应用数学和力学

Non-Linear Free Vibration Analysis of Piezoelastic Laminated Plates With Interfacial Damage

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

2009, 30(2): 127-141.

Abstract(2736) PDF(586)

Abstract:
A nonlinear model for piezoelastic laminated plates containing the damage effect of the intra-layers and inter-laminar interface is presented, and the discontinuity of displacement and electric potential on the interfaces were depicted by three shape functions. By using the Hamilton variation principle, the three-dimensional nonlinear dynamic equations of piezoelastic laminated plates with damage effect were derived. Then, using the Galerlan method, a mathematical solution was presented. In numerical results, the effects of different damage models, the thickness of piezoelectric layer, the side-to-thiclmess ratio and the length-to-width ratio and the natural frequencies and non-linear amplitude-frequency response characteristics of the simply-suppotted piezoelastic laminated plates with interfacial imperfections were discussed.

Convergence Theorem of Common Fixed Points for Lipschitzian Pseudocontraction Semigroups in Banach Spaces

ZHANG Shi-sheng

2009, 30(2): 142-148.

Abstract(2707) PDF(543)

Abstract:
Some weak convergence theorems of the impliaty iteration precess for a Iapschitaan pseu-docontractive semi-groups in general Banach spaces were established, which extend and improve the corcespondin A new results of Zhou, Chen, et al, Xu, et al and Osilike.

Large Eddy Simulation of Turbulent Statistical and Transport Properties in Stably Stratified Flows

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

2009, 30(2): 149-159.

Abstract(3103) PDF(1155)

Abstract:
Three dimensional large eddy simulation (LES) was 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 veloaty fluctuations in a strong stratified case. Turbulent mixing starts from small scale motions, and then extends to large scale motions.

Mechanism of Unsteady Aerodynamic Heating With a Sudden Change in Surface Temperature

CHEN Hao, BAO Lin

2009, 30(2): 160-170.

Abstract(3474) PDF(804)

Abstract:
The chazacteiistics and mechanism of the unsteady aerodynamic heating of a transient hypersonic borurdary layer caused by sudden change in surface temperature was studied, the complete time history of wall heat flax was presented by both analytical and numerical approaches. With analytical methods, the unsteady compressible boundary layer equation was solved. In the neighborhoods of initial and final steady state, the transient response can be expressed by a steady-state solution plus a perturbation series, respectively.By patching these two solutions, the complete solution in the elrtire time domain wag achieved. In the region where the assumptions of analytical approach are satisfied, the numerical and analytical results were matched well, proving the reliability of the methods. The result showed two distinct features of the unsteady response. In the short period just after a sudden increase in the wall temperature, the direction of the wall heat flux reverted, a new inflexion near the wall arose in the profile of the thermal boundary layer, which is a typical unsteady characteristic. However, these unsteady responses only exist in a very short period in hypersonic flows, which means that, in a long-term aerodynamic heating process concidering only rinsready surface temperature, the unsteady characteristics of the flow can be ignored and the traditional quasi-steady aerodynamic heating prediction methods are still valid.

High Accurate Non-Equidlstant Method for Singular Perturbation Reaction-Diffusion Problem

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

2009, 30(2): 171-178.

Abstract(2825) PDF(637)

Abstract:
Singular pertubation reaction-diffusion problem with Dirichlet boundary condition is considered. this is a multi-scale problem. The presence of small parameter leads to bomdary Dyer phenomena on both sides of region. Non-equidistant finite difference method wag presented according to the property of boundary layer. The region was divided into the inner botmdary layer region and the outside botutdaty layer regiart according to transition point of Shishkin. The step length is equidistant on the outside bowdaty layer region. The step length is gradually increased on the inner boiutdacy layer region such that half of the step length is digerent firm each other. Tnutcation error was estimated. The new method is stable and uniform convergence with order higher than 2. Finally, numerical results were given, which are in agreement with the theoretical result.

Explicit Formulations and Performance Study of LSFD Method on Cartesian Mesh

CAI Qing-dong

2009, 30(2): 179-191.

Abstract(2675) PDF(544)

Abstract:
The performance of the ISFD (least square-based flute difference) method is compared with the conventional FD(fiute difference) schemes. For the approximation of the first and second order derivatives by the conventional central difference schemes, 9-point stencils for the 2D case and 27-point stencils for the 3D case are usually used. When the same stencils are used, the explicit ISFD formulations for apprrntimation of the fist and second order derivatives were present. the ISFD formutations are actually the combination of conventional central difference schemes along relevant mesh lines. It is found that ISFD formulations need much less iteration steps than the conventional FD schemes to get the converged solution, and the ratio of mesh spacing in the x and y directions is an important parameter in the ISFD application, which has a great effect on the stability of ISFD computation.

Nonconforming Stabilized Combined Finite Element Method for the Reissner-Mindlin Plate

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

2009, 30(2): 192-202.

Abstract(2901) PDF(883)

Abstract:
Based on the combination of two variational principles, a nonoonfornung stabilized futile element method was presented for the Reissner-Mindlin plates.

Mathemtical Model and Numerical Method for Spontaneous Potential Log in Heterogeneous Formations

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

2009, 30(2): 203-212.

Abstract(2868) PDF(683)

Abstract:
A new spontaneous potential log model for the case when formation resistivity is not piecewise constant was introduced. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on interfaces. It was proved that the elliptic interface problem has a unique weak solution. lluthemwre, a jump ooaidition capturing finite difference scheme was proposed and applied to solve such elliptic problems. The validity and effectiveness of the proposed method were demonstrated through numerical examples.

Magneto-Thermo-Elastic Waves in an Infinite Perfectly Conducting Elastic Solid With Energy Dissipation

Payel Das, M. Kanoria

2009, 30(2): 213-220.

Abstract(3028) PDF(491)

Abstract:
The generalized theory of thermo-elastiaty, r.e., Green and Naghdi (G-N)Ⅲ theory, with energy dissipation(TEWED) is employed in the study of time-harmonic plane wave prpagation in an unbounded, perfectly electxiically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with complex coefficients was obtained for coupled magneto-themlo-elastic wave which is solved in complex domain by using Leguerre's method. It is revealed that the coupled magneto-themlo-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

PAN Sheng-tao, SUN Ji-tao

2009, 30(2): 221-228.

Abstract(2932) PDF(595)

Abstract:
Robust filter design for linear discrete-time impulsive systems with uncertainty under H_∞ performance is invested. Fust,an impulsive linear filter and robust H_∞ filtering problem were introduced for a discrete-time impulsive systems. Then, sufficient condition of asymptotical stability and H_∞ performance for the filteaing error system was provided by discrete-time Liapunov fiuiction method, and the filter gains can be obtained by solving a set of linear matrix inequalities (LMIs).Finally, a numerical example was also included to illustrate the effectiveness of the proposed result.

Parametric Studies on the Relationships of Flutter Derivatives of Slender Bridge(Ⅰ)

XU Xu

2009, 30(2): 229-237.

Abstract(2648) PDF(558)

Abstract:
Based on the semi-analytical flutter derivatives of flexible structure provided by authors(XU Xu, CAO Zhi-yuan. Linear and nonlinear aerodynamic theory of interaction between flexible long structivre and wind, Applied Mathematical and Mechanics, 22(12):1299-1308.),the relationships of the flutter derivatives of slender bridge were investigated, and then their intrinsic relations were validated, by the test data of flutter derivatives of two bridges. The changing of flutter derivatives with the aerodynamic center, notation speed and angles variation were also researched by parametric method. The results not only prove the conectiress of expressions of flutter derivatives given by author, but also indicate that some certain relations exist in them. Tlutirermore, the semi-analytical flutter derivatives are showed to be applicable to the bridge with streamlined cross-section.

Algorithm for the Inverse of a General Tridiagonai Matrix

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

2009, 30(2): 238-244.

Abstract(5092) PDF(2416)

Abstract:
An algorithm for the inverse of a general tridiagonal matrix is presented. First, for the tridiagonal matzix having Doolittle factorization, an algorithm for the inverse was established. Then the algorithm was generalized to a general tridiagonal matrix without aqy restrictive condition. Some comparison with other methods operations of the algorithm for the inverse was discussed in the end. It is shown that the arithmetic operations of the algorithm are low and it is applicable to a general tridiagonal matrix.

Approximation for the First Passage Probability of Systems Under Nonstationary Random Excitation

HE Jun

2009, 30(2): 245-252.

Abstract(2818) PDF(675)

Abstract:
An approximate method is presented for obtaining analytical solutions for the conditional fast passage piubability of systems under modulated white noise excitation, the method is based on VanMarcke's approximation, however, because the normalization of the response was 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 stnrcrures. Explicit solutions for the second-moment statistics of the response were given. The accuracy, efficiency and usage of the proposed method were demonstrated by the fast passage analysis of single-degree-of freedom (SDOF) linear systems under two special types of modulated white noise excitations.

2009 Vol. 30, No. 2