Uniformly convergent numerical method for singularly perturbed convection-diffusion type problems with nonlocal boundary condition

In this article, we consider a class of singularly perturbed differential equations of convection-diffusion type with nonlocal boundary conditions. A uniformly convergent numerical method is constructed via nonstandard finite difference and numerical integration methods to solve the problem. The nonlocal boundary condition is treated using numerical integration techniques. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ϵ -uniformly convergent.     

Experimental and numerical studies of intestinal frictions for propulsive force optimisation of a vibro-impact capsule system

This paper studies the intestinal frictions acting on a millimetre-scale self-propelled capsule (26 mm in length and 11 mm in diameter) for small bowel endoscopy by considering different capsule–intestine contact conditions under a wide range of capsule’s progression speeds. According to the experimental results, intestinal frictions vary from 7 mN to 4.5 N providing us with a guidance for designing the propelling mechanism of the controllable capsule endoscope. Our calculations show that the proposed vibro-impact mechanism can perform as a force magnifier generating a much larger propulsive force on the capsule than its original driving force. Therefore, the self-propelled capsule is capable of moving in the small intestine under a wide range of friction variation.

     

Theory and application of numerical simulation method of capillary force enhanced oil production

A kind of second-order implicit upwind fractional step finite difference methods are presented for the numerical simulation of coupled systems for enhanced(chemical)oil production with capillary force in the porous media.Some techniques,e.g.,the calculus of variations,the energy analysis method,the commutativity of the products of difference operators,the decomposition of high-order difference operators,and the theory of a priori estimate,are introduced.An optimal order error estimate in the l~2 norm is derived.The method is successfully used in the numerical simulation of the enhanced oil production in actual oilfields.The simulation results are satisfactory and interesting.     

Displacement modal identification method of elastic system under operational condition

Modal identification of engineering structure in operation deals with the estimation of modal parameters from vibration data obtained in working conditions rather than laboratory conditions. After one structure destruction during a flight test, it was strongly required to carry out full-scale model testing to acquire the low-frequency vibration acceleration data of the investigated rocket (its structural dynamic properties could be represented by a beam). These vibration data were used to assess the modal properties of the modified structure. In this paper, a new modal identification method based on vibration displacement is suggested. The displacements of the measured points on the rocket are obtained by the integration of the low-frequency vibration accelerations during free flight test. In the method, the data are filtered through wavelet transform. For comparison, several methods are used to extract the modal frequencies of the investigated beam. In terms of the results of standard deviation of identified frequencies, it is believed that the generalized displacement-based modal identification method is more practicable in modal identification for similar problems.     

Direct numerical simulation of particulate flows with a fictitious domain method

Our works on the fictitious domain method for the direct numerical simulation of particulate flows are reviewed, and particularly our recent progresses in the simulations of the motion of particles in Poiseuille flow at moderately high Reynolds numbers are reported. The method is briefly described, and its capability to simulate the motion of spherical and non-spherical particles in Newtonian, non-Newtonian and non-isothermal fluids is demonstrated. In addition, the applications of the fictitious domain method reported in the literature are also reviewed, and some comments on the features of the fictitious domain method and the immersed boundary method are given.     

对图乘法的发展

将能量偏导数定理应用于力法中,探索了超静定结构力法计算的新思路．传统的力法是利用基本体系在基本未知力处的变形(连续)条件来建立力法方程的．为了克服传统力法中弯矩图乘时由于Mi和Mp图取自同一基本结构而产生的不便,利用卡氏第二定理,得到了力法的基本方程,证明了在力法中可以混合采用不同的基本结构来分别计算Mi和Mp,并分析了所得基本方程的物理意义．通过实例计算和比较,证明该方法完全正确,且大大简化了计算,使力法的实用性更进一步加强,有较大的使用价值．     

Application of a hybrid numerical method to the nonlinear dynamic analysis of a micro gas bearing system

This paper employs a hybrid numerical method combining the differential transformation method (DTM) and the finite difference method (FDM) to analyze the nonlinear dynamic behavior of a rigid rotor supported by a micro gas bearing system (MGBS). It is shown that the results obtained for the orbits of the rotor center are in good agreement with those obtained using the traditional FDM approach. Moreover, the hybrid method avoids the divergence problem suffered by the FDM scheme at low values of the rotor mass and computational time step. The results presented in this study summarize the changes which take place in the dynamic behavior of the MGBS as the rotor mass and bearing number are increased over the ranges 0.01–0.16 and 1.0–5.0, respectively, and therefore provide a useful insight into the nonlinear dynamics of the bearing system.     

An original numerical calculation method for impacting contact model of spur gear under lightly loaded condition

Meccanica - In this study, an impacting contact model of spur gear under lightly loaded condition is constructed by considering the pinion and the wheel as rigid body, in which the lubricant is...     

Characterization of force networks in a dense high-shear system

We detect strong force networks in a dense high-shear system and study their structure and stability in response to variations in the shearing rate. The presence of strong force networks, which usually have a heterogeneous structure, restricts particle movements and can impose non-local mechanisms of momentum transfer. We identify such networks in a dense high-shear system using a community detection algorithm. Moreover, we explain the association between the mechanisms of momentum transfer and the structure, population, strength, and stability of the force networks by tracking the spatial and temporal evolution of the detected networks. In addition, we show that the assumption of a monodisperse assembly of particles leads to an unrealistic enlargement of the force networks, underestimating both the rate of energy dissipation and the rate of mixing.     

GENERALIZED VARIATIONAL DATA ASSIMILATION METHOD AND NUMERICAL EXPERIMENT FOR NON-DIFFERENTIAL SYSTEM

The generalized variational data assimilation for non-differential dynamical systems is studied. There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in the traditional way. The weak form of the original system was introduced, and then the generalized adjoint model was derived. The generalized variational data assimilation methods were developed for non-differential low dimensional system and non-differential high dimensional system with global and local observations. Furthermore, ideas in inverse problems are introduced to 4DVAR ( Fourdimensional variational ) of non-differential partial differential system with local observations.     

A numerical method for fractional integral with applications

IntroductionThefractionalcalculushasalonghistoryandthereareamassofworkstodiscussthefractionalderivativesandfractionalintegralswitharbitrary (realorcomplex)order[1- 3 ].Thefractionalcalculushasawideapplicationbackground ,especiallyinthefieldsofchemistry ,electromagnetics,materialscienceandmechanics.Forexample,Gement[4 ]proposedthefractionalderivativeconstitutivemodelsofaviscoelasticmaterialatfirst.Themodelshavereceivedincreasingattention[5 - 7].Onlyafewparametersarecontainedinthemodelsandthemo…     

Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method

The stochastic response of a noisy system with non-negative real-power restoring force is investigated. The generalized cell mapping (GCM) method is used to compute the transient and stationary probability density functions (PDFs). Combined with the global properties of the noise-free system, the evolutionary process of the transient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.     

Computational and numerical analysis of a nonlinear mechanical system with bounded delay

Modern structures are increasingly resistant and complex. In many cases, such systems are modeled by numerical approximations methods, due to its complexities. In the study of vibration levels in the response of a system is important to consider issues like reliability and efficient design, since that such vibrations are undesirable phenomena that may cause damage, failure, and sometimes destruction of machines and structures. In this paper we investigated a modeling strategy of nonlinear system with damping, subject the time delayed. From models widely used in literature and with the help of numerical simulations a nonlinear damped system with two degree-of-freedom is analyzed. The system is constituted of a primary mass attached to the ground by a spring and damping with linear or nonlinear characteristics (primary system), and the secondary mass attached to the primary system by a spring and damping with linear or nonlinear characteristics (secondary system). It is well known that time delayed systems, due to its own nature, has singular behavior in its dynamics and that such singularities propagate over the time. Based on this, the main concerns of the present paper is to analyze the stability of a delayed system with two degree of freedom by means of the techniques development in [1] (Hu andWang, 2002). We also obtain the solution using the integration of equations of motions performing a Fourth Order Runge-Kutta Method. The behavior of a nonlinear main system with nonlinear secondary system will be investigated to many cases of resonances. In this case, various time delayed values are used to confirm its influence on the attenuation of vibrations, but, unfortunately, also the increase of nonlinearity (instable responses) of the system in question is observed.     

Aerodynamic force measurement using 3-component accelerometer force balance system in a hypersonic shock tunnel

A new three-component accelerometer force balance has been designed, calibrated and tested in hypersonic shock tunnel (HST2) of Indian Institute of Science. The newly designed balance is able to measure aerodynamic forces (within test time of one millisecond) on test models at angles of attack from 0 to 12°. Two models, a blunt cone with after body and a blunt cone with after body and frustum are used to establish the accuracy of the force balance. The tests were conducted for the above two configurations with a constant Mach number of 8 and total enthalpy of 2.0 MJ/kg. The effectiveness of the balance is demonstrated by comparing the forces and moments of measured data with AGARD models. The flow fields around the test model are simulated using a 3D axisymmetric Navier–Stokes solver and the simulated results were compared with the measured values. Measured and computed force data are matched within ±10% for two different models tested here. The accuracy of the force balance is also estimated with the Newtonian theory and the values are approximately ±10% for the axial component and ±8% for the normal and pitching moment components.      

A numerical method for rapid estimation of drawbead restraining force based on non-linear,anisotropic constitutive equations

Numerical procedures to predict drawbead restraining forces (DBRF) were developed based on the semi-analytical (non-finite-element) hybrid membrane/bending method. The section forces were derived by equating the work to pull sheet material through the drawbead to the work required to bend and unbend the sheet along with frictional forces on drawbead radii. As a semi-analytical method, the new approach was especially useful to analyze the effects of various constitutive parameters with less computational cost. The present model could accommodate general non-quadratic anisotropic yield function and non-linear anisotropic hardening under the plane strain condition. Several numerical sensitivity analyses for examining the effects of process parameters and material properties including the Bauschinger effect and the shape of yield surface on DBRF were presented. Finally, the DBRFs of SPCC steel sheet passing a single circular drawbead were predicted and compared with the measurements.