Numerical simulation of a solitary wave interaction with submerged multi-bodies

The problems of a solitary wave passing over rectangular cylinders have been analysed. The numerical simulation is based on the full nonlinear two-dimensional Navier-Stokes equations which are solved by the finite difference method. The free surface is dealt with by the Volume of Fluid method (VOF). Results for a solitary wave passing over a single cylinder are compared with the experimental data of Seabra-Santos, Penouard and Temperville^[2] and better agreement is obtained than those obtained from the long wave equation based on the potential flow theory. Results are also given for two cylinders with different gaps. The project supported by the National Natural Science Foundation of China and the Development Foundation of Science and Technology of Shanghai Education Committee and the Royal Society.     

A combined vortex and panel method for numerical simulations of viscous flows: a comparative study of a vortex particle method and a finite volume method

This paper describes and compares two vorticity‐based integral approaches for the solution of the incompressible Navier–Stokes equations. Either a Lagrangian vortex particle method or an Eulerian finite volume scheme is implemented to solve the vorticity transport equation with a vorticity boundary condition. The Biot–Savart integral is used to compute the velocity field from a vorticity distribution over a fluid domain. The vorticity boundary condition is improved by the use of an iteration scheme connected with the well‐established panel method. In the early stages of development of flows around an impulsively started circular cylinder, and past an impulsively started foil with varying angles of attack, the computational results obtained by the Lagrangian vortex method are compared with those obtained by the Eulerian finite volume method. The comparison is performed separately for the pressure fields as well. The results obtained by the two methods are in good agreement, and give a better understanding of the vorticity‐based methods. Copyright © 2005 John Wiley & Sons, Ltd.     

Analysis of Natural Convection During Solidification of a Pure Metal

A numerical study of solidification of gallium in a closed cavity is presented and the influence of natural convection on phase change is investigated.

The mathematical formulation is based on the enthalpy-porosity method, while the equations are discretized on a fixed grid by means of a finite volume technique. Advancing in time is obtained using the SIMPLE algorithm, while the solution of the elliptic equation for pressure correction is obtained by means of a preconditioned BI-CGStab method.

As a test case a square cavity with Ra ranging from 4.68 × 10³ to 9.36 × 10⁵ is adopted. Results will be presented in terms of streamlines, isotherms, solid-liquid interface position and Nu and compared, when possible with available data.     

Mixed boundary value problem of elasticity for a quarter space

We consider the static elasticity problem for a quarter space with zero displacements on one of its surfaces and with given stresses on the other. The method for solving this problem is based on the use of newunknown functions in the formof a linear combination of the desired displacements, which reduces the system of three Lamé equations to two equations to be solved simultaneously and one equation to be solved separately. The exact solution of this problem was obtained earlier by the same method [1]. But it was shown in [2] that such a solution is exact only under certain restrictions on the given functions. In the present paper, the solution of this problem is constructed without restrictions on the given functions, which necessitates solving a one-dimensional integro-differential equation; this can be done approximately by the orthogonal polynomial method. We present numerical results obtained on the basis of our solution.     

Characterization of the Damping Behavior of a Nanoindentation Instrument for Carrying Out Dynamic Experiments

A new displacement modulation based dynamic indentation method is demonstrated and shown to be effective for viscoelastic characterization of a glassy polymer. The analysis of dynamic experiments requires a complete understanding of the measuring system’s dynamic characteristics especially the damping. Accordingly, an improved method, based on the use of a wire spring, is developed for determining the damping characteristics. In general, damping in an indentation instrument is contributed by two elements: the eddy current damping from the electromagnetic loading coil and the squeeze film damping from the capacitive displacement transducer. Therefore, a method to determine the relative contribution from the different damping elements present in the system is demonstrated and the results are compared with the calibration obtained from the wire spring method. Finally, dynamic indentation tests are carried out on a glassy polymer to obtain the complex modulus; the values of which are compared with those obtained from bulk dynamic mechanical analysis (DMA) tests. Storage modulus values are found to be in good agreement with bulk data but some divergence in the case of loss modulus is observed. The calibration procedure of the measuring instrument is critically examined in view of these observations. Overall, displacement modulation based dynamic indentation is shown to be a promising method for viscoelastic characterization at the micron length scales. An erratum to this article can be found at     

Slow rotation of a sphere in a confined volume of a dilute gas

The axially symmetric motion of a gas in a volume confined between an external immobile surface of rotation and a coaxial surface of a rotating sphere is considered. A solution is obtained by the moment method based on the Boltzmann equation with a collision integral of Maxwellian molecules. The gas-velocity distribution and an expression for the friction torque exerted on the sphere are obtained for arbitrary Knudsen numbers and for an arbitrary shape of the outer surface. The proportionality of the gas slip velocity over the surface of the sphere to the friction strain is shown. The friction torque is investigated for specific shapes of the outer surface. The motion of a gas filling the space between concentric spheres, each of which rotates about an arbitrary axis, is treated. In the limiting case of small Knudsen numbers the expressions obtained are compared with the corresponding results for a continuous medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 117–124, July–August, 1978.The authors are grateful to the participants of the seminars guided by G. I. Petrov and A. M. Golovnyi for discussions concerning this work.     

A Pressure Field in an Acoustic Medium Containing a Cylindrical Solid and a Sphere Oscillating in a Predetermined Manner

A problem on the interaction of a spherical body oscillating in a predetermined fashion and a rigid cylinder is formulated. The bodies do not intersect, are immersed into an ideal compressible liquid, and their centers are in one plane. The solution is based on the possibility of representing the partial solution of the Helmholtz equation, written in cylindrical coordinates, in terms of partial solutions in spherical coordinates, and vice versa. An infinite system of linear algebraic equations is obtained by satisfying the boundary conditions on the sphere and cylinder surfaces. The system is intended for determining the coefficients of the expansion of the velocity potential into a series in terms of spherical and trigonometric functions. The system obtained is solved by the reduction method. The appropriateness of this method is substantiated. The hydrodynamic characteristics of the liquid surrounding the spherical and cylindrical bodies are determined. A comparison is made with the problem on a sphere oscillating in an infinite incompressible liquid that contains also a cylinder and in a compressible liquid that contains nothing more. Two types of motion of the sphere — pulsation and oscillation — are considered     

Studying the free vibrations of multilayer plates with a complex planform

An efficient method is developed to solve the free-vibration problems for arbitrarily shaped orthotropic multilayer plates in a refined formulation. The method is based on the R-function and Ritz methods. Sequences of coordinate functions satisfying kinematic boundary conditions are constructed in an analytic form. The method is used to solve the vibration problem for multilayer square and arbitrarily shaped plates. The results obtained for square plates are analyzed. A comparison of these results with those available in the literature demonstrates the efficiency of the method __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 119–125, January 2006.     

Nonlinear vibration analysis of viscoelastic plates based on a refined Timoshenko theory

Nonlinear vibrations of viscoelastic orthotropic and isotropic shells are mathematically modeled using a geometrically nonlinear Timoshenko theory. Nonlinear problems are solved by using the Bubnov-Galerkin method and a numerical method based on quadrature formulas. Results obtained from different theories are compared and analyzed. For each problem, the Bubnov-Galerkin method is tested for convergence. The influence of the viscoelasticity and inhomogeneity of materials on the vibrations of plates is demonstrated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 120–131, May 2006.     

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.     

On the torsion of a cylinder with several cracks

In this paper, based on paper [1], the analytic expression of the torsion function for a cylinder containing arbitrary oriented cracks is obtained. The problem is reduced to solve a system of singular integral equations for the unknown dislocation density functions. Using the numerical method of the singular integral equations^[2,7] the torsional rigidities and stress intensity factors are evaluated for several multicracked cylinders. Next, the creak-cutting method^[5] is firstly extended to lve the torsion problem for a rectangular prism. The numerical results show that the method presented here is successful. Projects Supported by the Science Fund of the Chinese Academy of Sciences.     

Small vibrations of a sphere in a spherical volume of viscous fluid

Problems of the vibration of bodies in confined viscous fluids have been solved to determine the added masses and damping coefficients of rods [1–3] and floats [4–5]. The solutions of these problems, based on the use of simplifications of the boundary-layer method [4–6], are obtained analytically in general form and are in good agreement with the experimental data. However, in each specific case the possibility of using such solutions for given values of the fluid viscosity and vibration frequency must be justified either experimentally [2, 4, 5] or theoretically as, for example, in [1], where an analytic solution was obtained for concentric cylinders. The present paper offers a general solution of the problem of the small vibrations of a sphere in a spherical volume of fluid valid over a broad range of variation of the dimensionless kinematic viscosity. The limiting cases of this solution for both high and low viscosity are considered. The asymptotic expressions obtained are compared with calculations based on the analytic solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 29–34, March–April, 1986.     

Time-dependent motion of a two-dimensional floating elastic plate

Three methods are presented to determine the motion of a two-dimensional finite elastic plate floating on the water surface, which is released from rest and allowed to evolve freely. The first method is based on a generalized eigenfunction expansion and it is valid for all water depths. The second method is based on an integral equation derived from the Fourier transform, and it is valid for all water depths, although computations are made only for water of infinite depth. These two methods are both based on the frequency-domain solution—however no obvious connection exists between the two methods. The third method is valid only for shallow water, and it expresses the solution as the sum over decaying modes. We present a new derivation of the integral equation for a floating plate based on the Fourier transform of the equations of motion in the time domain. The solution obtained by each method is compared in the appropriate regime, and excellent agreement is found, thereby providing benchmark solutions. We also investigate the regime of validity of the infinite and shallow-depth solutions, and show that both give good results for a quite wide range of depths.     

Nonlinear and chaotic analysis of a financial complex system

In this paper,determination of the characteristics of futures market in China is presented by the method of the phase-randomized surrogate data.There is a significant difference in the obtained critical values when this method is used for random timeseries and for nonlinear chaotic timeseries.The singular value decomposition is used to reduce noise in the chaotic timeseries.The phase space of chaotic timeseries is decomposed into range space and null noise space.The original chaotic timeseries in range space is restructured.The method of strong disturbance based on the improved general constrained randomized method is further adopted to re-deternination.With the calculated results,an analysis on the trend of futures market of commodity is made in this paper.The results indicate that China＇s futures market of commodity is a complicated nonlinear system with obvious nonlinear chaotic characteristic.     

Modeling of a magnetorheological damper by recursive lazy learning

Nowadays dampers based on magnetorheological (MR) fluids are receiving significant attention specially for control of structural vibration and automotive suspensions systems. In most cases, it is necessary to develop an appropriate control strategy which is practically implementable when a suitable model for MR dampers is available. It is not a trivial task to model the dynamic of MR dampers because of their inherent non-linear and hysteretic dynamics. In this paper, a recursive lazy learning method based on neural networks is considered to model the MR damper behavior. The proposed method is validated by comparison with experimental obtained responses. Results show the estimated model correlates very well with the data obtained experimentally. The method proposed learns quickly that it is only necessarily a learning cycle, it can learn on-line and it is easy to select the network structure and calculate the model parameters.     

Geometric nonlinear formulation and discretization method for a rectangular plate undergoing large overall motions

In the present paper, the geometric nonlinear formulation is developed for dynamic stiffening of a rectangular plate undergoing large overall motions. The dynamic equations, which take into account the stiffening terms, are derived based on the virtual power principle. Finite element method is employed for discretization of the plate. The simulation results of a rotating rectangular plate obtained by using such geometric nonlinear formulation are compared with those obtained by the conventional linear method without consideration of the stiffening effects. The application limit of the conventional linear method is clarified according to the frequency error. Furthermore, the accuracy of the assumed mode method is investigated by comparison of the results obtained by using the present finite element method and those obtained by using the assumed mode method.     

Thermal instability in a rotating anisotropic porous layer saturated by a viscoelastic fluid

Linear and non-linear thermal instability in a rotating anisotropic porous medium, saturated with viscoelastic fluid, has been investigated for free-free surfaces. The linear theory is being related to the normal mode method and non-linear analysis is based on minimal representation of the truncated Fourier series analysis containing only two terms. The extended Darcy model, which includes the time derivative and Coriolis terms has been employed in the momentum equation. The criteria for both stationary and oscillatory convection is derived analytically. The rotation inhibits the onset of convection in both stationary and oscillatory modes. A weak non-linear theory based on the truncated representation of Fourier series method is used to find the thermal Nusselt number. The transient behaviour of the Nusselt number is also investigated by solving the finite amplitude equations using a numerical method. The results obtained during the analysis have been presented graphically.     

Spectral element method for viscoelastic flows in a planar contraction channel

A new algorithm, which combines the spectral element method with elastic viscous splitting stress (EVSS) method, has been developed for viscoelastic fluid flows in a planar contraction channel. The system of spectral element approximations to the velocity, pressure, extra stress and the rate of deformation variables is solved by a preconditioned conjugate gradient method based on the Uzawa iteration procedure. The numerical approach is implemented on a planar four‐to‐one contraction channel for a fluid governed by an Oldroyd‐B constitutive equation. The behaviour of the Oldroyd‐B fluids in the contraction channel is investigated with various Weissenberg numbers. It is shown that numerical solutions obtained here agree well with experimental measurements and other numerical predictions. Copyright © 2003 John Wiley & Sons, Ltd.     

Vibration analysis of a circular disk tensioned by rolling using finite element method

Summary The paper proposes a method in finite element analysis for estimating natural frequencies of a disk tensioned by rolling, without the use of eigenvalue analysis. The natural frequencies of a disk vary when the localized plastic deformation caused by roll-tensioning induces residual stresses. Tensioning is used for improving the dynamic stability of circular saws; the optimal condition of rolling can be predicted from natural frequency characteristics. In the proposed method, the natural frequencies after rolling are easily estimated from the mode shapes of the disk before rolling and the stress distribution after rolling. The method is based on ideas similar to thermal stress and sensitivity analysis rather than on eigenvalue analysis. The effectiveness of the method is shown by comparing the natural frequency characteristics obtained by this method with those by eigenvalue analysis. Received 18 June 1998; accepted for publication 8 April 1999     

Drop evaporation in a turbulent gas jet

Evaporation of a semidispersive drop system in a turbulent gas jet is considered. A method for calculating drop evaporation in a turbulent gas jet is proposed based on a simplified solution of the scattering problem for an evaporating admixture. Evaporation of water as it is atomized in a turbulent air jet is experimentally studied. Approximate agreement is obtained between the results of the calculations and experiments.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 73–79, January–February 1976.