应用数学和力学

2013 Vol. 34, No. 11

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Close Eigenvalues of Periodic Structures With Finite Unit Cells

WU Feng, GAO Qiang, ZHONG Wan-xie

2013, 34(11): 1119-1129. doi: 10.3879/j.issn.1000-0887.2013.11.001

Abstract(1508) PDF(1105)

Abstract:
For a periodic structure with finite unit cells, the range where eigenvalues existed was estimated based on the eigenproblem of the unit cell. A more precise estimate of the eigenvalue distriution range for a one dimensional periodic structure with finite unit cells was presented based on the energy band theory in solid physics. In terms of the estimated range of eigenvalues, the close eigenvalue phenomenon was made clear. The analysis results show that, for a periodic structure with finite unit cells, the larger the number of the unit cells is, the closer the eigenvalues are. Numerical tests demonstrate the correctness of the proposed conclusions.

Model of the Unsteady Vertical Water-Entry and Water-Exit Cavities

CHEN Wei-qi, WANG Bao-shou, YAN Kai, LU Hai-yan

2013, 34(11): 1130-1140. doi: 10.3879/j.issn.1000-0887.2013.11.002

Abstract(1213) PDF(1210)

Abstract:
The unsteady vertical water-entry and water-exit cavities produced by a high-speed body were investigated theoretically, the mathematical models of the water-entry and water-exit cavities were proposed, and the solutions of the cavity shape varying with water depth were derived. Based on the solutions, the cavity length, cavity volume，closure depth of water-entry cavity and the condition for the formation of supercavity were obtained. The results show that the volume of the water-exit cavity increases with the reduction in water depth. Therefore, in order to maintain (or increase) the pressure of the water-exit cavity, more volume of gas injection is required in contrast to horizontal cavity, which also means that it is harder for the water-exit cavity to form supercavity, but simultaneously the advantage is that the water-exit cavity is hard to leak gas due to the increase in its volume. On the contrary, with the increase in water depth, the water-entry cavity has the tendency to shrink its volume, and squeeze gas within the cavity to jet out from the rear end of the cavity, with the gas reduction within cavity due to the gas jet, the pressure of the cavity will decrease, if the pressure falls below the environmental pressure, the rear end of the cavity will be closed by the environmental high-pressure, and thus the gas jet will terminate. As a result, a periodic impulsive process that consists of successive jetting-closure phases will be formed at the rear end of the cavity, resulting in the formation of a series of small bubbles in the wake of the cavity and wavelike fluctuations on the surface of the cavity due to the fluctuations of the pressure within the cavity.

Finding New Types of Peakon Solutions for FitzHugh-Nagumo Equation by an Analytical Technique

ZOU Li, WANG Zhen, LIANG Hui, ZONG Zhi, ZOU Hao

2013, 34(11): 1141-1149. doi: 10.3879/j.issn.1000-0887.2013.11.003

Abstract(1579) PDF(1062)

Abstract:
The FitzHugh-Nagumo equation was studied with an approximate analytical method: the differential transform method. Peakon soliton solutions to this equation were presented. As a result, more new types of peakon solutions were obtained. The convergence region and rate of the differential transform method were also analyzed. The differential transform method was successfully combined with the Padé approximation technique, to construct an explicit, totally analytical and uniformly valid peakon soliton solution to FitzHugh-Nagumo equation. The main idea was to limit the boundary conditions while let the derivative at the crest of the solitary wave not exist but the solitary waves of the derivative exist at both sides. The obtained results show that the differential transform method can avoid the limitation of perturbation under conditions of very small parameters. The present method provides a powerful and effective mathematical tool to obtain new types of precise peakon solutions for FitzHugh-Nagumo equation.

Numerical Simulation of Nanoindentation for the LD and HD Calcium Silicate Hydrates

ZHAO Jing-jing, ZHANG Qing, HUANG Dan, SHEN Feng

2013, 34(11): 1150-1156. doi: 10.3879/j.issn.1000-0887.2013.11.004

Abstract(1627) PDF(1960)

Abstract:
Calcium silicate hydrate(C-S-H) is the key component to determine the performance of the Portland cement based material C-S-H is a continuous solid material in hydration products. It accounts for 50%~60% of the hydrated cement slurry volume. C-S-H is the main ingredient to decide the hardened cement slurry’s physical structure and performance. At the same time, C-S-H is one of the important influential factors for concrete structure coherence and durability in macro view. Models became increasingly important to predict the bulk properties of cement and concrete, such as shrinkage, creep, permeability and cracking. Two numerical models were presented respectively for the low-density and high-density C-S-H gel phases in cement paste. C-S-H was introduced as an assemblage of discrete granular particles at nanoscale with realistic particle-level properties. With the molecular dynamics method, nanoindentation simulation was performed on each phase. Through control of particle volume fraction of C-S-H and with the other particle-level material properties kept constant, the results further show that the indentation modulus and hardness conform well to the law of the data from nanoindentation experiments in literature.

Noise-induced Vibration Experiment of Aircraft Structure and Vibro-Acoustic Coupling Response Analysis

ZHANG Guo-jun, YAN Yun-ju, LI Peng-bo

2013, 34(11): 1157-1164. doi: 10.3879/j.issn.1000-0887.2013.11.005

Abstract(1246) PDF(1421)

Abstract:
Aimed at the hypersonic aircraft X-43A in the research, the FE model was established. Natural frequency testing of the aircraft structure model was performed. The numerical values of natural frequency were compared with the experiment results, with errors at about 1%, which showed that the FE model of the aircraft was correct. A noise-induced vibration experiment of the aircraft model was completed in the high intensity sound laboratory, which could obtain the results of PSD and noise pressure. Comparison of the simulation values with the experiment results shows that the method of numerical simulation is reliable in prediction of the vibration and noise environment of the aircraft cabin. The trend of the numerical vibro-acoustic response is well consistent with that of the test results: there is little difference in low-frequency range the elastic cavity structural vibration of the aircraft model caused by high-frequency noise field outside the cavity makes the main components of structural vibration, especially of the low-order structural vibration. Noise in the aircraft cabin transmitted from the outer noise field is through the low-order vibration of the aircraft shell. The main components of the response noise frequencies in the closed cabin belong to structural low-order modal vibration, even if the noise excitation outside the cabin is broadband.

Numerical Simulation of Fluid-Structure Interaction for Tube Bundles

FENG Zhi-peng, ZHANG Yi-xiong, ZANG Feng-gang

2013, 34(11): 1165-1172. doi: 10.3879/j.issn.1000-0887.2013.11.006

Abstract(1419) PDF(1589)

Abstract:
A numerical model for three-dimensional flow induced vibration was proposed. It was conducted in order to further improve the solution of fluid-structure interaction problems, occurring in the nuclear power field such as the behavior of PWR fuel rod, stream generators and other heat exchangers’tubes. A three-dimensional unsteady Navier-Stokes equation was computed with LES model. The numerical method was based on finite volume discretization large eddy simulation approach on structured grids combined with the technique of dynamic mesh. The model presented a three dimensional fully-coupled approach to solving simultaneously the fluid flow and the structure vibration, for the tube bundles in cross flows. The flow induced vibration characteristics of a single tube was first analyzed based on the FSI method. Both the dynamic response and flow characteristics were obtained. Secondly, the mutual influence of two tubes, either inline or parallel set was investigated based on the FIV numerical model for tube bundles. Finally, the flow induced vibration characteristics of 3×3 tube bundles were studied.

Analysis of Slope Stability Based on Gradient-Dependent Non-Local Friction Model

FU Ming-fu, XIE Bang-hua, LIAO Xiao-hong, YU li

2013, 34(11): 1173-1181. doi: 10.3879/j.issn.1000-0887.2013.11.007

Abstract(1446) PDF(1019)

Abstract:
The stability of the slope with arc-shaped slip surface was studied based on the gradient-dependent non-local friction model and the gradient-dependent non-local material parameters were discussed. The material parameters, influence on the safety factor of slope stablity was analyzed from a microview with the mechanism of macro engineering problems probed. It is found that, when the non-local material parameters with microscopic properties change, the change of the slope safety factor will be not so big, but the trend will be very obvious. To discuss the influence of soil parameters on the safety factor, the gradient-dependent non-local friction model was compared with the local friction model, and the safety factor was found to be sensitive to the soil internal friction angle. The results provide useful reference for the engineering of soil slope treatment.

Nonlinear Dynamic Response and Bifurcation Analysis of the Elastically Constrained Shallow Arch

YI Zhuang-peng, ZHANG Yong, WANG Lian-hua

2013, 34(11): 1182-1196. doi: 10.3879/j.issn.1000-0887.2013.11.008

Abstract(1475) PDF(954)

Abstract:
When the ends are elastically constrained in vertical and rotation directions for the shallow arch, the natural frequencies and modes are quite different from those of the case of ideal hinged or fixed boundary condition, and the different constraint stiffness will change the nonlinear responses and the parameter fields of various bifurcations under external excitation. The dimensionless dynamic equation was established by introducing the fundamental assumptions of shallow arch, and the method that the effects by the boundary constraint stiffness were considered in the natural frequencies and modes solution was employed, then the full-basis Galerkin discretization and the multi-scale perturbation methods were used to obtain the polar- and Cartesian-type averaging equations, of which the coefficients have one-to-one correspondence with the values of constraint stiffness. With the application of numerical calculation, the dynamic behaviors of the vertical elastically constrained system in the case of one-to-two internal resonance between the lowest two modes under periodic excitation were studied. Both the comparison of calculated results with finite element results and the convergence of the coefficients in averaging equations proved the feasibility of the present method. Also, the numerical results show that there exist several bifurcation points with the variation of the amplitude and frequency of excitation, and the parameter distributions for the occurrence of bifurcations are associated with the values of constraint stiffness. Moreover, there are a series of steady-state solution, periodic solution, quasi-periodic solution and chaotic solution windows in the vicinity of the unstable areas or resonance regions which are connected by the bifurcation points, and the period-doubling bifurcation can be observed with the variation of parameters.

Research on Reissner Plate With an Inclusion or Flaw

JIANG Quan, WEI Hai-e, ZHOU Zhi-dong

2013, 34(11): 1197-1208. doi: 10.3879/j.issn.1000-0887.2013.11.009

Abstract(1260) PDF(1294)

Abstract:
The bending problems for the Reissner plate with arbitrarily shaped inclusion or flaw were solved with the conformal transformation method and Faber series expanding. The analytical functions were expanded with Faber series, and the wave functions were expressed by n-order first-kind and second-kind modified Bessel functions in/out the unit circle in the transform domain. The linear equations were obtained under the continuous displacement, shear force and bending moment conditions along the interface of the unit circle. The numerical examples and the theoretical analysis were presented for the Reissner plate with an elliptic inclusion or flaw under cylindrical bending. It is concluded that, the inner torques in the plate are sensitive to the ratio a/h for the soft inclusion, and are insensitive for the stiff one.

Optimization of SIFT-Based Image Retrieval

XIAO Man-yu, LU Jiang-hu, XIE Gong-nan

2013, 34(11): 1209-1215. doi: 10.3879/j.issn.1000-0887.2013.11.010

Abstract(2264) PDF(2340)

Abstract:
In order to deal with the great discrepancy between the expectations of users and the real performance in image retrieval, some improvement on building tree, retrieval and matching methods were made with great success both in accuracy and in efficiency. More precisely, a new clustering strategy was firstly redefined during the building of vocabulary tree, which combined the classification and the conventional K-means method. Then a new matching method to eliminate the error caused by large-scale SIFT was introduced. What was more, a new unit mechanism was adopted to shorten the cost of indexing time. Finally, the numerical results show that an excellent performance is obtained after these improvements. A vocabulary tree with more distinguished nodes is achieved, of which the height is defined automatically and the index accuracy is enhanced greatly. Furthermore, a faster indexing procedure is realized, of which the indexing time is much less than 1 s.

On the Convergence of Trust Region Method With Dogleg Step for Nonlinear Inequalities Systems

HE Yu-bo, LIN Xiao-yan

2013, 34(11): 1216-1224. doi: 10.3879/j.issn.1000-0887.2013.11.011

Abstract(1294) PDF(948)

Abstract:
The solutions of a class of nonlinear inequalities were studied.The nonlinear inequalities were approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions, then a smoothing trust region method with dogleg steps was applied to solve the parameterized optimization problems.The global convergence of the proposed method was established under some weak conditions. Numerical results show that the method performs well.