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Separation of Variable Treatment for Solving Time—Dependent Potentials
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作者 QIANShang-Wu GUZhi-Yu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2001年第2期149-150,共2页
We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable... We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthén potential. 展开更多
关键词 time-dependent system separation of variable treatment time-dependent Coulomb potential time-dependent Hulthen potential WAVEFUNCTION
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Closed form solutions for free vibrations of rectangular Mindlin plates 被引量:7
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作者 Yufeng Xing Bo Liu The Solid Mechanics Research Center, Beihang University,100191 Beijing, China 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第5期689-698,共10页
A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three c... A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigensolutions, which are solved from the two differential equations by means of the method of separation of variables are identical with those via Kirchhoff plate theory for thin plate, and can be employed to predict frequencies for any combinations of simply supported and clamped edge conditions. The free edges can also be dealt with if the other pair of opposite edges are simply supported. Some of the solutions were not available before. The frequency parameters agree closely with the available ones through pb-2 Rayleigh-Ritz method for different aspect ratios and relative thickness of plate. 展开更多
关键词 Mindlin plate Free vibration Closed form solution separation of variable
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Functional Separable Solutions of Nonlinear Heat Equations in Non-Newtonian Fluids 被引量:1
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作者 GOU Ming QU Chang-Zheng 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第2期257-262,共6页
We study the functional separation of variables to the nonlinear heat equation: ut = (A(x)D(u)ux^n)x+ B(x)Q(u), Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables... We study the functional separation of variables to the nonlinear heat equation: ut = (A(x)D(u)ux^n)x+ B(x)Q(u), Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained. 展开更多
关键词 group foliation method functional separation of variable nonlinear heat equation symmetry group
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Restrained Bending of Thin-Walled Box Beam with Honeycomb Core
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作者 臧庆来 张行 吴国勋 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2005年第3期223-229,共7页
Restrained bending of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are e... Restrained bending of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are established and solved. The boundary conditions are satisfied rigorously and the solutions are expressed by means of eigen function expansions. The diagram of shearing force is formulated by trigonometric series and used to determine the coefficients in above expansions. The computational resuits give the chord and span wise distributions of nomal and shear stress in the cover plate and the honeycomb core. At the same time, the attenuation of additional stress from fixed end to free end along the length of beam is shown clearly. 展开更多
关键词 box beam HONEYCOMB restrained bending method of variable separation eigen function expansion
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Restrained Torsion of Thin-walled Box Beam with Honeycomb Core
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作者 臧庆来 张行 吴国勋 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2005年第4期336-345,共10页
Restrained torsion of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are e... Restrained torsion of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are established and solved. The boundary conditions are satisfied rigorously and the solutions are expressed by means of eigen function expansions. The diagram of torque is formulated by trigonometric series and used to determine the coefficients in above expansions. The results of computation provide the chord-wise and span-wise distributions of normal and shear stress in the face plate along with shear stress in the honeycomb core. 展开更多
关键词 box beam HONEYCOMB restrained torsion method of variable separation eigen function expansion
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Functional Separable Solutions to Nonlinear Diffusion Equations by Group Foliation Method 被引量:5
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作者 HU Jia-Yi QU Chang-Zheng YIN Hui 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第2期193-199,共7页
We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term: ut = (A(x)D(u)ux)x + B(x)Q(u), Ax ≠ 0. The functional separation of variables to thi... We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term: ut = (A(x)D(u)ux)x + B(x)Q(u), Ax ≠ 0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained. 展开更多
关键词 group foliation method functional separation of variable nonlinear diffusion equation symmetry group
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SYMPLECTIC SOLUTION SYSTEM FOR REISSNER PLATE BENDING 被引量:3
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作者 姚伟岸 隋永枫 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第2期178-185,共8页
Based on the Hellinger_Reissner variatonal principle for Reissner plate bending and introducing dual variables,Hamiltonian dual equations for Reissner plate bending were presented.Therefore Hamiltonian solution system... Based on the Hellinger_Reissner variatonal principle for Reissner plate bending and introducing dual variables,Hamiltonian dual equations for Reissner plate bending were presented.Therefore Hamiltonian solution system can also be applied to Reissner plate bending problem,and the transformation from Euclidian space to symplectic space and from Lagrangian system to Hamiltonian system was realized.So in the symplectic space which consists of the original variables and their dual variables,the problem can be solved via effective mathematical physics methods such as the method of separation of variables and eigenfunction_vector expansion.All the eigensolutions and Jordan canonical form eigensolutions for zero eigenvalue of the Hamiltonian operator matrix are solved in detail,and their physical meanings are showed clearly.The adjoint symplectic orthonormal relation of the eigenfunction vectors for zero eigenvalue are formed.It is showed that the all eigensolutions for zero eigenvalue are basic solutions of the Saint_Venant problem and they form a perfect symplectic subspace for zero eigenvalue.And the eigensolutions for nonzero eigenvalue are covered by the Saint_Venant theorem.The symplectic solution method is not the same as the classical semi_inverse method and breaks through the limit of the traditional semi_inverse solution.The symplectic solution method will have vast application. 展开更多
关键词 Reissner plate Hamiltonian system symplectic geometry separation of variable
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