Table of Content

11 February 2009, Volume 30 Issue 2

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Articles

Nonlinear free vibration analysis of piezoelastic laminated plates with interface damage

Yi-ming FU;Sheng LI;Ye-jie JIANG

2009, 30(2):  129-144 .  doi:10.1007/s10483-009-0201-y

Abstract ( 1559 )   PDF (448KB) ( 1594 )  

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This paper presents a nonlinear model for piezoelastic laminated plates with damage effect of the intra-layers and inter-laminar interfaces. Discontinuity of displacement and electric potential on the interfaces are depicted by three shape functions. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage effect are derived. Then, by using the Galerkin method, a mathematical solution is presented. In the numerical studies, effects of various factors on the natural frequencies and nonlinear amplitude-frequency response of the simply-supported peizoelastic laminated plates with interfacial imperfections are discussed. These factors include different damage models, thickness of the piezoelectric layer, side-to-thickness
ratio, and length-to-width ratio.

Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces

Shi-sheng ZHANG

2009, 30(2):  145-152 . 

Abstract ( 1454 )   PDF (139KB) ( 1080 )  

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The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.

Large eddy simulation of turbulent statistical and transport properties in stably stratified flows

Xiang QIU;Yong-xiang HUANG;Zhi-ming LU;Yu-lu LIU

2009, 30(2):  153-162 . 

Abstract ( 1346 )   PDF (516KB) ( 953 )  

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Three dimensional large eddy simulation (LES) is performed in the investigation of stably stratified turbulence with a sharp thermal interface. Main results are focused on the turbulent characteristic scale, statistical properties, transport properties, and temporal and spatial evolution of the scalar field.Results show that the buoyancy scale increases first, and then goes to a certain constant value. The stronger the mean shear, the larger the buoyancy scale. The overturning scale increases with the flow, and the mean shear improves the overturning scale. The flatness factor of temperature departs from the Gaussian distribution in a fairly large region, and its statistical properties are clearly different from those of the velocity fluctuations in strong stratified cases. Turbulent mixing starts from small scale motions,and then extends to large scale motions.

Mechanism of unsteady aerodynamic heating with sudden change in surface temperature

Hao CHEN;Lin BAO

2009, 30(2):  163-174 . 

Abstract ( 1405 )   PDF (331KB) ( 836 )  

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The characteristics and mechanism of unsteady aerodynamic heating of a transient hypersonic boundary layer caused by a sudden change in surface temperature are studied. The complete time history of wall heat flux is presented with both analytical and numerical approaches. With the analytical method, the unsteady compressible boundary layer equation is solved. In the neighborhood of the initial and final steady states, the transient responses can be expressed with a steady-state solution plus a perturbation series. By combining these two solutions, a complete solution in the entire time domain is achieved. In the region in which the analytical approach is applicable, numerical results are in good agreement with the analytical results, showing reliability of the methods. The result shows two distinct features of the unsteady response. In a short period just after a sudden increase in the wall temperature, the direction of the wall heat flux is reverted, and a new

High accuracy non-equidistant method for singular perturbation reaction-diffusion problem

Xin CAI;Dan-lin CAI;Rui-qian WU;Kang-he XIE

2009, 30(2):  175-182 . 

Abstract ( 1364 )   PDF (164KB) ( 1245 )  

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Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.

Explicit formulations and performance of LSFD method on Cartesian mesh

Qing-dong CAI

2009, 30(2):  183-196 . 

Abstract ( 1421 )   PDF (483KB) ( 1223 )  

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Performance of the LSFD method is compared with conventional FD schemes. Generally, 9-point stencils for 2D cases and 27-point stencils for 3D cases are used for the approximation of the first and second order derivatives obtained with conventional central difference schemes. When the same stencils are used, explicit LSFD formulations for approximation of the first and second order derivatives are presented. The LSFD formulations are actually a combination of conventional central difference schemes along relevant mesh lines. It has been found that LSFD formulations need much less iteration steps than the conventional FD schemes to converge, and the ratio of mesh spacing in the x and y directions is an important parameter in the LSFD application, with a great impact on stability of LSFD computation.

Nonconforming stabilized combined finite element method for Reissner-Mindlin plate

Min-fu FENG;Yan YANG;Tian-xiao ZHOU

2009, 30(2):  197-207 . 

Abstract ( 1326 )   PDF (308KB) ( 913 )  

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Based on combination of two variational principles, a nonconforming stabilized finite element method is presented for the Reissner-Mindlin plates. The method is convergent when the finite element space is energy-compatible. Error estimates are derived. In particular, three finite element spaces are applied in the computation. Numerical results show that the method is insensitive to the mesh distortion and has better performence than the MITC4 and DKQ methods. With properly chosen parameters, high accuracy can be obtained at coarse meshes.

Mathematical model and numerical method for spontaneous potential log in heterogeneous formations

Ke-jia PAN;Yong-ji TAN;Hong-ling HU

2009, 30(2):  209-219 . 

Abstract ( 1359 )   PDF (240KB) ( 1092 )  

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This paper introduces a new spontaneous potential log model for the case in which formation resistivity is not piecewise constant. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on the interfaces. It has been shown that the elliptic interface problem has a unique weak solution. Furthermore, a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic problems. Numerical results show validity and effectiveness of the proposed method.

Magneto-thermo-elastic waves in an infinite perfectly conducting elastic solid with energy dissipation

Payel Das;Mridula Kanoria

2009, 30(2):  221-228 . 

Abstract ( 1393 )   PDF (190KB) ( 1039 )  

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The generalized thermo-elasticity theory, i.e., Green and Naghdi (G-N) III theory, with energy dissipation (TEWED) is employed in the study of time-harmonic plane wave propagation in an unbounded, perfectly electrically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with complex coefficients is obtained for coupled magneto-thermo-elastic wave solved in complex domain by using the Leguerre's method. It reveals that the coupled magneto-thermo-elastic wave corresponds to modified dilatational and thermal wave propagation with finite speeds modified by finite thermal wave speeds, thermo-elastic coupling, thermal diffusivity, and the external magnetic field. Numerical results for a copper-like material are presented.

Robust H_∝ filtering for discrete-time impulsive systems with uncertainty

Sheng-tao PAN;Ji-tao SUN

2009, 30(2):  229-236 . 

Abstract ( 1429 )   PDF (164KB) ( 1306 )  

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This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H_∝ performance. First, an impulsive linear filter and a robust H_∝ filtering problem are introduced for a discrete-time impulsive systems. Then, a sufficient condition of asymptotical stability and H_∝ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to show effectiveness of the obtained result.

Parametric studies on relationships between flutter derivatives of slender bridge (I)

Xu XU

2009, 30(2):  237-245 . 

Abstract ( 1284 )   PDF (597KB) ( 1158 )  

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Relationships between flutter derivatives of slender bridge are investigated based on our previously proposed semi-analytical flutter derivatives of flexible structure. The intrinsic relations are validated with test data of flutter derivatives of two bridges. Changes in flutter derivatives with the erodynamic center, rotation speed, and angle variation are also studied by using a parametric method. The results show correctness of the proposed expressions of flutter derivatives given by authors in Ref.[1], and indicate that certain relations exist between these derivatives. It is also shown that semi-analytical flutter derivatives are applicable to bridges with a streamlined
cross-section.

An inversion algorithm for general tridiagonal matrix

Rui-sheng RAN;Ting-zhu HUANG;Xing-ping LIU;Tong-xiang GU

2009, 30(2):  247-253 . 

Abstract ( 1472 )   PDF (146KB) ( 1229 )  

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An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established. The algorithm is then generalized to deal with a general tridiagonal matrix without any restriction. Comparison with other methods is provided, indicating low computational complexity of the proposed algorithm, and its applicability to general tridiagonal matrices.

An approximation of the first passage probability of systems under nonstationary random excitation

Jun HE

2009, 30(2):  255-262 . 

Abstract ( 1271 )   PDF (325KB) ( 939 )  

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An approximate method is presented for obtaining analytical solutions for the conditional first passage probability of systems under modulated white noise excitation. As the method is based on VanMarcke's approximation, with normalization of the response introduced, the expected decay rates can be
evaluated from the second-moment statistics instead of the correlation functions or spectrum density functions of the response of considered structures. Explicit solutions to the second-moment statistics of the response are given. Accuracy, efficiency and usage of the proposed method are demonstrated by the first passage analysis of single-degree-of-freedom (SDOF) linear systems under two special types of modulated white noise excitations.