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| 1 | CHARACTERISTIC EQUATIONS AND CLOSED-FORM SOLUTIONS FOR FREE VIBRATIONS OF RECTANGULAR MINDLIN PLATES显示文摘The direct separation of variables is used to obtain the closed-form solutions for the free vibrations of rectangular Mindlin plates. Three different characteristic equations are derived by using three different methods. It is found that the deflection can be expressed by means of the four characteristic roots and the two rotations should be expressed by all the six characteristic roots,which is the particularity of Mindlin plate theory. And the closed-form solutions,which satisfy two of the three governing equations and all boundary conditions and are accurate for rectangular plates with moderate thickness,are derived for any combinations of simply supported and clamped edges. The free edges can also be dealt with if the other pair of opposite edges is simply supported. The present results agree well with results published previously by other methods for different aspect ratios and relative thickness. | Yufeng Xing Bo Liu | 2009 | Acta Mechanica Solida Sinica2009，22，2： | 5 |
| 2 | EXACT SOLUTIONS FOR FREE IN-PLANE VIBRATIONS OF RECTANGULAR PLATES显示文摘All possible exact solutions are successfully obtained in terms of 10 sets of distinct eigensolutions for the free in-plane vibration of isotropic rectangular plates. The plates have simply supported condition at two opposite edges and any combination of classical boundary conditions at the other two edges. The exact solutions are validated through both mathematical proof and comparisons with the solutions of differential quadrature method. Some unusual phenomena are revealed in free in-plane vibrations of rectangular plates due to one of the eigenvalues being zero. This work constitutes an improved version of very recent corresponding work by the same authors [Int. J. Mech. Sci., 2009, 51: 246-255]. Both the solution forms and solving procedures in the previous work are substantially simplified. Some new results are also given, which are useful for validation purpose in future. | Bo Liu Yufeng Xing | 2011 | Acta Mechanica Solida Sinica2011，24，6： | 5 |
| 3 | Closed form solutions for free vibrations of rectangular Mindlin plates显示文摘A new two-eigenfunctions theory, using theamplitude deflection and the generalized curvature as twofundamental eigenfunctions, is proposed for the freevibration solutions of a rectangular Mindlin plate. The threeclassical eigenvalue differential equations of a Mindlin plateare reformulated to arrive at two new eigenvalue differentialequations for the proposed theory. The closed form eigen-solutions,which are solved from the two differential equationsby means of the method of separation of variables areidentical with those via Kirchhoff plate theory for thin plate,and can be employed to predict frequencies for any combinationsof simply supported and clamped edge conditions.The free edges can also be dealt with if the other pair ofopposite edges are simply supported. Some of the solutionswere not available before. The frequency parameters agreeclosely with the available ones through pb-2 Rayleigh-Ritzmethod for different aspect ratios and relative thickness ofplate. | Yufeng Xing Bo Liu The Solid Mechanics Research Center, Beihang University,100191 Beijing, China | 2009 | Acta Mechanica Sinica2009，25，5： | 5 |
| 4 | New exact solutions for free vibrations of thin orthotropic rectangular plates 显示文摘 | Xing Yufeng Liu Bo | 2009 | Composite Structures2009，89，4： | 1 |
| 5 | Comprehensive exact solutions for free in-plane vibrations of orthotropic rectangular plates显示文摘 | Bo Liu Yufeng Xing | 2011 | European Journal of Mechanics / A Solids2011，，3： | 1 |
| 6 | Exact solutions for free vibrations of orthotropic rectangular Mindlin plates显示文摘 | Bo Liu Yufeng Xing | 2011 | Composite Structures2011，，7： | 1 |
| 7 | Accurate closed-form eigensolutions of three-dimensional panel flutter with arbitrary homogeneous boundary conditions显示文摘Highly accurate closed-form eigensolutions for flutter of three-dimensional(3D)panel with arbitrary combinations of simply supported(S),glide(G),clamped(C)and free(F)boundary conditions(BCs),such as cantilever panels,are achieved according to the linear thin plate theory and the first-order piston theory as well as the complex modal analysis,and all solutions are in a simple and explicit form.The iterative Separation-of-Variable(iSOV)method proposed by the pre-sent authors is employed to obtain the highly accurate eigensolutions.The flutter mechanism is studied with the benefit of eigenvalue properties from mathematical senses.The effects of boundary conditions,chord-thickness ratios,aerodynamic damping,aspect ratios and in-plane loads on flut-ter properties are examined.The results are compared with those of Kantorovich method and Galerkin method,and also coincide well with analytical solutions in literature,verifying the accu-racy of the present closed-form results.It is revealed that,(A)the flutter characteristics are domi-nated by the cross section properties of panels in the direction of stream flow;(B)two types of flutter,called coupled-mode flutter and zero-frequency flutter which includes zero-frequency single-mode flutter and buckling,are observed;(C)boundary conditions and in-plane loads can affect both flutter boundary and flutter type;(D)the flutter behavior of 3D panel is similar to that of the two-dimensional(2D)panel if the aspect ratio is up to a certain value;(E)four to six modes should be used in the Galerkin method for accurate eigensolutions,and the results converge to that of Kantorovich method which uses the same mode functions in the direction perpendicular to the stream flow.The present analysis method can be used as a reference for other stability issues characterized by complex eigenvalues,and the highly closed-form solutions are useful in parameter designs and can also be taken as benchmarks for the validation of numerical methods. | Qiaozhen SUN Yufeng XING Bo LIU Bocheng ZHANG Zekun WANG | 2023 | Chinese Journal of Aeronautics2023，36，1： | 1 |
| 8 | C^1 conforming quadrilateral finite elements with complete secondorder derivatives on vertices and its application to Kirchhoff plates显示文摘The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the C^1 conformity on the interfaces of quadrilateral elements,complete second-order derivatives are used at the element vertices,and the information of geometrical mapping is also considered into the construction of shape functions.It is found that the shape functions and the polynomial spaces of the present elements vary with element shapes.However,the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular shapes.Therefore,very fast convergence can be achieved.A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular elements.Since the present elements are over conforming on element vertices,an approach for handling problems of material discontinuity is also proposed.Numerical examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements. | WU Yang XING YuFeng LIU Bo | 2020 | Science China(Technological Sciences)2020，63，6： | 0 |
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