力学学报

NUMERICAL STUDY OF THE STABILITY OF HYPERSONIC BASE FLOW OVER A BLUNT BODY AND APOLLO COMMAND MODULE

Zhu Dehua, Shen Qing, Wang Qiang, Yuan Xiangjiang

The structural instabilities of base flow are presented by using numerical simulation in this paper in hypersonic base flow over blunt cone with M_∞=6, Re=1.71× 10⁶(based on the nose radius) and Apollo command module with M_∞=6, Re=1.71 × 10⁶(based on the nose radius). Stable solutions are first obtained to show a primary separation and a secondary separation zone in flow over blunt body at M_∞=6. Later, without any arbitrary disturbance imposed, the structural instability still occurs after a certain critical time. The evolving process of the structure of flow over blunt body is a periodic behavior in the forepart, but there is non-periodic behavior observed at M_∞=6 in spite of long calculation time. For Apollo command module, the simulation result is similar to that of the blunt body, while the base flow of Apollo command is more instability than that of blunt cone. This research indicates that the present numerical simulation method can be used for the study of the stability of base flow.

2012, (3): 465-472. doi: 10.6052/0459-1879-2012-3-20120301

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EXPERIMENTAL INVESTIGATION ON A SPHERICAL HEAVY-GAS INTERFACE ACCELERATED BY A CYLINDRICAL CONVERGING SHOCK WAVE

Wang Xiansheng, Si Ting, Luo Xisheng, Yang Jiming

The Richtmyer-Meshkov instability of the interaction between a cylindrical converging shock wave and a spherical heavy-gas interface is studied experimentally using the high-speed schlieren photography. The shock tube test section is well-designed based on the shock dynamics theory, which can convert a planar incident shock wave with Mach number of 1.2 into a cylindrical converging shock wave. The spherical gas interface is formed by filling a soap bubble with sulfur hexafluoride (SF₆) surrounded by air. The high-speed video camera is used to record the complete process of the shock movement, which validates the method for generating cylindrical shock waves. The evolution of the wave propagation and the interface deformation after the passage of the cylindrical converging shock and the reshock is obtained during a single run. The results indicate that after the cylindrical shock passes across the bubble, the left interface of the bubble moves at a nearly constant velocity; the right interface of the bubble forms a jet and the main body of the bubble develops into a vortex ring. Subsequently, with the reshock impacting with the evolving interface, the disordered motion of the interface is intensified and the flow field quickly turns into a turbulent mixing.

2012, (3): 473-480. doi: 10.6052/0459-1879-2012-3-20120302

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EFFECT OF MAGNETIC FIELD ON THERMOCAPILLARY CONVECTION IN A DOUBLE-DIFFUSIVE LIQUID LAYER

Li Wei, Jiang Yanni, Yan Junyi, Chen Qisheng

Effect of magnetic field on thermocapillary convection in a double-diffusive liquid layer was investigated by numerical simulation, in which both the thermal Marangoni effect and solutal Marangoni effect were considered. The computational results show that thermocapillary convection is effectively weakened by external magnetic field and the convective pattern is changed. With magnetic field intensity increasing, the convective intensity is decreased gradually; the diffusive effect in the process of heat and mass transfer is strengthened, and the solute concentration distribution indicates a gradient along the horizontal direction. Therefore, the pure diffusion process in crystal growth can be realized as magnetic field intensity is sufficiently large.

2012, (3): 481-486. doi: 10.6052/0459-1879-2012-3-20120303

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PARAMETRIC STUDY ON THE BLENDING FUNCTION IN TRANSITION ZONE OF THE LES/RANS METHOD

Chen Ti, Liu Weidong, Sun Mingbo, Fan Xiaoqiang, Liang Jianhan

Two-equation k-ω SST turbulence model was combined with Sagaut's mixed-length subgrid-scale model with a blending function to construct a hybrid large-eddy/Reynolds-averaged Navier-Stokes method. The method was used to compute a plate turbulent boundary layer at Mach number 2.8 with fifth-order WENO scheme. A recycling/rescaling method was used to generate and sustain turbulent fluctuations at the inlet. The RANS to LES transition parameters and mesh resolution were considered in order to assess the method. The results showed that the hybrid method could capture the large-scale structure in the turbulent boundary-layer and no shift of the inlet mean parameters was observed. The blending function should be designed to transition to LES toward the outer part of the logarithmic region and the transition should be sharp to obtain the correct Reynolds shear stress. Single point-second order velocity fluctuations statistics might be obtained and accepted on streamwise and spanwise meshes scaled by Escudier mixing length.

2012, (3): 487-493. doi: 10.6052/0459-1879-2012-3-20120304

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A MODIFIED CBS FINITIE ELEMENT APPROACH FOR FLUID-STRUCTURE INTERACTION

Zhou Dai, He Tao, Tu Jiahuang

This paper performed a finite element analysis of fluid-structure interaction (FSI) problems under the arbitrary Lagrangian-Eulerian (ALE) description. The loosely-coupled partitioned algorithm was employed where Navier-Stokes equations were solved by the semi-implicit characteristic based split (CBS) scheme while the equation of motion for structure was solved by the Newmark-β technique. A mass source term, in accordance with the so-called geometric conservation law (GCL) when computing on moving meshes, was adopted in the pressure Poisson equation, the efficient moving submesh approach (MSA) was used for the mesh deformation in the computation of fluid-structure interaction, and a smoothing algorithm was introduced to avoid the degradation of moving meshes if a long-playing simulation was carried out. Such a technique as modified combined interface boundary condition (MCIBC) method was applied on the velocity and momentum fluxes along the interface. Consequently, the present loosely-coupled partitioned procedure achieved better accuracy and stability on the study of fluid-structure interaction. Moreover, the proposed method was applied to the flow-induced vibration analysis of one single circular cylinder and two circular cylinders. The numerical results showed high efficiency and a good agreement with the existing experimental and numerical data.

2012, (3): 494-504. doi: 10.6052/0459-1879-2012-3-20120305

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HIGHER-ORDER ACCURATE, NON-OSCILLATORY, THREE-NODES CENTRAL DIFFERENCE SCHEME FOR THE CONVECTIVE-DIFFUSION EQUATION CONSTRUCTED BY USING PHYSICAL VISCOSITY

Gao Zhi

Several higher-order accurate, non-oscillatory, three-nodes central difference schemes for the convective-diffusion equation are given by perturbationally reconstructing the diffusion scheme in the second-order accurate central difference scheme(2-CDS). Excellent properties of higher-order accurate and high resolution of the present new schemes (diffusion perturbation schemes, DPS) are verified by theoertical analyses and three numerical tests which include one-dimensional linear and non-linear and two-dimensional convective-diffusion equations. In all numerical tests, the 2-CDS oscillates and diverges on coarse grids, while part of DPS do not oscillates and can capture discontinuities with high resolution. The mean square root L₂ errors of all DPS are greatly less than those of 2-CDS in all numerical tests. The DPS are the results of introducing diffusion-motion law(i.e. physical viscosity smoothing out space-distribution of diffusion quantities) into 2-CDS. The present method is obviously different from the well-known those of constructing high-order accurate and high resolution schemes. In addition, we prove that DPS are completely consistent with those schemes of introducing convection-motion law(i.e. law of that the downstream does not affect the upstream) into 2-CDS, to show that the perturbational operation to 2-CDS not only raises the scheme's accurate and stability but also reveals intrinsic relation between the convective discrete scheme and diffusion discrete scheme, and that the upstream-downstream splitting is a very useful method for reconstructing high-order accurate, high resolution CFD scheme without artificial viscosity or limiter.

2012, (3): 505-512. doi: 10.6052/0459-1879-2012-3-20120306

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NUMERICAL SIMULATION OF BUBBLE DYNAMICS IN COMPRESSIBLE FLUID

Wang Shiping, Sun Shili, Zhang Aman, Chen Yu

Most studies on bubble dynamics adopting the boundary element method (BEM) were based on the incompressible potential flow theory, and the motion and deformation of a bubble in a compressible liquid was rarely studied by using BEM. An approximate theory is developed for a nonlinear and non-spherical bubble in a compressible fluid by using the doubly asymptotic approximation method. Wave equation is approximated in the early and late stages, respectively, resulting in the so-called local and global approximation equations. Matching between these two equations provides the model for the non-spherical bubble behavior in a compressible fluid domain. The numerical model is validated against the Prospertti & Lezzi equation for spherical bubbles in weakly compressible liquids with excellent agreement being obtained for the bubble radius evolution up to the second oscillation. Both numerical result and theoretical analysis show that the maximum radius decreases as the bubble oscillates. Numerical analyses are further performed for non-spherical oscillating bubbles. Bubble evolution and jet formation are simulated. Compared with that of the incompressible model, the jet velocity in the present model is smaller. Bubble oscillation near a solid boundary is further simulated based on the present model.

2012, (3): 513-519. doi: 10.6052/0459-1879-2012-3-20120307

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THERE DIMENSIONAL VORTEX METHOD SIMULATION OF UNSTEADY FLOW IN HYDRAULIC TURBINE

Wang Longbu, Zhu Baoshan, Wang Hong, Cao Shuliang

A fast Lagrangian vortex method presented in this paper is employed to simulate the flow inside a francis turbine runner. The normal flux boundary condition is satisfied by superimposing a potential flow on the vortical field, which is solved by the boundary element method (BEM), while the no-slip boundary condition is by generating vortex tiles on solid boundaries. The generalized Biot-Savart's law is adopted to calculate the vortical field in the Lagrangian frame of reference and the adaptive fast multipole method is utilized to reduce the computation complexity. The calculation results of a sample Francis turbine on design condition and off-design conditions agrees adequately well with experiment data, which confirms that the method is verified and practicable to simulate the complex interior unsteady flow with high Re.

2012, (3): 520-527. doi: 10.6052/0459-1879-2012-3-20120308

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OPTIMUM TOPOLOGY DESIGN OF STRUCTURAL PART FOR CONCENTRATION FORCE TRANSMISSION

Niu Fei, Wang Bo, Cheng Gengdong

For complicated structures assembled by several parts, like launch vehicle, external load in the form of concentrated load exerted on several points is transmitted to a given section of the structure. Therefore, some measures should be taken in the structural design to diffuse the concentrated force. In order to optimize the structure for diffusing the concentrated force, a theoretical model based on the continuum topology optimization is presented in this paper. The minimum structural compliance is taken as the object function subject to structural materials' volume constraint. Constraints on uniformity of the internal force are also considered in this model. Two-dimensional and three-dimensional examples are presented to illustrate the effectiveness of the formulation and algorithm. Finally, based on the actual forces and displacement constraints, a feasible conceptual design is presented for the short shell of a rocket's storage trunk.

2012, 44(3): 528-536. doi: 10.6052/0459-1879-2012-2-20120309

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ANALYSIS AND TOPOLOGY OPTIMIZATION OF ELASTIC SUPPORTS FOR STRUCTURES UNDER THERMO-MECHANICAL LOADS

Yang Jungang, Zhang Weihong, Wang Dan, Cai Shouyu

Elastic supports are recognized as an efficient means for structural designs under thermo-mechanical loads. Their introduction is beneficial not only for the achievement of the specific structure stiffness but also for the reduction of stress intensities to match the thermal deformation of the structure. In this paper, both theoretical and numerical studies are carried out to optimize the elastic support under thermo-mechanical loads. First, the analytical expression of the maximal thermo-mechanical stress is derived for a beam model with elastic support to illustrate the effects of the load-bearing and thermal deformation coordination of the elastic support. On this basis, a general topology optimization model and related topology optimization methods are proposed. Numerical examples and results are presented to demonstrate the validity of the proposed approach.

2012, (3): 537-545. doi: 10.6052/0459-1879-2012-3-20120310

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AN APPROXIMATE EFFECT ANALYSIS OF STRUCTURAL SYSTEM WITH FUZZY DISTRIBUTION PARAMETERS

Wang Pan, L? Zhenzhou, Tang Zhangchun

In order to analyze the effect of the epistemic uncertainty of the random input variables' distribution parameters on the structure system, the fuzzy variables are introduced to describe the epistemic uncertainty and the membership levels are employed to measure the degree of the epistemic uncertainty. Two effect indicators, main effect and total effect, for the output response and failure probability are proposed at each possibility level, respectively, and then their relationships with the membership levels are investigated in detail. Finally the expected effect indicators are presented to define the effect of each parameter on the system. In order to reduce the computational cost of the proposed indicators, a new method is proposed by the Taylor expansion for the moments of the output response. Three examples are utilized to demonstrate the reasonability of the proposed indices and the efficiency of the proposed method.

2012, (3): 546-556. doi: 10.6052/0459-1879-2012-3-20120311

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A PRECISE INTEGRATION APPROACH FOR THE DYNAMIC-STIFFNESS MATRIX OF STRIP FOOTINGS ON A LAYERED MEDIUM

Lin Gao, Han Zejun, Li Weidong, Li Jianbo

A precise integration method (PIM) is applied to the evaluation of dynamic-stiffness matrix of strip footings on a layered medium. PIM is an efficient and accurate numerical method to study the wave motion in layered earth strata. Through Fourier transform, the governing equation of wave propagation is formulated in the frequency-wavenumber domain as a set of ordinary differential equations with two-point boundary value conditions, and the Green's functions are solved by PIM. Finally, the dynamic-stiffness matrix of rigid strip footing on layered medium is converted from frequency-wavenumber domain into frequency-spatial domain. The proposed algorithm has the advantages that it avoids the exponential overflow generally encountered in the case of transmission matrix. In addition, it is versatile and adaptable to various cases of footings. It ensures convergence at high-frequency range, while perfect accuracy can be achieved.

2012, (3): 557-567. doi: 10.6052/0459-1879-2012-3-20120312

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THE HYBRID NATURAL ELEMENT METHOD FOR ELASTICITY

Dong Yi, Ma Yongqi, Feng Wei

Because for the inaccurate stress solution and poor ability to solve the stress of node, the traditional natural element method (NEM) are rarely used to solve the complex questions. In this paper, the hybrid finite element method was introduced into NEM to be the hybrid natural element method (HNEM). On the basis of HNEM and Hellinger-Reissner principle, the HNEM for elasticity is present. Compare with NEM, the HNEM has more precision solution of stress and can solve the stress of node directly.

2012, (3): 568-575. doi: 10.6052/0459-1879-2012-3-20120313

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RELAXATION BURSTING OF A FAST-SLOW COUPLED OSCILLATOR AS WELL AS THE MECHANISM OF NON-SMOOTH BIFURCATION

Zhang Xiaofang, Chen Xiaoke, Bi Qinsheng

By introducing suitable values of the parameters, a fast-slow coupled oscillator has been obtained. Under the analysis of the equilibrium points as well as the characteristics of the coupled system and the subsystems, combining the theory of Clarke differential inclusions, the singularities on the non-smooth boundaries are explored, which reveals that the non-conventional bifurcation composed of Hopf bifurcation and Fold bifurcation may occur when the trajectory passes across the boundary for suitable parameters. Different types of bursting phenomena associated with the corresponding parameters conditions have been obtained, the oscillating characteristics of which is discussed in details. It is pointed out that the frequency of the spiking in bursters may depend on the frequency related to Hopf bifurcation of the fast subsystem on the non-smooth boundary, while the natural frequency of the slow subsystem may influence the oscillating period of the bursters. The bifurcation mechanism of the different periodic bursters caused by the non-smooth bifurcation are presented in the end.

2012, (3): 576-583. doi: 10.6052/0459-1879-2012-3-20120314

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THE PRELIMINARY INVESTIGATION ON DESIGN AND EXPERIMENTAL RESEARCH OF NONLINEAR CHARACTERISTICS OF SD OSCILLATOR

Chen Enli, Cao Qingjie, Feng Ming, Tian Ruilan

Since the discovery of SD oscillator in 2006, which allows the transition from smooth to discontinuous dynamics of strongly geometric nonlinearity, a variety of significant phenomena have been explored through theoretical research. However, there has no report in literature about the experimental research due to the barrier of large displacement associated with bistability. Here in this paper, we propose an experimental rig of SD oscillator, which is smooth at the first stage, to investigate the nonlinear dynamic responses experimentally under the harmonic excitation with different excitation frequencies and amplitudes. Vibration parameters existed in the rig are measurable and adjustable. Vibration signals are collected by a high speed camera to overcome the conventional barrier. The experimental results presented in this paper showed the excellent agreement with the analytical results, periodic vibration, period-5 solution and chaotic phenomena under the chosen certain parameters.

2012, (3): 584-590. doi: 10.6052/0459-1879-2012-3-20120315

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A MODELING STUDY OF BLOOD FLOW AND OXYGEN TRANSPORT IN THE CIRCLE OF WILLIS

Ji Changjin, He Ying

Sufficient blood supply is of importance in maintaining the normal function of brain. If the brain cells are lack of oxygen for more than a few minutes due to decreased flow and perfusion pressure, they will be irreversibly damaged. In this study, blood flow and oxygen transport in the circle of Willis are modeled using one-dimensional equations derived from the axisymmetric Navier-Stokes equations for flow in elastic and compliant vessels and the convective-diffusive equation with the consideration of the diffusion from the lumen to artery wall and the metabolism produced by the wall cells. The nonlinear equations for hemodynamics were numerically solved using the two-step Lax-Wendroff scheme, and the upwind scheme was used in the discretization of the oxygen transport equations. The computational results were obtained, which were in good agreement with the available physiological data in normal and stenosis condition. It is shown that, when the degree of stenosis existing at the right internal carotid artery is up to 80%, the flow rate of the middle cerebral artery is reduced significantly. Furthermore, the oxygen partial pressure in ipsilateral vessels decreases with the increasing of stenosis degree, while the oxygen partial pressure of the vessel in another side increases.

2012, (3): 591-599. doi: 10.6052/0459-1879-2012-3-20120316

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FLOW CHARACTERISTICS OF LIQUID FILMS DRIVEN BY PERIODIC ELECTRO-OSMOSIS IN BIOCHIPS

Tang Wenyue, Hu Guohui

The flow of a thin film on a solid substrate driven by periodic electro-osmosis is studied in the present paper. To describe the relation between potential of electric double layer and charge density, the Poisson-Boltzmann equation is utilized under the Debye-Hückel approximation. An analytical solution for the film is obtained by solving the periodic electro-osmosis driven system, coupling with the Navier-Stokes equation for incompressible viscous fluid. Results indicate that amplitude of the flow velocity in the thin film strongly depends on the Reynolds number, i.e., the amplitude decreases as the Reynolds number increasing. The influence of the ζ potential, as well as the viscosity, is also analyzed on the flow velocity at the free surface and phase difference of the oscillating velocity.

2012, (3): 600-606. doi: 10.6052/0459-1879-2012-3-20120317

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NUMERICAL SIMULATION OF INTRANASAL TEMPERATURE FIELD AND ITS RELATIONSHIP WITH THE AIRFLOW DURING INSPIRATION

Su Yingfeng, Sun Xiuzhen, Liu Yingxi, Yu Shen, Wang Jizhe, Gao Fei

To explore the characteristic of warming function of nasal cavity and its relationship with the airflow, a three dimensional model throughout human nasal cavity is established based on CT scan data. Then the airflow fields and temperature fields at time points of 0.15s, 0.45s and 0.75s during inspiration at the ventilation volume of 12L/min are simulated using computational fluid dynamics (CFD) method. The detailed results of airflow field and temperature field at the above three time points during inspiration show that the airflow in both sides is asymmetry, and the air passes mainly through the left side. The volumes of the airflow in the middle and ventral medial regions are larger than those in olfactory split, middle and inferior meatuses in both sides. As to the temperature field, the temperature increases gradually from anterior part of nasal cavity till nasopharynx. The main temperature-increase happens characteristically within the anterior nasal segment including the airway among ostium internum and heads of inferior and middle turbinates at the above three time points, while temperature increases slightly after the head of middle turbinate. The length of the main temperature-increase segment of airway does not lengthen obviously as to the increase of the volume of airflow at the above three time points. Not the same as the airflow distribution difference between both nasal cavity or different parts in either side, the temperature fields in both sides are almost symmetry, and the temperature difference between both sides or different parts in either side is less than 1℃.

2012, (3): 607-613. doi: 10.6052/0459-1879-2012-3-20120318

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NANOINDENTATION EXPERIMENT AND FINITE ELEMENT SIMULATION FOR BIOMECHANICAL BEHAVIOR OF RED BLOOD CELL

Li Weiwei, Yang Qingsheng, Liu Zhiyuan

This paper studies the biomechanical behaviors of a red blood cell (RBC) by nanoindentation technique and finite element simulation. The Young's modulus and load-displacement curve of RBC are measured by nanoindentation. Then a 3D finite element model of RBC is built to simulate the naoindentation process. The load-displacement curves of RBC are obtained by altering friction coefficients between the tip and curvature radius of the tip. It is shown that the FEM results are agreement with the experimental data for nanoindentation of RBC. The deformation of RBC is obviously influenced by the curvature radius of the tip but slightly by the friction coefficient between the tip and the cell.

2012, (3): 614-621. doi: 10.6052/0459-1879-2012-3-20120319

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EVALUATION OF ROUND WINDOW STIMULATION BY A FE MODEL OF HUMAN AUDITORY PERIPHERY

Wang Xuelin, Hu Yujin

The round window placement of a vibratory transducer is a new approach for coupling an implantable hearing system to the cochlea. To evaluate the vibration transfer to the cochlear fluids and partition in response to normal acoustic stimulation and to mechanical stimulation of the round window, an acoustic-structure coupled finite element (FE) analysis was conducted by utilizing recently developed FE model which consists of the external ear canal, middle ear and cochlea. The middle ear and cochlear transfer functions such as the sound pressure gain across middle ear, intracochlear pressures, as well as basilar membrane vibration, were derived, during normal forward sound stimulation as well as reverse RW stimulation. The present results show that the round window stimulation with a harmonic pressure produces basilar membrane response similar to normal forward sound stimulation. Then a model was proposed to calculate the force required of an actuator at the round window to produce a basilar membrane displacement that is equivalent to a stimulus produced in normal ear by a given external ear-canal pressure. The information is essential for supporting the optimization of the actuators and adapting existing prostheses specifically for round window stimulation in order to insure sufficient acoustic output.

2012, (3): 622-630. doi: 10.6052/0459-1879-2012-3-20120320

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THE EFFECT OF THE ACL SINGLE-BUNDLE/DOUBLE-BUNDLE RECONSTRUCTION ON THE BIOMECHANICS OF TIBIO-FEMORAL JOINT AT DIFFERENT FLEXION ANGLES

Xu Qiang, Huang Rongying, Xu Yonggang, Guo Yunfei, Zheng Hongguang

In this paper, through the simulation of the clinical pivot test at knee flexion angle of 0? for the models A and B, the accuracy and validity of the pairs of models for healthy adult A were proved. After that, MRI images of the normal human knee at different flexion angles of 0?/25?/60?/80? were obtained through SONATA MAESTRO 1.5T Scanning. Then, the corresponding 3D tibio-femoral joint models of normal/ACL single bundle/double bundle reconstruction were established. In the experiment, axial force and combined loads (axial force and torque) were applied to these models to analyze and compare the changes of the stress distribution of cartilages/meniscus/ligaments and the tension characteristic of ligaments before and after the ACL reconstruction. The results show that: (1) The stresses on cartilages and meniscus after ACL single bundle/double bundle reconstruction change with the flexion angles, and especially the stress distributions on the cartilages change significantly at some angle. (2) Single-bundle reconstruction can lead to the obvious increment of the equivalent stresses on cartilages and meniscus, and the maximum increment is to 40%. However, the corresponding values after double bundle reconstruction at different flexion angles are closer than that after single-bundle reconstruction. (3) Although ACL single-bundle reconstruction will reduce the equivalent stress on PCL, stress on medial/lateral collateral ligament will significantly increase at high-flexion angle. The maximum stress on MCL changes obviously with the flexion angles after double-bundle reconstruction, but the maximum stress on LCL and PCL show the corresponding trend to normal joint. (4) The average tension of MCL is higher than that of the other two after single or double bundle reconstruction. Besides, the tension characteristic of ligaments after the double-bundle reconstruction is closer to the normal joint than that after single-bundle. In short, considering the stress and tension of cartilages, meniscus and ligaments after ACL reconstruction, the tibio-femoral joint mechanical contact characteristic after ACL double-bundle reconstruction is closer to the normal joint than that after single-bundle reconstruction. And whether ACL single-bundle or double bundle reconstruction, the change of stress distribution and the increase of peak stress on cartilages, meniscus and ligaments would induce chronic degeneration of joints and be the main reason for the disease knee.

2012, (3): 631-637. doi: 10.6052/0459-1879-2012-3-20120321

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RHEOLOGICAL PARAMETERS INVERSION BY THEORETICAL ANALYSIS OF COMPRESSIVE CREEP TESTS

Yang Wendong, Zhang Qiangyong, Chen Fang, Li Shucai, Li Wengang, Wang Jianhong, He Ruping, Zeng Jiquan

Long-term stability of the dam foundation is an important guarantee for the safety of dam operations, and the weak interlayer in the rock mass of dam foundation is an important factor which affects the stability and deformation. In order to study the deformation mechanism of the weak interlayer in diabase dikes under long-term load at Dagangshan hydropower dam foundation, in-situ large-scale compressive creep test using circular rigid bearing plate is carried out which is perpendicular to the weak interlayer in test cavern of dam slope. The five-parameter generalized Kelvin model is identified to describe the creep property of weak interlayer, which avoids the defects of three-parameter generalized Kelvin model that has the problem of unwanted rapid convergence. Based on the Boussinesq problem in elastic mechanics, the visco-elastic deformation formula of five-parameter generalized Kelvin model for rock mass under rigid bearing plate is derived for the first time through Laplace transform and inverse transform, and the rheological parameters are inversed.

2012, (3): 638-642. doi: 10.6052/0459-1879-2012-3-20120322

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ANALYSIS OF 1:3 INTERNAL RESONANCES FOR UNILATERAL PLATES PARTIALLY IMMERSED IN FLUID AND MOVING IN AXIAL DIRECTION

Li Hongying, Guo Xinghui, Wang Yanqing, Li Jian, Xie Liyang, Chen Bo

Based on the nonlinear vibration equation of a unilateral plate partially immersed in fluid and moved in the axial direction, which is derived from von K醨m醤 thin plate equation with large deflection, the 1:3 internal resonances characteristics of the unilateral plate under an external excitation are studied. The speed and tension of the unilateral plate in the axial direction, fluid-structure interaction and damping are considered. Galerkin method is used to disperse the vibration equation. The nonlinear modal equations are solved by applying numerical and approximate analytical techniques, respectively, and complex frequency-response curves with internal resonance are obtained. The stability of periodical solutions is discussed. At last, the bifurcation phenomenon of the averaged equations with 1:3 internal resonances is studied.

2012, (3): 643-647. doi: 10.6052/0459-1879-2012-3-20120323

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FIRST EXCURSION PROBABILITIES OF DYNAMICAL SYSTEMS BY IMPORTANCE SAMPLING

Ren Limei, Xu Wei, Xiao Yuzhu, Wang Wenjie

Based on the Girsanov transformation, this paper develops a method for estimating the first excursion probability of dynamical systems with stationary gauss white noise. The focus is to construct control function that concentrates on the samples paths in the “most important part” of the sample space, to achieve the purpose of variance reduction. The paper uses design point to construct control function. For linear systems, the present approach combines with the time-invariant structure reliability theory to get design points by solving the problem of the optimization. For non-linear systems, the paper uses mirror-images method to get design points. Finally the paper gives two examples. The results show the method of this paper to be correct and effective by comparing with the primitive Monte Carlo method.

2012, (3): 648-652. doi: 10.6052/0459-1879-2012-3-20120324

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2012 Vol. 44, No. 3

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