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Applied in Theoretical Mechanics

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Print ISSN: 1991-8747
E-ISSN: 2224-3429

Volume 8, 2013

Issue 1, Volume 8, January 2013

Title of the Paper: Thermochemical Non-Equilibrium Reentry Flows in Three-Dimensions – Part I – Structured Solutions

Authors: Edisson Sávio De Góes Maciel, Amilcar Porto Pimenta

Abstract: This work presents a numerical tool implemented to simulate inviscid and viscous flows employing the reactive gas formulation of thermal and chemical non-equilibrium. The Euler and Navier-Stokes equations, employing a finite volume formulation, on the context of structured and unstructured spatial discretizations, are solved. These variants allow an effective comparison between the two types of spatial discretization aiming verify their potentialities: solution quality, convergence speed, computational cost, etc. The aerospace problem involving the hypersonic “hot gas” flow around a blunt body, in three-dimensions, is simulated. The reactive simulations will involve an air chemical model of five species: N, O, N2, O2 and NO. Seventeen chemical reactions, involving dissociation and recombination, will be simulated by the proposed model. The Arrhenius formula will be employed to determine the reaction rates and the law of mass action will be used to determine the source terms of each gas species equation. In this first part, only the structured solutions are presented. The unstructured solutions are shown in the second part of this study.

Keywords: Thermochemical non-equilibrium, Reentry flow, Five species chemical model, Arrhenius formula, Structured and unstructured solutions, Euler and Navier-Stokes equations, Three-Dimensions.

Title of the Paper: Thermochemical Non-Equilibrium Entry Flows in Mars in Two-Dimensions – Part I

Authors: Edisson Sávio De Góes Maciel, Amilcar Porto Pimenta

Abstract: This work, first part of this study, describes a numerical tool to perform thermochemical non-equilibrium simulations of reactive flow in two-dimensions. The Van Leer and Liou and Steffen Jr. schemes, in their first- and second-order versions, are implemented to accomplish the numerical simulations. The Euler and Navier-Stokes equations, on a finite volume context and employing structured and unstructured spatial discretizations, are applied to solve the “hot gas” hypersonic flows around a blunt body, around a double ellipse, and around an entry capsule, in two-dimensions. The second-order version of the Van Leer and Liou and Steffen Jr. schemes are obtained from a “MUSCL” extrapolation procedure in a context of structured spatial discretization. In the unstructured context, only first-order solutions are obtained. The convergence process is accelerated to the steady state condition through a spatially variable time step procedure, which has proved effective gains in terms of computational acceleration. The reactive simulations involve a Mars atmosphere chemical model of nine species: N, O, N2, O2, NO, CO2, C, CO, and CN, based on the work of Kay and Netterfield. Fifty-three chemical reactions, involving dissociation and recombination, are simulated by the proposed model. The Arrhenius formula is employed to determine the reaction rates and the law of mass action is used to determine the source terms of each gas species equation. The results have indicated the Van Leer TVD scheme as the most accurate one, both inviscid and viscous cases. In this paper is presented the blunt body results. In Part II is presented the results with the double ellipse and the entry capsule.

Keywords: Thermochemical non-equilibrium, Mars entry, Nine species model, Hypersonic “hot gas” flow, Finite volume, Euler and Navier-Stokes equations, Two-dimensions

Title of the Paper: Thermochemical Non-Equilibrium Reentry Flows in Two-Dimensions: Seven Species Model – Part II

Authors: Edisson Sávio De Góes Maciel, Amilcar Porto Pimenta

Abstract: This work, second part of this study, presents a numerical tool implemented to simulate inviscid and viscous flows employing the reactive gas formulation of thermochemical non-equilibrium. The Euler and Navier-Stokes equations, employing a finite volume formulation, on the context of structured and unstructured spatial discretizations, are solved. These variants allow an effective comparison between the two types of spatial discretization aiming verify their potentialities: solution quality, convergence speed, computational cost, etc. The aerospace problems of the hypersonic “hot gas” flows around a double ellipse and around a reentry capsule, in two-dimensions, are simulated. The reactive simulations will involve an air chemical model of seven species: N, O, N2, O2, NO, NO+ and e-. Eighteen chemical reactions, involving dissociation, recombination and ionization, will be studied. The Arrhenius formula will be employed to determine the reaction rates and the law of mass action will be used to determine the source terms of each gas species equation.

Keywords: Euler and Navier-Stokes equations, Reactive formulation, Thermochemical non-equilibrium, Hypersonic flow, Van Leer algorithm, Finite Volumes, Unstructured discretization

Title of the Paper: Three-Dimensional Two-Impulsive Orbital Maneuvers with Time Limit

Authors: Evandro Marconi Rocco, Antonio Fernando Bertachini De Almeida Prado, Marcelo Lopes De Oliveira E Souza

Abstract: The problem of three-dimensional two-impulsive orbital maneuvers between two elliptical orbits with minimum fuel consumption, but having a time limit, is considered in the present paper. This limit in the time generates a new characteristic to the problem, which eliminates the majority of the methods available in the literature. Equations available in the literature are used and some new ones are developed to consider cases with different geometries. Those equations are then solved and a software is implemented to perform the orbital maneuvers. The original equations are presented in the literature without any numerical results, so, the new cases considered and the solutions and implementation of the method available in the literatures are the contributions shown here. The software was used with success in several different situations.

Keywords: Orbital Maneuvers, Astrodynamics, Impulsive Control

Issue 2, Volume 8, April 2013

Title of the Paper: Flexural Rigidity Characterization of Retrofitted FRP Plates

Authors: Steven J. Makonis, Stella B. Bondi, Zia Razzaq

Abstract: Presented herein is a procedure and numerical results for flexural rigidity characterization of Fiber Reinforced Polymer (FRP) plates retrofitted with various types of fabrics. The FRP plates were retrofitted with Kevlar® 49 (Aramid), Carbon Fiber (Harness-Satin H5), and Unidirectional Carbon Fiber (T700 Aerospace Grade) fabrics, respectively. The FRP plate flexural rigidity values were calculated with a central finitedifference iterative scheme while utilizing the experimental load-deflection relations based on bending tests. The tests were performed on each plate by applying a concentrated load at the center. A fourth-order partial differential equation of plate equilibrium was adopted to estimate the plate flexural rigidities and ultimately obtain the theoretical load-deflection relations. The results were verified with Navier’s solution for the same type of loading. Excellent agreement was found between the two approaches. The flexural rigidity estimation procedure can be used for more complex retrofitted plates while utilizing homogenous plate deflection equations. The FRP plates showed a significant increase in flexural rigidity, with the Aerospace Grade Carbon fiber fabric providing the most significant increase.

Keywords: FRP, Kevlar, Carbon Fiber, finite-difference, flexural rigidity, retrofitting

Title of the Paper: Supersonic and Hypersonic Flows on 2D Unstructured Context: Part IV Other Turbulence Models

Authors: Edisson Sávio De Góes Maciel

Abstract: In this work, the fourth of this study, numerical simulations involving supersonic and hypersonic flows on an unstructured context are analyzed. The Van Leer and the Radespiel and Kroll schemes are implemented on a finite volume formulation, using unstructured spatial discretization. The algorithms are implemented in their first and second order spatial accuracies. The second order spatial accuracy is obtained by a linear reconstruction procedure based on the work of Barth and Jespersen. Several non-linear limiters are studied using the linear interpolation based on the work of Jacon and Knight. To the turbulent simulations, the Wilcox, the Menter and Rumsey and the Yoder, Georgiadids and Orkwis models are employed. The compression corner problem to the supersonic inviscid simulations and the re-entry capsule problem to the hypersonic viscous simulations are studied. The results have demonstrated that the Van Leer algorithm yields the best results in terms of the prediction of the shock angle of the oblique shock wave in the compression corner problem and the best value of the stagnation pressure at the configuration nose in the re-entry capsule configuration. The spatially variable time step is the best choice to accelerate the convergence of the numerical schemes, as reported by Maciel. In terms of turbulent results, the Wilcox model yields the best results, proving the good capacity of this turbulence model in simulate high hypersonic flows. This paper is continuation of Maciel’s works started in 2011 and treats mainly the influence of turbulence models on the solution quality.

Keywords: Unstructured spatial discretization; Euler and Navier-Stokes equations; Van Leer algorithm; Radespiel and Kroll algorithm; Wilcox turbulence model; Menter and Rumsey turbulence model; Yoder, Georgiadids and Orkwis turbulence model

Title of the Paper: Performance Study of an Airlift Pump with Bent Riser Tube

Authors: A.-F. Mahrous

Abstract: Airlift pump is a type of deep well pumps. Sometimes, it is used for removing water from mines or pumping slurry of sand and water or other solutions. This work presents a numerical investigation into necessary ways to reduce momentum loss associated with local bends of the riser tube section of the airlift pump and consequently an improvement in pump performance would be attained. The investigated local tube bend are in the form of an S-shaped like duct. A numerical model of airlift pump, with bent riser tube, based on the concept of momentum balance was developed and validated against available experimental data. Parametric predictive studies on model airlift pumps with different riser tube configurations, including position, orientation, and graduation of the S-bend straight tube section, were carried out. The numerical results showed that gradually enlarging the riser tube S-bend straight section would significantly improve the airlift pump discharge rate. This is attributed to reduced acceleration loss followed the expansion of air phase in the enlarged S-bend section of the riser tube. Increasing the degree of tube expansion of the gradually enlarged S-bend straight tube section, the predicted results illustrated an improvement in the pump discharge rate that is limited by the value of tube expansion ratio. On the other hand, the numerical results showed that setting local S-bend of the riser tube at different positions from the air injector has a negligible effect on the pump performance.

Keywords: Airlift pumps, two-phase flow, pumping devices, bent riser tube, S-bend

Title of the Paper: Generation of Machined Multiple Flat Surfaces on Circular Bar by its Rotation and in Synchronism with Cutting Tool

Authors: J. A. Martins, C. Schuermann, D. Leite, I. Kövesdy, E. A. Duarte, E. Romão

Abstract: The operation of machining by lathe is one of the most common operations in automobile and machinery industries. The process is able to generate cylindrical bars under a wider variety of diameters / staggerings and using different materials, metallic’s or non-metallic’s (cupper, wood, aluminum, brass, steel, etc…). However, when more complex geometries are required, additional machines are used, like milling machine and/or machines under numerical control (CNC) and multiple axles. The possibility of joining circles, polygons, angular motion and synchronism, open the mind to multiple figures (shapes) and movements, which can generate different geometries. This paper aims to demonstrate that both operations (turning and milling), can be made at the same time and at the same machine, special but simpler lathe. The studies of geometry, associated with calculus (trigonometry) and angular motion give basis and sustain this statement. Tests in bench materialize the idea and reinforce this thesis.

Keywords: geometry, machining, special machine

Title of the Paper: Non-Linear Mathematical Models for the Jets Penetrating Liquid Pool of Different Density under Diverse Physical Conditions and Their Simulation

Authors: Ivan V. Kazachkov, Olexander V. Konoval

Abstract: The problem of modelling and simulation for the jets penetrating pool of other liquids is considered under different physical conditions and situations. It may happen for example in severe accidents at the nuclear power plants in touch with development and operation of the passive protection systems against severe accidents, as well as in many other problems. The specific peculiarities of the penetrating jets are discussed and mathematical modelling of the problem is considered. The non-linear second-order differential equation and the Cauchy problem is analyzed and solved analytically using the simultaneous transformation for both dependent and independent variables. The result obtained may be useful for theoretical and practical applications, where the liquid jet or solid rod is penetrating the pool of other liquid.

Keywords: Non-Linear, Second-Order, Differential, Equation, Analytical Solution, Jet, Penetration, Pool, Mathematical Modelling, Transformation

Title of the Paper: Peripheral Milling of Wooden Materials without Cutter-Marks – A Mechatronic Approach

Authors: Klaus Röbenack, Danish Ahmed, Stephan Eckhardt, Christian Gottlöber

Abstract: Peripheral milling is an important cutting procedure to shape work pieces of wood. Because of the kinematical principle there are so-called cutter-marks on the surface of the work pieces after cutting which influence the quality. These surface patterns cannot be avoided completely and most of the time there are some efforts to smooth the surface by sanding or linear cutting afterwards which cost extra time and money. To improve this situation a new mechatronic approach is introduced to eliminate the cycloid motion track when the cutting edge approaches the work piece. In this way, the effective motion of the cutting edge is changed to a linear motion by means of piezo actuators or magnetic bearings.

Keywords: Peripheral milling, cutter-marks, surface quality, wood and wood based materials, active magnetic bearings, flatness-based control

Issue 3, Volume 8, July 2013

Title of the Paper: Complementarities of Probabilistic and Evidence Approaches: An Uncertainty Assessment for Selection of Composite Material

Authors: Stella B. Bondi, Resit Unal, Patrick T. Hester, Trina M. Chytka

Abstract: A complimentary probabilistic and evidence theory approach is utilized to enhance uncertainty assessments in the area of critical safety characteristics for conceptual design. This research provides additional exploration into the failure modes necessary to utilize Fiber Reinforced Polymer (FRP) and various composites to their fullest potential and to minimize uncertainty by comparing probability and evidence theories. This combined approach has been applied to a selection of composite material that could provide uncertainty assessment design for a space transportation system. Uncertainty estimates presented are bounded by belief and plausibility functions. The results may provide additional information to the decision makers in critical system safety and uncertainty assessments. Benefits and limitations are discussed.

Keywords: Composite Material, Uncertainty, Probability theory, Evidence theory

Title of the Paper: Theoretical Calculation and Experimental Analysis of the Rigid Body Modes of Powertrain Mounting System

Authors: Yongjun Jin, Jianwu Zhang, Xiqiang Guan

Abstract: The performance of dynamic property of the mount is influenced by multiple factors and strongly depends on the working conditions. This means that the modal parameters of powertrain mounting system would make changes under different operating conditions. A novel approach to simulate the actual working condition is proposed in the testing of dynamic stiffness. Then the mechanical model of powertrain mounting system based on dynamic stiffness is established in this paper. In order to examine the rationality and accuracy of the computational model based on dynamic stiffness; experimental modal analysis is performed by multiple means and methods in this paper. Through the contrast analysis, advantages and disadvantages of these methods are illustrated and it is shown that using the method of Operational Modal Analysis could obtain more accurate and more reliable results. Based on the experimental and evaluation results, it is shown that there is smaller relative error and higher fitting degree between the calculation results based on dynamic stiffness and the results obtained from operational modal analysis. Moreover, the proposed method also enjoys satisfactory consistency with the actual working condition.

Keywords: Powertrain mounting system; Dynamic stiffness; Static stiffness; Operational Modal Analysis; Rigid body modes; Experimental modal analysis; Impact hammer testing

Title of the Paper: Determination of Parameters of EVP Material Model in Numerical Welding Simulations

Authors: Josef Bradáč

Abstract: Numerical simulations are used more and more frequently in technological processes, including welding processes. They are used especially for the selection of the right welding procedure, prediction and analysis of resulting deformations and distortions and also for the resulting structure of the weld metal. Size and placement determination of the residual inner stresses in the material after welding are equally important, mainly in reference to the capacity and stability of the welded structures and the prediction of their behavior during different types of load. The submission deals with determination of parameters of EVP (elastic viscoplastic) material model, by help of these parameters it is possible to describe more precisely the residual stresses during and after the welding process. In comparison with commonly used constitutive models, the advantage of this model is that it also covers viscoplastic processes, which in reality take place by stress relaxation at high temperatures.

Keywords: EVP material model, numerical simulations, viscoplastic processes, relaxation, Sysweld program

Title of the Paper: Wire Rope Springs for Passive Vibration Control of a Light Steel Structure

Authors: Stefano Pagano, Salvatore Strano

Abstract: The restoring force of wire rope springs is generated by the wire ropes deformation that, at the same time, dissipates energy due to the friction forces arising between its wires during the deformation of the rope. In this paper, the dynamic behavior of a light structure isolated by means of isolators, constituted by wire rope springs and a ball transfer unit, is investigated; the adopted structure simulates objects sensitive to seismic accelerations, like works of arts or cabinets containing electromechanical devices whose functioning must be ensured during seismic events. In the first part of the paper the system dynamic characteristics are evaluated by means of an experimental modal analysis conducted on a shaking table by assigning different laws of motion to its moving platform. The frequency response has been obtained through mono-frequential and multi-frequential excitations; the platform has been also moved with laws deduced from accelerograms recorded during seismic events to evaluate its insulation efficiency. The modal analysis has shown the frequency range where the proposed isolation system produces a beneficial action for the specific passive vibration control application. Experimental data have been used to validate a numerical model that can be adopted to simulate operating conditions different from those of the experimental tests; the results of several simulation are reported to highlight the influence of some parameters on the system dynamic behavior.

Keywords: Wire rope springs, shaking table tests, experimental modal analysis, nonlinear dynamics, vibration control

Title of the Paper: Researches in the Field of the Bearing Structure of Tank Wagon

Authors: Sorin Mihai Radu, Bogdan Tănăsoiu

Abstract: The paper deals with one of the (studied) possibilities of connecting and attaching the chassis to the tank. The adopted constructive and technological solution answers to the requirements imposed through the international regulations by the UIC. The paper also presents the determination of the resistance of the studied technical solution using the finite element method and its ratification through experimental trials considering a static stress regime. The comparison of the theoretical determinations to the experimental ones leads to a positive assessment of the accuracy and veracity of the determination method as well as the safety of using the constructive solution into operation. Moreover, the paper brings forward a theoretical as well as an experimental study of the resistance of the attachment (frame) tank-chassis to the dynamic stress due to the collision shock. The theoretical determinations of the resistance, using the finite element method for the cushioning action of the buffers, have constituted the fundamental information for choosing the verified dangerous sections. The paper also brings forward collision trials and the conclusions imposed by the experimental study.

Keywords: Bearing structure, relative deformation, pressure

Title of the Paper: Study on the Dynamic Performance of Heavy-duty Forging Manipulator

Authors: Qingsong Yang, Yuanxin Luo, Yongqin Wang, Xingchun Yan

Abstract: Cooperating with heavy forging press, the heavy-duty forging manipulator is used for handling the workpiece during the free-forging process. Therefore, the size accuracy of the forgings is related to the dynamics performance of the forging manipulator. This paper aims to study the dynamic performance of DDS heavy-duty forging manipulator. The kinematics model is firstly built to predict the trajectories of the tong. Then, the dynamics models are derived by using rigid-body method and flexible-body method respectively. Finally, the simulation results indicate that partially flexible-body model is well predicted the trajectory of the tong.

Keywords: Forging manipulator, Dynamics model, Partially Flexible-body method, Trajectory

Issue 4, Volume 8, October 2013

Title of the Paper: Development and Investigation of the Mathematical Models for Potentially Hazardous Nuclear Power Objects with Deviated Arguments

Authors: Jamshid Gharakhanlou, Ivan V. Kazachkov, Oleksandr V. Konoval

Abstract: The paper is devoted to one of the problems of system analysis for nuclear power plants (NPP) in touch with the modelling and simulation of the potentially hazardous objects in nuclear power safety including severe accidents at the nuclear power plants. Development and implementation of the mathematical models for analysis and computer simulations of the passive protection systems against severe accidents and mathematical modelling and simulation of the potentially hazardous objects (PHO) with account of different deviating arguments concerning the real features are considered. It has concern to a need of the planning and decision making in the environmental and other tasks.

Keywords: Potentially hazardous object, nuclear power, non-linear dynamical system, time shifts, control parameters, severe accident

Title of the Paper: Continuum Robotic Elements for Enabling Negotiation of Uneven Terrain in Unstructured Environments

Authors: Ivan Siles, Ian D. Walker

Abstract: We address the potential for continuous “continuum” robot elements to transform the nature of robotic traversal of uneven terrain. Continuum robots are “dual” to traditional robot structures, with their inherent capabilities featuring strengths in areas that are key weaknesses for conventional robots. These capabilities match well to current challenges in robot mobility, particularly in unstructured environments featuring uneven terrain. We demonstrate these capabilities via new and innovative mobile robot hardware, based on the combination of novel continuum body elements with wheel/leg (“whegs”) elements. This combination offers performance not possible with conventional “monolithic” wheeled or tracked mobile robots, or with current robot snakes.

Keywords: Continuum robots, design, mobility, locomotion

Title of the Paper: Least Squares Method to Solve 3D Convection–diffusion–reaction Equation with Variable Coefficients in Multi-Connected Domains

Authors: E. C. Romão, L. F. M. Moura

Abstract: This paper aims at analyzing 3D convection-diffusion-reaction in multi-connected domains. The objective is to create two types of domains (double and multi-connected), to analyze the influence of numerical results for the proposed methods (GFEM and LSFEM). The domain and the construction of the networks proposed in this paper are applications built with the aim of facilitating the comparison of works by other researchers.

Keywords: Convection-diffusion-reaction problems, GFEM, LSFEM, multi-connected domains

Title of the Paper: Evaluation of Mixed-Mode Stress Intensity Factor of Wood from Crack-Tip Displacement Fields Utilizing Digital Image Correlation

Authors: Jian Zhao, Dong Zhao

Abstract: The effects of anisotropy and varying initial crack angle during mixed mode tension loading were studied in Dahurian Larch wood. The mixed mode stress intensity factors (SIFs) were calculated using displacements from digital image correlation. With the crack angle increasing, the SIF of mode I in unilateral crack increase all along, but the SIF of mode II in unilateral crack shows an initial increase, followed by a decrease. Crack-tip plastic zones were determined using an anisotropic yield criterion. Strains in the plastic zone obtained from digital image correlation showed that the varying angles of crack growth have on the asymmetry of the plastic zone. Experimental results reveal that the DIC method is a practical and effective technique for SIF and crack-tip plastic size measurement.

Keywords: Digital image correlation, Stress intensity factor, Mixed mode, Crack-tip plastic zone

Title of the Paper: Dynamic Stability of Time-Delayed Feedback Control System by FFT based IHB Method

Authors: R. K. Mitra, A. K. Banik, S. Chatterjee

Abstract: The forced Duffing oscillator is investigated by intentional time-delayed displacement feedback by fast Fourier transform based incremental harmonic balance method along with continuation technique (FFT-IHBC). FFT-IHBC can efficiently develop frequency response curves with all stable and unstable solutions and solution branches. Appreciable reduction in peak value of response and gradual reduction in the skew-ness in frequency response curve is observed with the introduction of gain and delay. Further, frequency response curves with all stable solutions can be achieved with appropriate choice of gain and delay in the primary and secondary stability zones of linear stability analysis. The results obtained by this method are compared with numerical integration method and they match perfectly.

Keywords: Fast Fourier transform; incremental harmonic balance method; are length continuation; intentional time-delayed feedback; Floquet stability

Title of the Paper: The Changes of Material Properties of the Cement Paste with Fly Ash Exposed to High Temperatures

Authors: Pavel Padevět, Romana Lovichová

Abstract: The paper describes properties of cement paste included addition of the fly ash. Firstly is described the preparation of the cement paste. Next part is focused on the testing of the properties. Results of the testing are summarized in properties like a compression strength, Modulus of elasticity and strength in bending. Finally the relation between material properties and volume weight is discussed.

Keywords: Cement paste, fly-ash, concrete, compression strength, Modulus of elasticity, tensile strength in bending