Design method for fluid viscous dampers

A basic design method of doubly acting fluid viscous dampers with double guide bars is presented. The flow of the viscoelastic fluid between two parallel plates, one of which is started suddenly and the other of which is still, is analyzed. According to this solution, the velocity and the shear stress of the fluid at the fringe of the piston are solved approximately. A mathematical model of viscous dampers is derived, and the shock test is carried out. From experimental results, the parameters of the mathematical model are determined. Consequently, a semi-empirical design equation is obtained. Applying this equation to a certain practical damper, the damping material is chosen and the physical dimensions of the damper are determined. Shock tests using this damper are performed. Theoretical results are in good agreement with experimental results, which validates the reliability of the calculated physical dimensions of the specimen damper and the validity of the basic design equation. An erratum to this article can be found at     

An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory

The peridynamic theory is advantageous for problems involving damage since the peridynamic equation of motion is valid everywhere, regardless of existing discontinuities, and an external criterion is not necessary for predicting damage initiation and propagation. However, the current solution methods for the equations of peridynamics utilize explicit time integration, which poses difficulties in simulations of most experiments under quasi-static conditions. Thus, there is a need to obtain steady-state solutions in order to validate peridynamic predictions against experimental measurements. This study presents an extension of dynamic relaxation methods for obtaining steady-state solutions of nonlinear peridynamic equations.     

Computing the structural buckling limit load by using dynamic relaxation method

The numerical structural analysis schemes are extensively developed by progress of modern computer processing power. One of these approximate approaches is called "dynamic relaxation (DR) method." This technique explicitly solves the simultaneous system of equations. For analyzing the static structures, the DR strategy transfers the governing equations to the dynamic space. By adding the fictitious damping and mass to the static equilibrium equations, the corresponding artificial dynamic system is achieved. The static equilibrium path is required in order to investigate the structural stability behavior. This path shows the relationship between the loads and the displacements. In this way, the critical points and buckling loads of the non-linear structures can be obtained. The corresponding load to the first limit point is known as buckling limit load. For estimating the buckling load, the variable load factor is used in the DR process. A new procedure for finding the load factor is presented by imposing the work increment of the external forces to zero. The proposed formula only requires the fictitious parameters of the DR scheme. To prove the efficiency and robustness of the suggested algorithm, various geometric non-linear analyses are performed. The obtained results demonstrate that the new method can successfully estimate the buckling limit load of structures.     

变质量、变阻尼、变刚度结构系统的动力响应

本文首次提出了变质量、变阻尼、变刚度结构系统的动力响应问题,并根据抓斗卸船机的工作过程导出了结构系统的动力方程及解法。最后给出了工程实际算例。     

A three-dimensional fictitious domain method for incompressible fluid flow problems

A new Galerkin finite element method for the solution of the Navier–Stokes equations in enclosures containing internal parts which may be moving is presented. Dubbed the virtual finite element method, it is based upon optimization techniques and belongs to the class of fictitious domain methods. Only one volumetric mesh representing the enclosure without its internal parts needs to be generated. These are rather discretized using control points on which kinematic constraints are enforced and introduced into the mathematical formulation by means of Lagrange multipliers. Consequently, the meshing of the computational domain is much easier than with classical finite element approaches. First, the methodology will be presented in detail. It will then be validated in the case of the two-dimensional Couette cylinder problem for which an analytical solution is available. Finally, the three-dimensional fluid flow inside a mechanically agitated vessel will be investigated. The accuracy of the numerical results will be assessed through a comparison with experimental data and results obtained with a standard finite element method. © 1997 John Wiley & Sons, Ltd.     

A fast and robust fictitious domain method for modelling viscous flows in complex mixers: The example of propellant make‐down

This work deals with the development of a fast three‐dimensional numerical strategy for the simulation of viscous fluid flow in complex mixing systems. The proposed method is based on a distributed Lagrange multiplier fictitious domain method and the use of the low‐cost MINI finite element. Contrary to the previous fictitious domain method developed by our group a few years ago, the underlying partial differential equations are solved here in a coupled manner using a consistent penalty technique. The method is discussed in detail and its precision is assessed by means of experimental data in the case of an agitated vessel. A comparison made with our existing fictitious domain method and its decoupled Uzawa‐based solver clearly shows the advantages of resorting to the MINI finite element and fully coupled solution strategy. The new technique is then applied to the simulation of the flow of a Newtonian viscous fluid in a three‐blade planetary mixer in the context of the production of solid propellants. Copyright © 2008 John Wiley & Sons, Ltd.     

Design and mechanical characteristics analysis of a new viscous damper for piping system

In this paper, the design of a new viscous damper is presented and its mechanical characteristics are investigated experimentally. The motion equation of a system consisting of a drop machine and the damper is set up. By numerically simulating this equation, the curve of the damper cavity generatrix is obtained on the assumption that the resisting force is constant. Then the new damper with big capacity and high-energy dissipation rate is designed. Drop tests using this damper and a Pro225-damper bought in the market are performed, respectively. On one hand, the experimental resisting forces of the new damper approximate constants, which illustrates that the simulation is viable. On the other hand, some advantages of the new damper over the Pro225-damper are found.     

On the damping function of shear relaxation modulus for entangled polymers

Published data of the damping function of the shear relaxation modulus, h(), are reviewed. This is the ratio of the relaxation modulus measured at a finite magnitude of shear, , to that at the limit of = 0. Majority of the data are in accord with the universal function of the Doi-Edwards tube model theory, in which the damping or the decrease of h() is attributed to the contraction along the tube of extended polymer chains. The weaker damping seems to be attributed to 1) comb-branching such as in LDPE; 2) lack of entanglement in too short chains; 3) bimodal molecular weight distribution. However, a star-branching does not cause a deviation from the tube model theory and a broadness of molecular weight distribution is not a major origin of a weaker damping. A star-branched polystyrene with 15 arms exhibits no strain dependence: h() = 1. For highly entangled systems with more than 50 entanglement points per molecule, the strain dependence is stronger than that of the Doi-Edwards theory. This could be due to a slip or an instability of deformation in the material.     

Penalty finite element method for nonlinear dynamic response of viscous fluid-saturated biphase porous media

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空腔内粘性流问题与哈密顿体系方法

以双板驱动空腔粘性流问题为研究对象,根据其特点建立了哈密顿体系下的对偶正则方程,将问题归结为辛体系下的本征值问题.利用辛本征解空间的完备性、正交性和展开理论,形成一套封闭的求解问题方法.算例的数值结果揭示了一些空腔流动的特点.同时这种方法也为研究其他问题提供了一条思路.     

Effects of anti-symmetric nonlinear viscous damping on the force transmissibility of multi-degree of freedom structures

In the present study, the concept of the output frequency response function is applied to theoretically investigate the force transmissibility of multi-degree of freedom (MDOF) structures with a nonlinear anti-symmetric viscous damping. The results reveal that an anti-symmetric nonlinear viscous damping can significantly reduce the transmissibility over all resonance regions for MDOF structures while it has almost no effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to overcome the dilemma in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant region but increases the transmissibility over non-resonant regions.     

Semi-analytical finite element method for fictitious crack model in fracture mechanics of concrete

Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to develop a novel analytical finite element for the fictitious crack model in fracture mechanics of concrete. The new analytical element can be implemented into FEM program systems to solve fictitious crack propagation problems for concrete cracked plates with arbitrary shapes and loads. Numerical results indicate that the method is more efficient and accurate than ordinary finite element method.     

动力松弛方法中Rayleigh阻尼参数取值分析

论文阐述了动力松弛法计算静力问题的原理,分析了Rayleigh阻尼对计算的影响,提出了一种对质量阻尼和刚度阻尼参数取值的新方法。这种取值方法可以避免计算结果的振荡和过塑性的问题,并利用实例计算进行了对比分析,验证了本文中Rayleigh阻尼取值的合理性。     

A robust online parametric identification method for non-deteriorating and deteriorating distributed element models with viscous damping

The online parametric identification of deteriorating and non-deteriorating distributed element models (DEMs) with viscous damping is studied using a generalization of Masing model to provide the proper framework for identification. The approach renders the hysteretic response of the DEM into a time-independent single-valued mapping from equivalent displacement values into equivalent force values, while considering the effect of damping as a parallel element. This approach allows for parametric identification of this non-linear rate-dependent hysteretic behavior to be performed using non-linear optimization techniques. A changing objective function, defined as a norm of force estimation error over a shifting window of recent data, is employed so that classic non-linear optimization techniques can be used for the online identification problem. A variation of the steepest descent method is used with significant modifications. Special measures are taken to guarantee robustness of the results in presence of noise. The results show that the proposed identification method exhibits a very good performance in identifying the correct values of the parameters in real time, and is robust in dealing with noise. The proposed method can be applied to many other types of hysteretic behavior as well.     

A promising boundary element formulation for three‐dimensional viscous flow

In this paper, a new set of boundary‐domain integral equations is derived from the continuity and momentum equations for three‐dimensional viscous flows. The primary variables involved in these integral equations are velocity, traction, and pressure. The final system of equations entering the iteration procedure only involves velocities and tractions as unknowns. In the use of the continuity equation, a complex‐variable technique is used to compute the divergence of velocity for internal points, while the traction‐recovery method is adopted for boundary points. Although the derived equations are valid for steady, unsteady, compressible, and incompressible problems, the numerical implementation is only focused on steady incompressible flows. Two commonly cited numerical examples and one practical pipe flow problem are presented to validate the derived equations. Copyright © 2004 John Wiley & Sons, Ltd.     

A lattice Boltzmann method for viscous free surface waves in two dimensions

We propose a new method based on the combination of the lattice Boltzmann equation (LBE) and the kinematic boundary condition (KBC) method to simulate viscous free surface wave in two dimensions. In our method, the flow field is modeled by LBE, whereas the free surface is explicitly tracked by the local height function, which is calculated by the KBC method. The free surface boundary condition (FSBC) for LBE is revised from previous researches. Interpolation‐supplemented lattice Boltzmann (ISLB) method is introduced, which enables our approach to be applied on arbitrary, nonuniform mesh grids. Five cases are simulated respectively to validate the LBE–KBC method: the stationary flow and the solitary waves simulated by the revised‐FSBC are more accurate than the one obtained by the former‐FSBC; numerical results of standing waves show that our method is compatible to the existing two‐dimensional finite‐volume scheme; cases of small amplitude Stokes wave and waves traveling over a submerged bar show good agreement on wave celerity, wavelength, wave amplitude and wave period between numerical results and corresponding analytical solutions and/or experiment data.Copyright © 2012 John Wiley & Sons, Ltd.     

A fictitious domain approach for the Stokes problem based on the extended finite element method

In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by extended finite element method and studied for the Poisson problem in a paper of Renard and Haslinger of 2009. The method allows computations in domains whose boundaries do not match. A mixed FEM is used for the fluid flow. The interface between the fluid and the structure is localized by a level‐set function. Dirichlet boundary conditions are taken into account using Lagrange multiplier. A stabilization term is introduced to improve the approximation of the normal trace of the Cauchy stress tensor at the interface and avoid the inf‐sup condition between the spaces for the velocity and the Lagrange multiplier. Convergence analysis is given, and several numerical tests are performed to illustrate the capabilities of the method. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical implementation of Aristov–Pukhnachev's formulation for axisymmetric viscous incompressible flows

In the present work a finite‐difference technique is developed for the implementation of a new method proposed by Aristov and Pukhnachev (Doklady Phys. 2004; 49 (2):112–115) for modeling of the axisymmetric viscous incompressible fluid flows. A new function is introduced that is related to the pressure and a system similar to the vorticity/stream function formulation is derived for the cross‐flow. This system is coupled to an equation for the azimuthal velocity component. The scheme and the algorithm treat the equations for the cross‐flow as an inextricably coupled system, which allows one to satisfy two conditions for the stream function with no condition on the auxiliary function. The issue of singularity of the matrix is tackled by adding a small parameter in the boundary conditions. The scheme is thoroughly validated on grids with different resolutions. The new numerical tool is applied to the Taylor flow between concentric rotating cylinders when the upper and lower lids are allowed to rotate independently from the inner cylinder, while the outer cylinder is held at rest. The phenomenology of this flow is adequately represented by the numerical model, including the hysteresis that takes place near certain specific values of the Reynolds number. Thus, the present results can be construed to demonstrate the viability of the new model. The success can be attributed to the adequate physical nature of the auxiliary function. The proposed technique can be used in the future for in‐depth investigations of the bifurcation phenomena in rotating flows. Copyright © 2009 John Wiley & Sons, Ltd.     

A multi-dimensional time-marching method of characteristics for viscous and heat-conducting flows

Summary A numerical scheme is presented which employs the characteristic surfaces in space-time for solving Navier-Stokes equations for compressible fluid flow. We consider the general case of a three-dimensional flow, a simplification of which yields the equations of the two-dimensional case. Emphasis is put on the method itself. We apply it to simulate a laminar hypersonic flow around a circular cylinder of a five-components gas mixture of nitrogen and oxygen with thermally perfect constituents and at chemical nonequilibrium. First, the partial differential equations are transformed into a standard form with directional derivatives, enabling to attain the compatibility conditions, including the viscosity terms. These conditions are discretized by approximating their integrals along the corresponding characteristic surfaces. The result is an explicit time-marching numerical scheme. Using a grid fitted between the shock and the cylinder, and starting from roughly estimated initial conditions, a steady solution is searched. A comparison is made with the solution obtained under the assumption of a perfect gas. Received 6 April 1999; accepted for publication 13 May 1999