficient identification,is designed to optimize the test operations and evaluate the calibration results.The effect of the main errors on calibration uncertainty is analyzed and the relative sensitivity function is proposed to further optimize the test positions.Experimental and simulation results verify that the proposed 10-position calibration method can improve calibration uncertainties after compensating for the related errors.The order of calibration uncertainties of the second-and third-order coefficients are decreased to 10^(-8)(rad.s^(-1))/g^(2)and 10^(-8)(rad.s^(-1))/g3,respectively.Compared with the other two classical calibration methods,the calibration uncertainties of PIGA’s nonlinear error coefficients can be effectively reduced and the proportional residual errors are decreased less than 3×10-6(rad.s^(-1))/g by using the proposed calibration method.展开更多
The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated.Governing equations of the pile-soil system are established based on elastodyn...The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated.Governing equations of the pile-soil system are established based on elastodynamics.Threedimensional wave equations of soil are decoupled through differential transformation and variable separation.Consequently,expressions of soil displacements and horizontal resistances can be obtained.An analytical solution of the pile is derived based on continuity conditions between the pile and soil,subsequently from which expressions of the complex impedances are deduced.Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile.Some conclusions can be summarized as follows： stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.展开更多
基金support from the Innovative Research Groups of the National Natural Science Foundation of China (No.50921002)the National Natural Science Foundation of China (Nos.50574091 and 50774084)+1 种基金the "333 Project" Foundation of Jiangsu Provincethe Key Laboratory of Coal Processing & Efficient Utilization,Ministry of Education Foundation (No.CPEUKF 08-02) for this work
文摘A virtual sieving experimental simulation system was built using physical simulation principles.The effects of vibration frequency and amplitude,the inclination angle of the screen-deck and the vibration direction angle of screen on single particle kinematics were predicted.Properties such as the average velocity and the average throw height were studied.The results show that the amplitude and the angle of vibration have a great effect on particle average velocity and average height.The vibration frequency and the screen-deck inclination angle appear to have little influence on these responses.For materials that are difficult to screen the vibration frequency and amplitude,the screen-deck inclination angle and the vibration angle should be set to 14 Hz,6.6 mm,6° and 40°,respectively,to obtain optimal particle kinematics.A screening process can be simulated reliably by means of a virtual experiment and these results provide references for both screening theory research and sieving practice.
基金Projects(50574091, 50774084) supported by the National Natural Science Foundation of ChinaProject(50921001) supported by the Innovative Research Group Science Foundation,ChinaProject supported by Jiangsu Scientific Researching Fund Project ("333" Project),China
文摘A new concept of banana vibrating screen which has the same effect as traditional banana vibrating screen in a new way was put forward.The dynamic model of vibrating screen was established and its working principle was analyzed when the action line of the exciting force did not act through the centroid of screen box.Moreover,the dynamic differential equations of centroid and screen surface were obtained.The motions of centroid and screen surface were simulated with actual parameters of the design example in Matlab/Simulink.The results show that not only the amplitude has a significant decrease from 9.38 to 4.10 mm,but also the throwing index and vibrating direction angle have a significant decrease from 10.49 to 4.59,and from 58.10° to 33.29°,respectively,along the screen surface,which indicates that motion characteristics of vibrating screen are consistent with those of traditional banana vibrating screen only by means of a single angle of screen surface.What's more,such banana vibrating screen of variable linear trajectory with greater processing capacity could be obtained by adjusting the relative position of force center and the centroid of screen box properly.
文摘This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).
基金This work was supported by National Natural Science Foundation of China(No.60710002)Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT).
文摘In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.
基金National Natural Science Foundations of China(Grant No.52075085)Fundamental Research Funds for the Central Universities of China(Grant No.N2103019).
文摘In previous studies about the synchronization of vibrators,the restoring forces of springs are mainly treated as linear directly,whereas the nonlinear features are rarely considered in vibrating systems.To make up this drawback,a dynamical model of a nonlinear vibrating mechanical system with double rigid frames(RFs),driven by two vibrators,is proposed to explore the synchronization and stability of the system.In this paper,the nonlinearity is reflected in nonlinear restoring forces of springs characterized by asymmetrical piecewise linear,where the nonlinear stiffness of springs is linearized equivalently using the asymptotic method.Based on the average method and Hamilton’s principle,the theory conditions to achieve synchronization and stability of two vibrators are deduced.After the theory analyses,some numerical qualitative analyses are given to reveal the coupling dynamical characteristics of the system and the relative motion properties between two RFs.Besides,some experiments are carried out to examine the validity of the theoretical results and the correctness of the numerical analyses results.Based on the comparisons of the theory,numeric and experiment,the ideal working regions of the system are suggested.Based on the present work,some new types of vibrating equipment,such as vibrating discharging centrifugal dehydrators/conveyers/screens,can be designed.
文摘A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.
基金Supported by the National Natural Science Foundation of China(11101096 )Guangdong Natural Science Foundation (S2012010010376, S201204006711)
文摘The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations.
文摘The nonlinear vibrational model of a slightly curved single-walled carbon nanotube （SWCNT） resting on a Winkler-type elastic foundation is developed using nonlocal Euler- Bernoulli elastic theory. The SWCNT is assumed to vibrate under an external harmonic electric force field and an analytical solution is proposed to obtain the nonlinear resonant frequencies. The results show good agreement with the numerical simulation and the obtained analytical frequency is com- pletely related to the curvature of the nanotube. Our model predicts that although the model is nonlinear in nature, the curved SWCNT could behave linearly in a certain amount of curvatures and this quasi-linear vibrational behavior of curved SWCNT is a function of aspect ratio, nonlocal parameter, and stiffness of the foundation.
文摘The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.
基金Supported by the National Natural Science Foundation of China(No.11101302 and No.11471241)
文摘Given a real finite-dimensional or infinite-dimensional Hilbert space H with a Jordan product, the second-order cone linear complementarity problem(SOCLCP)is considered. Some conditions are investigated, for which the SOCLCP is feasible and solvable for any element q?H. The solution set of a monotone SOCLCP is also characterized. It is shown that the second-order cone and Jordan product are interconnected.
文摘This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented.
基金This work was supported by the Chinese National Natural Science Foundation ( No. 69925308).
文摘A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.
文摘In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.
基金Supported by the National Natural Science Foundation of China(50735002)~~
文摘A linear ultrasonic motor using longitudinal vibration of bar with varying section is proposed. The lin- ear ultrasonic motor has two varying section bars connected by semi-circumferential structure. Elliptical trajecto- ries of particles are formed on top of the semi-circumferential structure outer surface where a driving foot is locat- ed. And a mover is pushed to move linearly when the driving foot is pressed onto it. Finite element model of sta- tor is built and results of harmonic analysis verify its principle. Moreover, design requirements of the motor are analyzed through finite element analysis and the results of sensitive analysis provide an efficient way to design the type of linear ultrasonic motor. Prototype test shows that the motor can afford load of 10 N at the speed of 100 mm/s.
文摘This paper deals with the vertical vibration, the horizontal translatory and flexural vibrations of plate gate with a flat bottom under the action of unstable submerged underflow. Based on a non linear resonant oscillator model by which the coupled excitation mechanism between the unstable vortices and gate motion can be simulated, the differential equations for the three types of gate vibrations are established. The parameters in the equations are determined by model experiments. Then, the steady state non linear responses of the three types of gate vibrations are calculated. The calculation results are in good agreement with the experimental data of gate vibrations with different reduced velocity and gate parameters by previous researchers.
基金supported by National Science and Technology Major Projects of China (Grant Nos. 2011ZX04016-011,2009ZX04010-022)
文摘Due to low damping ratio, fiat permanent magnet linear synchronous motor＇s vibration is difficult to be damped and the accuracy is limited. The vibration suppressing results are not good enough in the existing research because only the longitudinal direction vibration is considered while the normal direction vibration is neglected. The parameters of the direct-axis current controller are set to be the same as those of the quadrature-axis current controller commonly. This causes contradiction between signal noise and response. To suppress the vibration, the electromagnetic force model of the flat permanent magnet synchronous linear motor is formulated first. Through the analysis of the effect that direct-axis current noise and quadrature-axis current noise have on both direction vibration, it can be declared that the conclusion that longitudinal direction vibration is only related to the quadrature-axis current noise while the normal direction vibration is related to both the quadrature-axis current noise and direct-axis current noise. Then, the simulation test on current loop with a low-pass filter is conducted and the results show that the low-pass filter can not suppress the vibration but makes the vibration more severe. So a vibration suppressing strategy that the proportional gain of direct-axis current controller adapted according to quadrature-axis reference current is proposed. This control strategy can suppress motor vibration by suppressing direct-axis current noise. The experiments results about the effect of Kp and Ti on normal direction vibration, longitudinal vibration and the position step response show that this strategy suppresses vibration effectively while the motor＇s motion performance is not affected. The maximum reduction of vibration can be up to 40%. In addition, current test under rated load condition is also conducted and the results show that the control strategy can avoid the conflict between the direct-axis current and the quadrature-axis current under typical load. Adaptive PI control strategy can effectively suppress the flat permanent magnet linear synchronous motor＇s vibration without affecting the motor＇s performance.
基金the National Natural Science Foundation of China (No. 11572215)the Fundamental Research Funds for the Central Universities (No. N160503002)the China Scholarship Council。
文摘The hybrid vibration isolation, which takes advantages of both the passive and active approaches, has been an important solution for space missions. The objective of this paper is to design a vibration isolation platform for payloads on spacecrafts with the robust, wide bandwidth, and multi-degree-of-freedom(MDOF). The proposed solution is based on a parallel mechanism with six voice-coil motors(VCMs) as the actuators. The linear active disturbance resistance control(LADRC) algorithm is used for the active control. Numerical simulation results show that the vibration isolation platform performs effectively over a wide bandwidth, and the resonance introduced by the passive isolation is eliminated. The system robustness to the uncertainties of the structure is also verified by simulation.
文摘Linear vibration table can provide harmonic accelerations to excite the nonlinear error terms of Pendulous Integrating Gyro Accelerometer(PIGA).Integral precession calibration method is proposed to calibrate PIGA on a linear vibration table in this paper.Based on the precise expressions of PIGA’s inputs,the error calibration model of PIGA is established.Precession angular velocity errors of PIGA are suppressed by integer periodic precession and the errors caused by non-integer periods vibrating are compensated.The complete calibration process,including planning,preparation,PIGA testing,and coefficient identification,is designed to optimize the test operations and evaluate the calibration results.The effect of the main errors on calibration uncertainty is analyzed and the relative sensitivity function is proposed to further optimize the test positions.Experimental and simulation results verify that the proposed 10-position calibration method can improve calibration uncertainties after compensating for the related errors.The order of calibration uncertainties of the second-and third-order coefficients are decreased to 10^(-8)(rad.s^(-1))/g^(2)and 10^(-8)(rad.s^(-1))/g3,respectively.Compared with the other two classical calibration methods,the calibration uncertainties of PIGA’s nonlinear error coefficients can be effectively reduced and the proportional residual errors are decreased less than 3×10-6(rad.s^(-1))/g by using the proposed calibration method.
基金National Natural Science Foundation of China under Grant Nos.51622803 and 51708064the National Key Research and Development Program of China under Grant No.2016YFE0200100
文摘The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated.Governing equations of the pile-soil system are established based on elastodynamics.Threedimensional wave equations of soil are decoupled through differential transformation and variable separation.Consequently,expressions of soil displacements and horizontal resistances can be obtained.An analytical solution of the pile is derived based on continuity conditions between the pile and soil,subsequently from which expressions of the complex impedances are deduced.Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile.Some conclusions can be summarized as follows： stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.
