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ACTA PHYSICA POLONICA A 2010年第1期118卷 17-22页

作者： Branski, A. Borkowski, M. Szela, S. WEil Rzeszow Univ Technol Acoust Lab PL-35959 Rzeszow Poland Univ Rzeszow Inst Technol PL-35959 Rzeszow Poland

The paper concerns an active vibration protection (p-reduction) of the structure. This problem corresponds to the active vibration reduction (a-reduction). The quantity and effectivness of the a-/p- reduction, measured with reduction and effectiveness coefficient respectively, depends on, inter alia, the PZT distribution on the structure subdomains with the largest curvatures (quasi optimal distribution) are considered. The aim of this paper is to determine such interacting forces PZT-structure, assuming QO distribution of PZTs, which maximize the effectiveness of p-reduction. The beam clamped at one end, vibrating separately with first three modes, is chosen as the research object. The interacting forces are searched requiring that the shear force and bending moment at the clamped side are equal to zero. The total p-reduction is achieved for separate modes. Assuming the QO distribution of the PZTs, the best, p-effectiveness is achieved. The validation of theoretical considerations is confirmed numerically.

关键词： ACTIVE noise & vibration control FREQUENCIES of oscillating systems EIGENFUNCTIONS boundary value problems -- numerical solutions MATHEMATICAL analysis CURVATURE SHEAR (Mechanics) BENDING (Metalwork) ACTUATORS

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A Simple and Accurate Ghost Cell Method for the Computation of Incompressible Flows Over Immersed Bodies with Heat Transfer

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numerical HEAT TRANSFER PART B-FUNDAMENTALS 2010年第1期58卷 17-39页

作者： Pan, Dartzi Natl Cheng Kung Univ Dept Aeronaut & Astronaut Tainan 70101 Taiwan

A simple, stable, and accurate ghost cell method is developed to solve the incompressible flows over immersed bodies with heat transfer. A two-point stencil is used to build the flow reconstruction models for both Dirichlet and Neumann boundary conditions on the immersed surface. Tests show that the current scheme is second-order-accurate in all error norms for both types of boundary condition, with the only exception that under Neumann condition the order of the maximum norm of temperature error is 1.44. Various forced- and natural-convection problems for cylinders immersed in open field or in a cavity are computed and compared with published data.

关键词： HEAT transfer FLUID dynamic measurements NEUMANN problem boundary value problems -- numerical solutions DIRICHLET problem

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Stress recovery procedure for solving boundary value problems in the mechanics of a deformable solid by the finite element method

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PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS 2010年第3期74卷 341-348页

作者： Rogovoi, A. A. Stolbova, O. S. [a] Perm Russia

A stress recovery procedure, based on the determination of the forces at the mesh points using a stiffness matrix obtained by the finite element method for the variational Lagrange equation, is described. The vectors of the forces reduced to the mesh points are constructed for the known stiffness matrices of the elements using the displacements at the mesh points found from the solution of the problem. On the other hand, these mesh point forces are determined in terms of the unknown forces distributed over the surface of an element and given shape functions. As a result, a system of Fredholm integral equations of the first kind is obtained, the solution of which gives these distributed forces. The stresses at the mesh points are determined for the values of these forces found on the surfaces of the finite element mesh (including at the mesh points) using the Cauchy relations, which relate the forces, stresses and the normal to the surface. The special features of the use of the stress recovery procedure are demonstrated for a plane problem in the linear theory of elasticity. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： STRAINS & stresses (Mechanics) boundary value problems -- numerical solutions DEFORMATIONS (Mechanics) FINITE element method FORCE & energy VARIATIONAL principles LAGRANGE equations INTEGRAL equations

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numerical Simulation of Ethanol-Water-NaCl Droplet Evaporation

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INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2010年第12期49卷 5631-5643页

作者： Jiang, Xingmao Ward, Timothy L. van Swol, Frank Brinker, C. Jeffrey Univ New Mexico Dept Chem & Nucl Engn Albuquerque NM 87106 USA Univ New Mexico Ctr Microengineered Mat Albuquerque NM 87106 USA Sandia Natl Labs Albuquerque NM 87185 USA

A quantitative description of droplet evaporation is important to aerosol research for nanofabrication, spray drying, fuel combustion, pollution control, and respiratory medical treatments. Evaporation is a moving-boundary problem with coupled mass and heat transport. An explicit finite-difference methodology and computer code has been developed for simulation of an evolving droplet, property data for size, and profiles for various compositions and temperature. The code accurately predicts the evaporation of pure water and pure ethanol droplets. To understand aerosol-assisted evaporation-induced self-assembly and the formation mechanism for single-crystal NaCl core/hexagonally ordered mesoporous silica shell particles, evaporation of ethanol-water-NaCl droplets in N-2 has been investigated by numerical simulation. The extended universal quasichemical (UNIQUAC) model with a Debye-Huckel term is used to describe the vapor liquid phase equilibrium. For 1-2-mu m-radius droplets with a number density of 10(7)similar to 10(8)/cm(3), it takes only tens of milliseconds to reach phase equilibrium after adiabatic or isothermal evaporation at 25 degrees C in the drying zone. The droplets entering a heating zone can be simply treated like a single-stage flash evaporation at 25 C. For a 1-mu um-radius droplet, after 0.18 ms of evaporation at 100 degrees C in N-2, the NaCl saturation ratio reaches levels as high as 1.3, first at the droplet center, where the initial NaCl nucleation and crystallization happens as a result of relatively quick evaporation and a steep gradient in the concentration of ethanol, an antisolvent for NaCl. NaCl crystallization "consumes" NaCl molecules near the droplet center and quenches the formation of new stable NaCl nuclei, favoring the formation of only one single-crystal NaCl core per droplet. The code provides guidance for the custom engineering of aerosol nanoparticle architectures.

关键词： ETHANOL SALT WATER EVAPORATION (Chemistry) SPRAY drying COMBUSTION boundary value problems -- numerical solutions COMPUTER simulation

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Identification of a moving boundary for a heat conduction problem in a multilayer medium

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HEAT AND MASS TRANSFER 2010年第7期46卷 779-789页

作者： Li, Y. S. Wei, T. Lanzhou Univ Sch Math & Stat Lanzhou 730000 Peoples R China

In this paper, we give a uniqueness theorem for the moving boundary of a heat problem in a composite medium. Through solving the Cauchy problem of heat equation in each subdomain, we finally find an approximation to the moving boundary for one-dimensional heat conduction problem in a multilayer medium. The numerical scheme is based on the use of the method of fundamental solutions and a discrete Tikhonov regularization technique with the generalized cross-validation choice rule for a regularization parameter. numerical experiments for five examples show that our proposed method is effective and stable.

关键词： HEAT conduction HEAT transfer boundary value problems -- numerical solutions CAUCHY problem -- numerical solutions HEAT equation -- numerical solutions TEMPERATURE measurements HARMONIC functions (Mathematics) APPROXIMATION theory

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Singular boundary characteristics of the Hamilton-Jacobi equation

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PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS 2010年第2期74卷 144-153页

作者： Melikyan, A. A. [a] Moscow Russia

Situations exist in boundary value problems for first order partial differential equations arising in physics (the Hamilton-Jacobi equation), optimal control theory (the Bellman equation) and the theory of differential games (the Isaacs equation) when the value of the required function is not given on a part of the boundary or not at all, or it is not the limit of the (generalized) solution of the problem. Nevertheless, such conditions are required for constructing the solution (by the method of characteristics, for example). It is shown that the required boundary values can be exposed as a specific continuation of the conditions that are known in the boundary submanifolds of the given part of the boundary. This extension of the conditions is accomplished using the characteristic curves starting in a known submanifold of the boundary and running along the boundary. The characteristics are a generalization of the classical characteristics associated with a partial differential equation. They are called singular characteristics, and the theory of these has been developed in a number of the author's papers. After obtaining these "natural" boundary conditions, the solution is constructed using the conventional method of integrating the equations of the classical characteristics. Conditions of the Dirichlet and Neumann type are considered. The technique is illustrated using a numerical example from the theory of differential games containing a number of parameters. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： boundary value problems -- numerical solutions HAMILTON-Jacobi equations -- numerical solutions PARTIAL differential equations -- numerical solutions SUBMANIFOLDS GENERALIZABILITY theory (Statistics) DIRICHLET problem

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On Coupled Klein-Gordon-Schrodinger Equations with Acoustic boundary Conditions

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boundary value problems 2010年第1期000卷 1-23页

作者： Ha, Tae Gab Park, Jong Yeoul Iowa State Univ Dept Math Ames IA 50011 USA Pusan Natl Univ Dept Math Pusan 609735 South Korea

We are concerned with the existence and energy decay of solution to the initial boundary value problem for the coupled Klein-Gordon-Schrodinger equations with acoustic boundary conditions.

关键词： KLEIN-Gordon equation SCHRODINGER equation boundary value problems -- numerical solutions INITIAL value problems -- numerical solutions DIFFERENTIAL equations -- numerical solutions MATHEMATICAL analysis MATHEMATICS

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Structure of Eigenvalues of Multi-Point boundary value problems

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ADVANCES IN DIFFERENCE EQUATIONS 2010年第1期2010卷 1-24页

作者： Gao, Jie Sun, Dongmei Zhang, Meirong Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China Weifang Univ Sch Math & Informat Sci Weifang 261061 Shandong Peoples R China Hainan Univ Coll Appl Sci & Technol Haikou 571101 Hainan Peoples R China

The structure of eigenvalues of -y '' + q(x)y = lambda y, y(0) = 0, and y(1) = Sigma(m)(k=1) a(k)y(eta), will be studied, where q is an element of L-1 ([0, 1], R), alpha = (alpha(k)) is an element of R-m, and 0 < eta(1) < ... < eta(m) < 1. Due to the nonsymmetry of the problem, this equation may admit complex eigenvalues. In this paper, a complete structure of all complex eigenvalues of this equation will be obtained. In particular, it is proved that this equation has always a sequence of real eigenvalues tending to +infinity. Moreover, there exists some constant A(q) > 0 depending on q, such that when alpha satisfies parallel to alpha parallel to <= A(q), all eigenvalues of this equation are necessarily real.

关键词： boundary value problems -- numerical solutions EIGENvalueS DIFFERENTIAL equations -- numerical solutions LINEAR operators DIRICHLET problem -- numerical solutions SEQUENCES (Mathematics) MATHEMATICAL proofs

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On Spectral Expansions of Piecewise Smooth Functions Depending on the Geodesic Distance

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DIFFERENTIAL EQUATIONS 2010年第6期46卷 827-839页

作者： Alimov, Sh. A. Moscow MV Lomonosov State Univ Tashkent Branch Tashkent Uzbekistan

We consider the expansion of a piecewise smooth function depending on the geodesic distance to some point in the eigenfunctions of the Beltrami-Laplace operator on an n-dimensional symmetric space of rank 1. We show that if the expansion converges at this point, then the function must have continuous derivatives up to and including the order (n - 3)/2.

关键词： EIGENFUNCTIONS boundary value problems -- numerical solutions DIFFERENTIAL equations -- numerical solutions INTEGRAL equations -- numerical solutions SPIN eigenfunctions

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Optimal resource allocation program in a two-sector economic model with a Cobb-Douglas production function

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DIFFERENTIAL EQUATIONS 2010年第12期46卷 1750-1766页

作者： Kiselev, Yu N. Orlov, M. V. Moscow MV Lomonosov State Univ Moscow Russia

We consider the resource allocation problem for a two-sector economic model with a two-factor Cobb-Douglas production function on a finite time horizon with a terminal functional. The problem is reduced to some canonical form by a scaling of the phase variables and time. We prove the optimality of the extremal solution constructed on the basis of the maximum principle. The solution of the boundary value problem of the maximum principle is constructed in closed form for three cases of location of the initial plant state.

关键词： RESOURCE allocation PRODUCTION functions (Economic theory) MAXIMUM principles (Mathematics) boundary value problems -- numerical solutions DIFFERENTIAL equations -- numerical solutions ECONOMIC aspects

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