According to the Mindlin plate theory and the first-order piston theory,this work obtains accurate closed-form eigensolutions for the flutter problem of three-dimensional(3D)rectangular laminated panels.The governing ...According to the Mindlin plate theory and the first-order piston theory,this work obtains accurate closed-form eigensolutions for the flutter problem of three-dimensional(3D)rectangular laminated panels.The governing differential equations are derived by the Hamilton's variational principle,and then solved by the iterative Separation-of-Variable(i SOV)method,which are applicable to arbitrary combinations of homogeneous Boundary Conditions(BCs).However,only the simply-support,clamped and cantilever panels are considered in this work for the sake of clarity.With the closed-form eigensolutions,the flutter frequency,flutter mode and flutter boundary are presented,and the effect of shear deformation and aerodynamic damping on flutter frequencies is investigated.Besides,the relation between panel energy and the work of aerodynamic load is discussed.The numerical comparisons reveal the following.(A)The flutter eigenvalues obtained by the present method are accurate,validated by the Finite Element Method(FEM)and the Galerkin method.(B)When the span-chord ratio is larger than 3,simplifying a 3D panel to 2D(two-dimensional)panel is reasonable and the relative differences of the flutter points predicted by the two models are less than one percent.(C)The reciprocal relationship between the mechanical energy of the panel and the work done by aerodynamic load is verified by using the present flutter eigenvalues and modes,further indicating the high accuracy of the present solutions.(D)The coupling of shear deformation and aerodynamic damping prevents frequency coalescing.展开更多
This paper reports establishment of a symplectic system and introduces a 3D sub-symplectic structure for transversely isotropic piezoelectric media. A complete space of eigensolutions is obtained directly. Thus all so...This paper reports establishment of a symplectic system and introduces a 3D sub-symplectic structure for transversely isotropic piezoelectric media. A complete space of eigensolutions is obtained directly. Thus all solutions of the problem are re- duced to finding eigenvalues and eigensolutions, which include zero-eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian matrix and non-zero-eigenvalue solutions. The classical solutions are described by zero-eigen- solutions and non-zero-eigensolutions show localized solutions. Numerical results show some rules of non-zero-eigenvalue and their eigensolutions.展开更多
Laplace's tidal equations are of great importance in various fields of geophysics. Here, the special case of zonal symmetry (zonal wavenumber m = 0) is investigated, where degenerate sets of eigensolutions appear....Laplace's tidal equations are of great importance in various fields of geophysics. Here, the special case of zonal symmetry (zonal wavenumber m = 0) is investigated, where degenerate sets of eigensolutions appear. New results are presented for the inclusion of dissipative processes and the case of unstable conditions. In both instances the (nonzero) eigenfrequencies are complex. In the latter case, additional stable (i.e. real) eigenfrequencies appear in the numerical results for the absolute value of the Lambparameter ε being larger than a critical value εc. Further, it is shown that any degeneracies are removed through the inclusion of dissipation. Moreover, asymptotic relations are derived employing the relation of Laplace's tidal equations for m = 0 to the spheroidal differential equation. The implications of these findings to numerical techniques are demonstrated and results of computations are presented.展开更多
This paper presents a symplectic method for two-dimensional transversely isotropic piezoelectric media with the aid of Hamiltonian system. A symplectic system is established directly by introducing dual variables and ...This paper presents a symplectic method for two-dimensional transversely isotropic piezoelectric media with the aid of Hamiltonian system. A symplectic system is established directly by introducing dual variables and a complete space of eigensolutions is obtained. The solutions of the problem can be expressed by eigensolutions. Some solutions, which are local and are neglected usually by Saint Venant principle, are shown. Curves of non-zero-eigenvalues and their eigensolutions are given by the numerical results.展开更多
The approximate analytical solutions of the Dirac equation under spin and pseudospin symmetries are examined using a suitable approximation scheme in the framework of parametric Nikiforov-Uvarov method.Because a tenso...The approximate analytical solutions of the Dirac equation under spin and pseudospin symmetries are examined using a suitable approximation scheme in the framework of parametric Nikiforov-Uvarov method.Because a tensor interaction in the Dirac equation removes the energy degeneracy in the spin and pseudospin doublets that leads to atomic stability,we study the Dirac equation with a Hellmann-like tensor potential newly proposed in this study.The newly proposed tensor potential removes the degeneracy from both the spin symmetry and pseudospin symmetry completely.The proposed tensor potential seems better than the Coulomb and Yukawa-like tensor potentials.展开更多
A finite element model updating technique for complicated beam-type structures is presented in this study.Firstly, a complicated beam-type structure is reduced to a reduced super beam model with a much smaller degree ...A finite element model updating technique for complicated beam-type structures is presented in this study.Firstly, a complicated beam-type structure is reduced to a reduced super beam model with a much smaller degree of freedom by using the reduced super beam method, which is based on the classic plane cross-section assumption and displacement interpolation function of beam theory.Then based on the reduced super beam, the analysis of eigensolutions and eigensensitivities from the reduced eigenequation are processed for model updating, which will greatly reduce the computational effort when compared to the traditional model updating methods performed on the global model.Optimization techniques are adopted for updating the difference of modal dynamic properties, resulting in optimal values of the structural parameters.Finally, a complicated stiffened cylindrical shell model and a practical missile structure, served as the illustrative examples, are employed for model updating application, which demonstrate that the reduced super beam-based method is both effective and highly efficient.展开更多
In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem...In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem is reduced to an eigenvalue and eigensolution problem. The solution and boundary conditions can be expanded by eigensolutions using adjoint relationships of the symplectic ortho-normalization between the eigensolutions. A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space. The results show that fundamental flows can be described by zero eigenvalue eigensolutions, and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in a rectangular domain and show effectiveness of the method for solving a variety of problems. Meanwhile, the method can be used in solving other problems.展开更多
基金support of the National Natural Science Foundation of China(No.12172023)。
文摘According to the Mindlin plate theory and the first-order piston theory,this work obtains accurate closed-form eigensolutions for the flutter problem of three-dimensional(3D)rectangular laminated panels.The governing differential equations are derived by the Hamilton's variational principle,and then solved by the iterative Separation-of-Variable(i SOV)method,which are applicable to arbitrary combinations of homogeneous Boundary Conditions(BCs).However,only the simply-support,clamped and cantilever panels are considered in this work for the sake of clarity.With the closed-form eigensolutions,the flutter frequency,flutter mode and flutter boundary are presented,and the effect of shear deformation and aerodynamic damping on flutter frequencies is investigated.Besides,the relation between panel energy and the work of aerodynamic load is discussed.The numerical comparisons reveal the following.(A)The flutter eigenvalues obtained by the present method are accurate,validated by the Finite Element Method(FEM)and the Galerkin method.(B)When the span-chord ratio is larger than 3,simplifying a 3D panel to 2D(two-dimensional)panel is reasonable and the relative differences of the flutter points predicted by the two models are less than one percent.(C)The reciprocal relationship between the mechanical energy of the panel and the work done by aerodynamic load is verified by using the present flutter eigenvalues and modes,further indicating the high accuracy of the present solutions.(D)The coupling of shear deformation and aerodynamic damping prevents frequency coalescing.
基金Project (Nos. 19902014 and 10272024) supported by the NationalNatural Science Foundation of China
文摘This paper reports establishment of a symplectic system and introduces a 3D sub-symplectic structure for transversely isotropic piezoelectric media. A complete space of eigensolutions is obtained directly. Thus all solutions of the problem are re- duced to finding eigenvalues and eigensolutions, which include zero-eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian matrix and non-zero-eigenvalue solutions. The classical solutions are described by zero-eigen- solutions and non-zero-eigensolutions show localized solutions. Numerical results show some rules of non-zero-eigenvalue and their eigensolutions.
文摘Laplace's tidal equations are of great importance in various fields of geophysics. Here, the special case of zonal symmetry (zonal wavenumber m = 0) is investigated, where degenerate sets of eigensolutions appear. New results are presented for the inclusion of dissipative processes and the case of unstable conditions. In both instances the (nonzero) eigenfrequencies are complex. In the latter case, additional stable (i.e. real) eigenfrequencies appear in the numerical results for the absolute value of the Lambparameter ε being larger than a critical value εc. Further, it is shown that any degeneracies are removed through the inclusion of dissipation. Moreover, asymptotic relations are derived employing the relation of Laplace's tidal equations for m = 0 to the spheroidal differential equation. The implications of these findings to numerical techniques are demonstrated and results of computations are presented.
基金Project (Nos. 19902014 and 10272024) supported by the NationalNatural Science Foundation of China
文摘This paper presents a symplectic method for two-dimensional transversely isotropic piezoelectric media with the aid of Hamiltonian system. A symplectic system is established directly by introducing dual variables and a complete space of eigensolutions is obtained. The solutions of the problem can be expressed by eigensolutions. Some solutions, which are local and are neglected usually by Saint Venant principle, are shown. Curves of non-zero-eigenvalues and their eigensolutions are given by the numerical results.
文摘The approximate analytical solutions of the Dirac equation under spin and pseudospin symmetries are examined using a suitable approximation scheme in the framework of parametric Nikiforov-Uvarov method.Because a tensor interaction in the Dirac equation removes the energy degeneracy in the spin and pseudospin doublets that leads to atomic stability,we study the Dirac equation with a Hellmann-like tensor potential newly proposed in this study.The newly proposed tensor potential removes the degeneracy from both the spin symmetry and pseudospin symmetry completely.The proposed tensor potential seems better than the Coulomb and Yukawa-like tensor potentials.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11402077)
文摘A finite element model updating technique for complicated beam-type structures is presented in this study.Firstly, a complicated beam-type structure is reduced to a reduced super beam model with a much smaller degree of freedom by using the reduced super beam method, which is based on the classic plane cross-section assumption and displacement interpolation function of beam theory.Then based on the reduced super beam, the analysis of eigensolutions and eigensensitivities from the reduced eigenequation are processed for model updating, which will greatly reduce the computational effort when compared to the traditional model updating methods performed on the global model.Optimization techniques are adopted for updating the difference of modal dynamic properties, resulting in optimal values of the structural parameters.Finally, a complicated stiffened cylindrical shell model and a practical missile structure, served as the illustrative examples, are employed for model updating application, which demonstrate that the reduced super beam-based method is both effective and highly efficient.
文摘In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem is reduced to an eigenvalue and eigensolution problem. The solution and boundary conditions can be expanded by eigensolutions using adjoint relationships of the symplectic ortho-normalization between the eigensolutions. A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space. The results show that fundamental flows can be described by zero eigenvalue eigensolutions, and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in a rectangular domain and show effectiveness of the method for solving a variety of problems. Meanwhile, the method can be used in solving other problems.
