Pumping of a fluid through a microchannel by means of a bubble driven by a light beam

A new method of pumping a fluid through a microchannel device using a gas bubble-piston, set in motion by the thermocapillary force induced by a light beam, is proposed. To demonstrate the method, a model micropump has been assembled. The model consists of two reservoirs connected by two channels with a bubble-piston driven by a light beam. The pumping rate and the volume per piston stroke are evaluated experimentally. The method proposed is compared with known microfluid pumping methods. Some advantages of the new method are indicated.     

Eigensolutions to a vibroacoustic interior coupled problem with a perturbation method

In this paper, an efficient and robust numerical method is proposed to solve non-symmetric eigenvalue problems resulting from the spatial discretization with the finite element method of a vibroacoustic interior problem. The proposed method relies on a perturbation method. Finding the eigenvalues consists in determining zero values of a scalar that depends on angular frequency. Numerical tests show that the proposed method is not sensitive to poorly conditioned matrices resulting from the displacement–pressure formulation. Moreover, the computational times required with this method are lower than those needed with a classical technique such as, for example, the Arnoldi method.     

Interaction of a deformable patch with a stressed strip

We consider the plane problem on the contact interaction of an elastic patch with an elastic strip loaded at infinity by a tensile force parallel to the strip boundaries. We assume that the patch resists extension and does not resist bending. We determine the contact tangential stresses under the patch, the patch point displacements, and the strip strain distortion factor. The problem is solved by the regular asymptotic method of “large λ” and the method of special orthonormal polynomials.In plane problems, the method of “large λ” was first used in [1], and the method of special orthonormal polynomials was first used in [2].     

Stress intensity factors of a rectangular crack meeting a bimaterial interface

Using the hypersingular integral equation method based on body force method, a planar crack meeting the interface in a three-dimensional dissimilar materials is analyzed. The singularity of the singular stress field around the crack front terminating at the interface is analyzed by the main-part analytical method of hypersingular integral equations. Then, the numerical method of the hypersingular integral equation for a rectangular crack subjected to normal load is proposed by the body force method, which the crack opening dislocation is approximated by the product of basic density functions and polynomials. Numerical solutions of the stress intensity factors of some examples are given.     

Contact Interaction Between a Laminated Shell of Revolution and a Rigid or Elastic Foundation

A method is proposed to solve the contact problem for laminated anisotropic shells of revolution. The method is based on a two-dimensional model that accounts for transverse shears and reduction. Also the method is based on the method of successive approximations, the generalized pseudo-force method, and a numerical-analytical method of solving boundary-value problems. The results obtained for a cylindrical shell of complex thickness structure are compared with those obtained in three-dimensional formulation__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 5, pp. 68–75, May 2005.     

Dynamics of a small bubble in a compressible fluid

An efficient (simplified) method for solving problems of spherically symmetric dynamics of a small gas bubble in a compressible fluid is proposed. The method is based on the joint use of the full problem statement (the gas dynamics equations for the gas and the fluid) and its relevant simplifications. Some approximate statements are discussed. In the proposed method, the rarefaction and compression of the gas during the slow motion of the bubble surface is assumed to be uniform over the bubble volume. At the same time the fluid in the thin zone adjacent to the bubble is considered to be slightly compressible. Otherwise the gas dynamics equations are used for the gas and the fluid. The dynamics of the fluid in the thick external zone are described by the linear acoustics only. The proposed simplified method and two others used in literature are estimated by comparison of their numerical results with those obtained in full statement. Copyright © 2000 John Wiley & Sons, Ltd.     

Dynamic response to a moving load of a Timoshenko beam resting on a nonlinear viscoelastic foundation

The present paper investigates the dynamic response of finite Timoshenko beams resting on a sixparameter foundation subjected to a moving load. It is for the first time that the Galerkin method and its convergence are studied for the response of a Timoshenko beam supported by a nonlinear foundation. The nonlinear Pasternak foundation is assumed to be cubic. Therefore, the efects of the shear deformable beams and the shear deformation of foundations are considered at the same time. The Galerkin method is utilized for discretizing the nonlinear partial differential governing equations of the forced vibration. The dynamic responses of Timoshenko beams are determined via the fourth-order Runge–Kutta method. Moreover, the efects of diferent truncation terms on the dynamic responses of a Timoshenko beam resting on a complex foundation are discussed. The numerical investigations shows that the dynamic response of Timoshenko beams supported by elastic foundations needs super high-order modes. Furthermore, the system parameters are compared to determine the dependence of the convergences of the Galerkin method.     

Interaction of a solitary wave and a front step simulated by level set method

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Design of a Structure Composed of a Plate Strengthened by Equidistant Stiffeners

ABSTRACT

An alternative method to the orthotropic plate analogy for analysis of plates strengthened by longitudinal equidistant stiffeners is introduced and is shown to give accurate results, compared with the finite element method. The alternative method uses the concept of undetermined multipliers. Its capabilities in the study of plates strengthened by stiffeners is demonstrated, and design criteria are obtained.     

Comparative study of forced convection of a power-law fluid in a channel with a built-in square cylinder

A detailed comparison between the lattice Boltzmann method and the finite element method is presented for an incompressible steady laminar flow and heat transfer of a power-law fluid past a square cylinder between two parallel plates. Computations are performed for three different blockage ratios (ratios of the square side length to the channel width) and different values of the power-law index n covering both pseudo-plastic fluids (n < 1) and dilatant fluids (n > 1). The methodology is validated against the exact solution. The local and averaged Nusselt numbers are also presented. The results show that the relatively simple lattice Boltzmann method is a good alternative to the finite element method for analyzing non-Newtonian fluids.     

Numerical simulation of solitary waves overtopping on a sloping sea dike using a particle method

Sea dikes, as a commonly used type of coastal protection structures, are often attacked or damaged by violent waves overtopping under tsunamis and storm surges. In this study, the behavior of solitary waves traveling on a sloping sea dike is simulated, and solitary wave overtopping characteristics are analyzed using a complete Lagrangian numerical method, the moving particle semi-implicit (MPS) method. To better describe the complicated fluid motions during the wave overtopping process, the original MPS method is modified by introducing a new free surface detection method, i.e., the area filling rate identification method, and a modified gradient operator to provide higher precision. Meanwhile, the approximation method for sloping boundaries in particle methods is enhanced, and a smooth slope approximation method is proposed and recommended. To verify the improved MPS method, a solitary wave traveling over a steep sloping bed is studied. The entire solitary wave run-up and run-down processes and exquisite water movements are reproduced well by the present method, and are consistent with the corresponding experimental results. Subsequently, the improved MPS method is applied to investigate the overtopping process of a single solitary wave over a sloping sea dike. The results show that the hydraulic jump phenomenon is also possible to occur during the run-down motion of the solitary wave overtopping. Finally, the characteristics of the propagation and overtopping of two successive solitary waves on a sloping sea dike are discussed. The result manifests that the interaction between adjacent solitary waves affects wave overtopping patterns and overtopping velocities.     

Synthesis of a controller for stabilizing the motion of a rigid body about a fixed point

A method for the approximate design of an optimal controller for stabilizing the motion of a rigid body about a fixed point is considered. It is assumed that rigid body motion is nearly the motion in the classical Lagrange case. The method is based on the common use of the Bellman dynamic programming principle and the averagingmethod. The latter is used to solve theHamilton–Jacobi–Bellman equation approximately, which permits synthesizing the controller. The proposed method for controller design can be used in many problems close to the problem of motion of the Lagrange top (the motion of a rigid body in the atmosphere, the motion of a rigid body fastened to a cable in deployment of the orbital cable system, etc.).     

Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack

Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and its numerical results coincide with those in references. Thus the method proposed here is verified. The project supported by National Natural Science Foundation of China     

Application of a hybrid numerical method to the bifurcation analysis of a rigid rotor supported by a spherical gas journal bearing system

The nonlinear dynamic behavior of a rigid rotor supported by a spherical gas journal bearing system is analyzed using a hybrid method combining the differential transformation method (DTM) and the finite difference method (FDM). The analytical results reveal that the bearing system has a complex dynamic behavior comprising periodic, subharmonic, and quasi-periodic responses of the rotor center. The evolution in the dynamic behavior of the bearing system is systematically examined as the rotor mass and bearing number are increased. The analytical results are found to be in good agreement with those of other numerical methods. Hence, the validity of the proposed hybrid method as a means of gaining insights into the nonlinear dynamics of spherical gas film rotor-bearing systems is confirmed.     

Surface friction in a turbulent boundary layer with a positive pressure gradient

A dependence of the relative friction coefficient on the form parameter of the aerodynamic curvature is proposed on the basis of measurements of the tangential stress on the wall during the flow of a liquid in a diffusor using the electrodiffusion method. The intensity of fluctuations of the tangential stress at the wall and the instant of appearance of reverse flows are investigated. The results of measurement of the friction coefficient by the electrodiffusion method and Clauser method are compared.     

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

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.     

On the trajectories of a mass point on a rotating surface

N. E. Zhukovskii proposed a special method [1] for determining the trajectories of amass point (particle) on a plane in the field of potential forces. In [2], this method was generalized to the case of particle motions on curvilinear surfaces. In the present paper, this method is generalized to the case in which the surface, together with the field of potential forces, rotates about a fixed axis. Several examples are considered.     

Simulation of flow around a thin,flexible obstruction by means of a deforming grid overlapping a fixed grid

This paper presents a numerical method for simulation of coupled flows, in which the fluid interacts with a thin deformable solid, such as flows in cardiovascular valves. The proposed method employs an arbitrary Lagrangian–Eulerian (ALE) method for flow near the solid, embodied in the outflow domain in which the mesh is fixed. The method was tested by modelling a two‐dimensional channel flow with a neo‐Hookean obstacle, an idealization of the coupled flow near a cardiovascular valve. The effects of the Reynolds number and the dimensionless elastic modulus of the material on the wall shear stress, the size of the downstream reverse flows, and the velocity and pressure profiles were investigated. The deformation of the obstacle, the pressure drop across the obstacle, and the size of the top reverse flow increased as the Reynolds number increased. Conversely, increasing the elastic modulus of the obstacle decreased the deformation of the obstacle and the size of the top reverse flows, but did not affect the pressure drop across the obstacle over the range studied. Copyright © 2007 John Wiley & Sons, Ltd.     

On a formulation for a multiscale atomistic-continuum homogenization method

The homogenization method is used as a framework for developing a multiscale system of equations involving atoms at zero temperature at the small scale and continuum mechanics at the very large scale. The Tersoff–Brenner Type II potential [Physical Review Letters 61(25) (1988) 2879; Physical Review B 42 (15) (1990) 9458] is employed to model the atomic interactions while hyperelasticity governs the continuum. A quasistatic assumption is used together with the Cauchy–Born approximation to enforce the gross deformation of the continuum on the positions of the atoms. The two-scale homogenization method establishes coupled self-consistent variational equations in which the information at the atomistic scale, formulated in terms of the Lagrangian stiffness tensor, concurrently feeds the material information to the continuum equations. Analytical results for a one dimensional molecular wire and numerical experiments for a two dimensional graphene sheet demonstrate the method and its applicability.     

Stokes flow over a cavity on a superhydrophobic surface containing a gas bubble

Within the approximation of Stokes hydrodynamics, several problems of a steady-state flow over a two-dimensional cavity containing a gas bubble are solved using the method of boundary integral equations. In contrast to previous publications, the method developed makes it possible to study the situation in which the cavity is only partially filled with gas, and the edges of a curved phase interface do not coincide with the cavity corners. Using periodic boundary conditions for the velocity, the flows with pure-shear and parabolic velocity profiles, and also the flow over a group of cavities were considered. The aim of the study was to calculate the effective (average) slip velocity over a microcavity, as applied to flows near textured superhydrophobic surfaces. A parametric numerical study of the effective velocity slip as a function of the radius of curvature of the interface and the position of the interface relative to the cavity boundaries was performed. The accuracy of the method is validated by the calculations of a number of limiting flows over a cavity, for which a quantitative agreement with the results known in the literature is demonstrated.