By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate wi...By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained.展开更多
An overview of the research conducted in the area of linear and nonlinear vibrations of loudspeakers and revolution shells was given in the turning-point frequency range in Chapter 1. It shows that some problems conce...An overview of the research conducted in the area of linear and nonlinear vibrations of loudspeakers and revolution shells was given in the turning-point frequency range in Chapter 1. It shows that some problems concerning vibrations of shells in the turning-point range have to be further studied. The linear vibrations of truncated revolution shells with the first-order turningpoint were systematically investigated in the turningpoint range from Chapter 2 to Chapter 6, including the general solutions for the free vibration, the eigenvalues under various boundary conditions, the forced vibrations driven by an edge force or an edge displacement and some related special effects, and the applications in loudspeaker vibrations. The nonlinear autoparametric vibration was examined in Chapter 7. Main results are listed as follows.展开更多
In this paper,under the non-uniformtransverse load,the problems of nonlinear bending for orthotropic rectangular plate are studied by using'the method of twovariable'[1]and 'the method of mixing perturba...In this paper,under the non-uniformtransverse load,the problems of nonlinear bending for orthotropic rectangular plate are studied by using'the method of twovariable'[1]and 'the method of mixing perturbation'[2].The uniformly valid asymptotic solutions of Nth-order for ε1 and Mth-order for ε2 for ortholropic rectangular plale with four clamped edges are oblained.展开更多
In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution...In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.展开更多
To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the met...To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the method of two-variable' and introducing four small parameters, the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied, and the uniformly valid asymptotic solution of Nth-order for epsilon(1) and Mth-order for epsilon(2) are obtained.展开更多
In this paper, we study the existence of the uniformly ultimately bounded solutions and periodic solutions for a class of third order nonlinear control systemx …+F(r)x ¨+G(r)x ·+H(r)x=e(t).(1)Using analy...In this paper, we study the existence of the uniformly ultimately bounded solutions and periodic solutions for a class of third order nonlinear control systemx …+F(r)x ¨+G(r)x ·+H(r)x=e(t).(1)Using analytic method of Liapunov Function, we established the sufficient conditions of the existence of the uniformly ultimately bounded solutions and periodic solutions of the system(1).展开更多
A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,the...A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,then there exists a periodic solution to the piston problem with the same period.展开更多
A piston problem of viscous polytropic gas equations is discussed. It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time, t...A piston problem of viscous polytropic gas equations is discussed. It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time, then there exists a periodic solution to the piston problem with the same period.展开更多
We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k...We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.展开更多
文摘By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained.
文摘An overview of the research conducted in the area of linear and nonlinear vibrations of loudspeakers and revolution shells was given in the turning-point frequency range in Chapter 1. It shows that some problems concerning vibrations of shells in the turning-point range have to be further studied. The linear vibrations of truncated revolution shells with the first-order turningpoint were systematically investigated in the turningpoint range from Chapter 2 to Chapter 6, including the general solutions for the free vibration, the eigenvalues under various boundary conditions, the forced vibrations driven by an edge force or an edge displacement and some related special effects, and the applications in loudspeaker vibrations. The nonlinear autoparametric vibration was examined in Chapter 7. Main results are listed as follows.
文摘In this paper,under the non-uniformtransverse load,the problems of nonlinear bending for orthotropic rectangular plate are studied by using'the method of twovariable'[1]and 'the method of mixing perturbation'[2].The uniformly valid asymptotic solutions of Nth-order for ε1 and Mth-order for ε2 for ortholropic rectangular plale with four clamped edges are oblained.
文摘In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.
文摘To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the method of two-variable' and introducing four small parameters, the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied, and the uniformly valid asymptotic solution of Nth-order for epsilon(1) and Mth-order for epsilon(2) are obtained.
文摘In this paper, we study the existence of the uniformly ultimately bounded solutions and periodic solutions for a class of third order nonlinear control systemx …+F(r)x ¨+G(r)x ·+H(r)x=e(t).(1)Using analytic method of Liapunov Function, we established the sufficient conditions of the existence of the uniformly ultimately bounded solutions and periodic solutions of the system(1).
文摘A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,then there exists a periodic solution to the piston problem with the same period.
文摘A piston problem of viscous polytropic gas equations is discussed. It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time, then there exists a periodic solution to the piston problem with the same period.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171339 and 11171261)National Center for Mathematics and Interdisciplinary Sciences
文摘We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.
