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Dynamics of a prey-predator system under Poisson white noise excitation

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Acta Mechanica Sinica 2014年第5期30卷 739-745页

作者： Shan-Shan Pan Wei-Qiu Zhu Department of Mechanics State Key Lab of Fluid Power Transmission and ControlZhejiang University

The classical Lotka-Volterra （LV） model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is in- vestigated by using the stochastic averaging method. The averaged generalized It6 stochastic differential equation and Fokkerlanck-Kolmogorov （FPK） equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter e2s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo （MC） simulation.

关键词： Prey-predator ecosystem Poisson white noise Stochastic averaging- Approximate stationary solution. Per turbation method

Three-dimensional elastostatic solutions for transversely isotropic functionally graded material plates containing elastic inclusion

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Applied Mathematics and Mechanics(English Edition) 2015年第4期36卷 417-426页

作者： Bo YANG Weiqiu CHEN Hao jiang DING Department of Civil Engineering Zhejiang Sci-Tech University Department of Engineering Mechanics Zhejiang University Department of Civil Engineering Zhejiang University

Based on the generalized England-Spencer plate theory, the equilibrium of a transversely isotropic functionally graded plate containing an elastic inclusion is studied. The general solutions of the governing equations are expressed by four analytic functions α（ζ）, β（ζ）, φ（ζ）, and ψ（ζ） when no transverse forces are acting on the surfaces of the plate. Axisymmetric problems of a functionally graded circular plate and an infinite func- tionally graded plate containing a circular hole subject to loads applied on the cylindrical boundaries of the plate are firstly investigated. On this basis, the three-dimensional （3D） elasticity solutions are then obtained for a functionally graded infinite plate containing an elastic circular inclusion. When the material is degenerated into the homogeneous one, the present elasticity solutions are exactly the same as the ones obtained based on the plane stress elasticity, thus validating the present analysis in a certain sense.

关键词： functionally graded plate elastic circular inclusion elasticity solution

Exact solutions for axisymmetric flexural free vibrations of inhomogeneous circular Mindlin plates with variable thickness

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Applied Mathematics and Mechanics(English Edition) 2017年第4期38卷 505-526页

作者： Jianghong YUAN Weiqiu CHEN Center for Mechanics and Materials and Key Laboratory of Applied Mechanics(AML) Department of Engineering MechanicsTsinghua UniversityBeijing 100084China State Key Laboratory of Traction Power Southwest Jiaotong UniversityChengdu 610031China School of Mechanics and Engineering Southwest Jiaotong UniversityChengdu 610031China Department of Engineering Mechanics Zhejiang UniversityHangzhou 310027China Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province Zhejiang UniversityHangzhou 310027China

Circular plates with radially varying thickness, stiffness, and density are widely used for the structural optimization in engineering. The axisymmetric flexural free vibration of such plates, governed by coupled differential equations with variable coefficients by use of the Mindlin plate theory, is very difficult to be studied analytically. In this paper, a novel analytical method is proposed to reduce such governing equations for circular plates to a pair of uncoupled and easily solvable differential equations of the Sturm-Liouville type. There are two important parameters in the reduced equations. One describes the radial variations of the translational inertia and fiexural rigidity with the consideration of the effect of Poisson＇s ratio. The other reflects the comprehensive effect of the rotatory inertia and shear deformation. The Heun-type equations, recently well-known in physics, are introduced here to solve the flexural free vibration of circular plates analytically, and two basic differential formulae for the local Heun-type functions are discovered for the first time, which will be of great value in enriching the theory of Heun-type differential equations.

关键词： free vibration circular Mindlin plate variable thickness inhomogeneous material Heun-type equation

Stochastic averaging of quasi integrable and resonant Hamiltonian systems excited by fractional Gaussian noise with Hurst index 1/2

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Acta Mechanica Solida Sinica 2017年第1期30卷 11-19页

作者： Q.F.Lü M.L.Deng W.Q.Zhu Department of Mechanics State Key Laboratory of Fluid Power and Mechatronic SystemsKey Laboratory of Soft Machines and Smart Devices of Zhejiang ProvinceZhejiang University

A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion （iBm） are briefly introduced. Then, the averaged fractional stochastic differential equations （SDEs） for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.

关键词： Quasi integrable and resonant Hamiltonian system Fractional Brownian motion Fractional Gaussian noise Stochastic averaging method Internal resonant

Stochastic averaging of quasi partially integrable Hamiltonian systems under fractional Gaussian noise

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2017年第9期18卷 704-717页

作者： Qiang-feng LU Mao-lin DENG Wei-qiu ZHU Department of Mechanics Zhefiang University Hangzhou 310077 China State Key Laboratory of Fluid Power and Mechatronic Systems Zhejiang University Hangzhou 310027 China Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province Zhejiang University Hangzhou 310027 China

A stochastic averaging method for predicting the response of quasi partially integrable and non-resonant Hamiltoniansystems to fractional Gaussian noise （fGla） with the Hurst index 1/2〈H〈l is proposed. The averaged stochastic differential equa-tions （SDEs） for the first integrals of the associated Hamiltonian system are derived. The dimension of averaged SDEs is less thanthat of the original system. The stationary probability density and statistics of the original system are obtained approximately fromsolving the averaged SDEs numerically. Two systems are worked out to illustrate the proposed stochastic averaging method. It isshown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of originalsystem agree well, and the computational time for the former results is less than that for the latter ones.

关键词： Fractional Brownian motion (fBm) Fractional Gaussian noise (fGn) Quasi partially integrable Hamiltonian system Stochastic averaging method Stationary response

Influence of surface scattering on the thermal properties of spatially confined GaN nanofilm

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Chinese Physics B 2016年第8期25卷 301-307页

作者：侯阳朱林利 Department of Engineering Mechanics and Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province Zhejiang University

Gallium nitride（GaN）, the notable representative of third generation semiconductors, has been widely applied to optoelectronic and microelectronic devices due to its excellent physical and chemical properties. In this paper, we investigate the surface scattering effect on the thermal properties of GaN nanofilms. The contribution of surface scattering to phonon transport is involved in solving a Boltzmann transport equation（BTE）. The confined phonon properties of GaN nanofilms are calculated based on the elastic model. The theoretical results show that the surface scattering effect can modify the cross-plane phonon thermal conductivity of GaN nanostructures completely, resulting in the significant change of size effect on the conductivity in GaN nanofilm. Compared with the quantum confinement effect, the surface scattering leads to the order-of-magnitude reduction of the cross-plane thermal conductivity in GaN nanofilm. This work could be helpful for controlling the thermal properties of Ga N nanostructures in nanoelectronic devices through surface engineering.

关键词： GaN nanofilm elastic model quantum confinement Boltzmann transport equation size effect,phonon thermal conductivity

Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling

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Acta Mechanica Sinica 2015年第5期31卷 601-626页

作者： Wei-Qiu Chen Department of Engineering Mechanics Zhejiang University

Significant progress has been made in mixed boundary-value problems associated with three-dimensional（3D） crack and contact analyses of advanced materials featuring more complexities compared to the conventional isotropic elastic materials.These include material anisotropy and multifield coupling,two typical characteristics of most current multifunctional materials.In this paper we try to present a state-of-the-art description of 3D exact/analytical solutions derived for crack and contact problems of elastic solids with both transverse isotropy and multifield coupling in the latest decade by the potential theory method in the spirit of V.I.Fabrikant.whose ingenious breakthrough brings new vigor and vitality to the old research subject of classical potential theory.We are particularly interested in crack and contact problems with certain nonlinear features.Emphasis is also placed on the coupling between the temperature field（or the like） and other physical fields（e.g.,elastic,electric,and magnetic fields）.We further highlight the practical significance of 3D contact solutions,in particular in applications related to modern scanning probe microscopes.

关键词： Crack Contact Mixed boundary-value problem Transverse isotropy Multifield coupling Potential theory Exact solution Scanning probe microscope

Growing actin networks regulated by obstacle size and shape

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Acta Mechanica Sinica 2017年第2期33卷 222-233页

作者： Bo Gong Ji Lin Jin Qian Department of Engineering Mechanics Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province Zhejiang University Hangzhou 310027 China

Growing actin networks provide the driving force for the motility of cells and intracellular pathogens. Based on the molecular-level processes of actin polymerization, branching, capping, and depolymerization, we have developed a modeling framework to simulate the stochastic and cooperative behaviors of growing actin networks in propelling obstacles, with an emphasis on the size and shape effects on work capacity and filament orientation in the growing process. Our results show that the characteristic size of obstacles changes the protrusion power per unit length, without influencing the orientation distribution of actin filaments in growing networks. In contrast, the geometry of obstacles has a profound effect on filament patterning, which influences the orientation of filaments differently when the drag coefficient of environment is small, intermediate, or large. We also discuss the role of various parameters, such as the aspect ratio of obstacles, branching rate, and capping rate, in affecting the protrusion power of network growth.

关键词： Actin network Growth dynamics Monte Carlo simulation Size effect Shape effect

Several three-dimensional solutions for transversely isotropic functionally graded material plate welded with circular inclusion

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Applied Mathematics and Mechanics(English Edition) 2016年第6期37卷 683-694页

作者： Bo YANG Weiqiu CHEN Haojiang DING Department of Civil Engineering Zhejiang Sci-Tech University State Key Laboratory of CAD & CG Zhejiang University Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province Soft Matter Research CenterDepartment of Engineering MechanicsZhejiang UniversityYuquan Campus Department of Civil Engineering Zhejiang University

The problem of a transversely isotropic functionally graded material （FGM） plate welded with a circular inclusion is considered. The analysis starts with the general- ized England-Spencer plate theory for transversely isotropic FGM plates, which expresses a three-dimensional （3D） general solution in terms of four analytic functions. Several analytical solutions are then obtained for an infinite FGM plate welded with a circular inclusion and subjected to the loads at infinity. Three different cases are considered, i.e., a rigid circular inclusion fixed in the space, a rigid circular inclusion rotating about the x-, y-, and z-axes, and an elastic circular inclusion with different material constants from the plate itself. The static responses of the plate and/or the inclusion are investigated through numerical examples.

关键词： plate functionally graded material （FGM） welded circular inclusion,analytical solution