The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin pl...The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin plate theory,considering geometric nonlinearity and using the principle of virtualwork,the nonlinearmotion partial differential equation of the rectangular conductive thin plate is deduced.Using the separate variable method and Galerkin’s method,the system motion partial differential equation is converted into the general equation of the Duffing equation;the Hamilton system is introduced,and the Melnikov function is used to analyze the Hamilton system,and obtain the critical surface for the existence of chaos.The bifurcation diagram,phase portrait,time history response and Poincarémap of the vibration system are obtained by numerical simulation,and the correctness is demonstrated.The results showthatwhen the ratio of external excitation amplitude to damping coefficient is higher than the critical surface,the system will enter chaotic state.The chaotic motion of the rectangular conductive thin plate is affected by different magnetic field distributions and airflow.展开更多
In order to study the multi-field coupling mechanical behavior of the simply-supported conductive rectangular thin plate under the condition of an externally lateral strong impulsive magnetic field, that is the dynami...In order to study the multi-field coupling mechanical behavior of the simply-supported conductive rectangular thin plate under the condition of an externally lateral strong impulsive magnetic field, that is the dynamic buckling phenomenon of the thin plates in the effect of the magnetic volume forces produced by the interaction between the eddy current and the magnetic fields, a FEM analysis program is developed to characterize the phenomena of magnetoelastic buckling and instability of the plates. The critical values of magnetic field for the three different initial vibrating modes are obtained, with a detailed discussion made on the effects of the lengththickness ratio a/h of the plate and the length-width ratio a/b as well as the impulse parameter on the critical value BOcr of the applied magnetic field.展开更多
In this paper, a new method, exact element method for constructing finite element, is presented. It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variab...In this paper, a new method, exact element method for constructing finite element, is presented. It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variable coefficient under arbitrary boundary condition. Its convergence is proved and its united formula for solving partial differential equation is given. By the present method, a noncompatible element can be obtained and the compatibility conditions between elements can be treated very easily. Comparing the exact element method with the general finite element method with the same degrees of freedom, the high convergence rate of the high order derivatives of solution can be obtained. Three numerical examples are given at the end of this paper, which indicate all results can converge to exact solution and have higher numerical precision.展开更多
基金funded by the Anhui Provincial Natural Science Foundation(Grant No.2008085QE245)the Natural Science Research Project of Higher Education Institutions in Anhui Province(2022AH040045)the Project of Science and Technology Plan of Department of Housing and Urban-Rural Development of Anhui Province(2021-YF22).
文摘The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin plate theory,considering geometric nonlinearity and using the principle of virtualwork,the nonlinearmotion partial differential equation of the rectangular conductive thin plate is deduced.Using the separate variable method and Galerkin’s method,the system motion partial differential equation is converted into the general equation of the Duffing equation;the Hamilton system is introduced,and the Melnikov function is used to analyze the Hamilton system,and obtain the critical surface for the existence of chaos.The bifurcation diagram,phase portrait,time history response and Poincarémap of the vibration system are obtained by numerical simulation,and the correctness is demonstrated.The results showthatwhen the ratio of external excitation amplitude to damping coefficient is higher than the critical surface,the system will enter chaotic state.The chaotic motion of the rectangular conductive thin plate is affected by different magnetic field distributions and airflow.
基金Project supported by the National Natural Sciences Foundation of China (Nos. 10132010 and 90405005).
文摘In order to study the multi-field coupling mechanical behavior of the simply-supported conductive rectangular thin plate under the condition of an externally lateral strong impulsive magnetic field, that is the dynamic buckling phenomenon of the thin plates in the effect of the magnetic volume forces produced by the interaction between the eddy current and the magnetic fields, a FEM analysis program is developed to characterize the phenomena of magnetoelastic buckling and instability of the plates. The critical values of magnetic field for the three different initial vibrating modes are obtained, with a detailed discussion made on the effects of the lengththickness ratio a/h of the plate and the length-width ratio a/b as well as the impulse parameter on the critical value BOcr of the applied magnetic field.
文摘In this paper, a new method, exact element method for constructing finite element, is presented. It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variable coefficient under arbitrary boundary condition. Its convergence is proved and its united formula for solving partial differential equation is given. By the present method, a noncompatible element can be obtained and the compatibility conditions between elements can be treated very easily. Comparing the exact element method with the general finite element method with the same degrees of freedom, the high convergence rate of the high order derivatives of solution can be obtained. Three numerical examples are given at the end of this paper, which indicate all results can converge to exact solution and have higher numerical precision.
