Considering magneto-electro-elastic thin plate, the von Karman plate theory of large deflection and the geometric nonlinearity, the mathematical model of nonlinear undamped forced vibration is established. Making use ...Considering magneto-electro-elastic thin plate, the von Karman plate theory of large deflection and the geometric nonlinearity, the mathematical model of nonlinear undamped forced vibration is established. Making use of the improved Lindstedt-Poincare （L-P） method, the undamped forced vibration problem is solved, and the amplitude-frequency response equation of thin plate is obtained. Furthermore, the amplitude frequency response curves of system under different condi- tions are obtained by numerical simulation. The results show that the thickness of the plate, mechanical excitation, parame- ter e, pure piezoelectric material of BaTiO3, pure piezomagnetic material of CoFe2 04, different magneto-electro-elastic ma- terials of BaTiO3/CoFe2 04 and Terfenol-D/PZT will have an impact on the system frequency response. The main effects in- volve principal resonance interval, spring stiffness characteristic and amplitude jumping phenomena.展开更多
Lp(Rn) boundedness is considered for the higher-dimensional Marcinkiewicz integral which was introduced by Stein. Some conditions implying the Lp(Rn) boundedness for the Marcinkiewicz integral are obtained.
In this paper, a semilinear elliptic-parabolic PDE system which arises in a two dimensional groundwater flow problem is studied. Existence and uniqueness results are established via the L￣p - L￣q a priori estimates ...In this paper, a semilinear elliptic-parabolic PDE system which arises in a two dimensional groundwater flow problem is studied. Existence and uniqueness results are established via the L￣p - L￣q a priori estimates and the inverse function theorem.展开更多
Let R be r-dimensional Euclidean space with . Denote by the unit sphere in For we denote by (f) its Cesàro means of order for spherical harmonic expansions. The special value of is known as the critical o...Let R be r-dimensional Euclidean space with . Denote by the unit sphere in For we denote by (f) its Cesàro means of order for spherical harmonic expansions. The special value of is known as the critical one. For , we set This paper proves that N^co u holds for a,ty f e L,0 (log+ L)2~po (log+ log+ L)'(,0~', forth I > 1.展开更多
The methods of L-p estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boundary values partial derivativeu/partial derivativet = Deltau -...The methods of L-p estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boundary values partial derivativeu/partial derivativet = Deltau - lambda \u\(gamma-1) u - betau ((x, t) is an element of Omega x (0, + infinity)), u(x, t) \(partial derivativeOmegax (0, +infinity)) = 0, u(x, 0) = u(0) (x) is an element of H-0(1) (Omega) boolean AND L1+gamma(Omega) (x is an element of Omega). Sufficient and necessary conditions about the extinction of the solutions is given. Here lambda > 0, gamma > 0, beta > 0 are constants, Omega is an element of R-N is bounded with smooth boundary partial derivativeOmega. At last, it is simulated with a higher order equation by using the present methods.展开更多
Using the improved L-P method, the authors seek to salve a class of problems of square strongly nonlinear free oscillations and of strongly nonlinear nonoscillations. Their first-order approximate solutions which has ...Using the improved L-P method, the authors seek to salve a class of problems of square strongly nonlinear free oscillations and of strongly nonlinear nonoscillations. Their first-order approximate solutions which has high accuracy are obtained. The method of this paper is different from the known L-P methods.展开更多
In this work, the reducibility of quasi-periodic systems with strong parametric excitation is studied. We first applied a special case of Lyapunov-Perron (L-P) transformation for time periodic system known as the Lyap...In this work, the reducibility of quasi-periodic systems with strong parametric excitation is studied. We first applied a special case of Lyapunov-Perron (L-P) transformation for time periodic system known as the Lyapunov-Floquet (L-F) transformation to generate a dynamically equivalent system. Then, we used the quasi-periodicnear-identity transformation to reduce this dynamically equivalent system to a constant coefficient system by solving homological equations via harmonic balance. In this process, we obtained the reducibility/resonance conditions that needed to be satisfied to convert a quasi-periodic system in to a constant one. Assuming the reducibility is possible, we obtain the L-P transformation that can transform original quasi-periodic system into a system with constant coefficients. Two examples are presented that show the application of this approach.展开更多
基金National Natural Science Foundation of China(No.11202190)Scientific Research Staring Foundation for the Returned Overseas Chinese Scholars,Ministry of Education,ChinaResearch Project Supported by Shanxi Scholarship Council of China(No.2013-085)
文摘Considering magneto-electro-elastic thin plate, the von Karman plate theory of large deflection and the geometric nonlinearity, the mathematical model of nonlinear undamped forced vibration is established. Making use of the improved Lindstedt-Poincare （L-P） method, the undamped forced vibration problem is solved, and the amplitude-frequency response equation of thin plate is obtained. Furthermore, the amplitude frequency response curves of system under different condi- tions are obtained by numerical simulation. The results show that the thickness of the plate, mechanical excitation, parame- ter e, pure piezoelectric material of BaTiO3, pure piezomagnetic material of CoFe2 04, different magneto-electro-elastic ma- terials of BaTiO3/CoFe2 04 and Terfenol-D/PZT will have an impact on the system frequency response. The main effects in- volve principal resonance interval, spring stiffness characteristic and amplitude jumping phenomena.
基金The research was supported by the NSF of Henan Province.
文摘Lp(Rn) boundedness is considered for the higher-dimensional Marcinkiewicz integral which was introduced by Stein. Some conditions implying the Lp(Rn) boundedness for the Marcinkiewicz integral are obtained.
文摘In this paper, a semilinear elliptic-parabolic PDE system which arises in a two dimensional groundwater flow problem is studied. Existence and uniqueness results are established via the L￣p - L￣q a priori estimates and the inverse function theorem.
文摘Let R be r-dimensional Euclidean space with . Denote by the unit sphere in For we denote by (f) its Cesàro means of order for spherical harmonic expansions. The special value of is known as the critical one. For , we set This paper proves that N^co u holds for a,ty f e L,0 (log+ L)2~po (log+ log+ L)'(,0~', forth I > 1.
文摘The methods of L-p estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boundary values partial derivativeu/partial derivativet = Deltau - lambda \u\(gamma-1) u - betau ((x, t) is an element of Omega x (0, + infinity)), u(x, t) \(partial derivativeOmegax (0, +infinity)) = 0, u(x, 0) = u(0) (x) is an element of H-0(1) (Omega) boolean AND L1+gamma(Omega) (x is an element of Omega). Sufficient and necessary conditions about the extinction of the solutions is given. Here lambda > 0, gamma > 0, beta > 0 are constants, Omega is an element of R-N is bounded with smooth boundary partial derivativeOmega. At last, it is simulated with a higher order equation by using the present methods.
文摘Using the improved L-P method, the authors seek to salve a class of problems of square strongly nonlinear free oscillations and of strongly nonlinear nonoscillations. Their first-order approximate solutions which has high accuracy are obtained. The method of this paper is different from the known L-P methods.
文摘In this work, the reducibility of quasi-periodic systems with strong parametric excitation is studied. We first applied a special case of Lyapunov-Perron (L-P) transformation for time periodic system known as the Lyapunov-Floquet (L-F) transformation to generate a dynamically equivalent system. Then, we used the quasi-periodicnear-identity transformation to reduce this dynamically equivalent system to a constant coefficient system by solving homological equations via harmonic balance. In this process, we obtained the reducibility/resonance conditions that needed to be satisfied to convert a quasi-periodic system in to a constant one. Assuming the reducibility is possible, we obtain the L-P transformation that can transform original quasi-periodic system into a system with constant coefficients. Two examples are presented that show the application of this approach.
