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CONTENTS
Volume 7, Number 4, August 2018
 

Abstract
This paper is concerned with the wave propagation behavior of rotating functionally graded temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field. Uniform, linear and nonlinear temperature distributions across the thickness are investigated. Thermo-elastic properties of FG beam change gradually according to the Mori-Tanaka distribution model in the spatial coordinate. The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function. The governing equations are derived by Hamilton\'s principle as a function of axial force due to centrifugal stiffening and displacement. By applying an analytical solution and solving an eigenvalue problem, the dispersion relations of rotating FG nanobeam are obtained. Numerical results illustrate that various parameters including temperature change, angular velocity, nonlocality parameter, wave number and gradient index have significant effect on the wave dispersion characteristics of the understudy nanobeam. The outcome of this study can provide beneficial information for the next generation researches and exact design of nano-machines including nanoscale molecular bearings and nanogears, etc.

Key Words
wave propagation; FGMs; nonlocal strain gradient theory; rotating nanobeam; refined beam theory

Address
Farzad Ebrahimi and Parisa Haghi: Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran


Abstract
This paper proposes a linear damping model of tire-soil system using semi-empirical method. A test rig was designed and developed to measure the vertical equivalent linear damping ratio of tire only and tire–soil system using Free-Vibration Logarithmic Decay Method. The test was performed with two kinds of tractor tires using a combination of five inflation pressure levels, two soil depths and four soil moisture contents in the paddy soil. The results revealed that the linear damping ratio of tires increased with decreasing tire inflation pressure; the linear damping ratio of tire-soil system also increased with decreasing tire inflation pressure and increased with the increasing soil depth (observed at 80 and 120 mm). It also increased with a relative increase of soil moisture contents (observed at 37.9%, 48.8%, 66.7% and 77.4%). The results also indicated that the damping ratio of tire-soil system was higher than that of tire only. A linear damping model of tire-soil system is proposed as a damping model in parallel which is established based on experimental results and vibration theory. This model will have a great significance in study of tractor vibration.

Key Words
linear damping ratio; logarithm decay method; tire-soil system; tractor vibration; semi-empirical method

Address
Do Minh Cuong and Nguyen Thi Ngoc: Department of Mechanical Engineering, University of Agriculture and Forestry,
Hue University, Vietnam
Ma Ran: School of Mechanical and Electrical Engineering, Jiangsu Normal University, Xuzhou 221116, Jiangsu, PR China
Zhu Sihong: College of Engineering, Nanjing Agricultural University, Nanjing 210031, PR China

Abstract
In solid-liquid two phase flow, the knowledge of how descending solid particles affected by the presence of downstream wall is important. This work studies at what interstitial distance the velocity of a vertically descending sphere is affected by a downstream wall as a consequence of wall-modified hydrodynamic forces through a validated dynamic model. This interstitial distance-the hydrodynamic coupling distance Sc-is found to decay monotonically with the approach Stokes number St which compares the particle inertia to viscous drag characterized by the quasi-steady Stokes\' drag. The scaling relation Sc-St-1 decays monotonically as literature below the value of St equal to 10. However, the faster diminishing rate is found above the threshold value from St=10-40. Furthermore, an empirical relation of Sc-St shows dependence on the drop height which clearly indicates the non-negligible effect of unsteady hydrodynamic force components, namely the added mass force and the history force. Finally, we attempt a fitting relation which embedded the particle acceleration effect in the dependence of fitting constants on the diameter-scaled drop height.

Key Words
hydrodynamic coupling; Stokes number; wall effect; added mass force; history force

Address
Cheng-Chuan Lin, Hung-Tien Huang and Fu-Ling Yang: Department of Mechanical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan (R.O.C.)


Abstract
In this study, a computational method for wall shear stress combined with an implicit direct-forcing immersed boundary method is presented. Near the immersed boundaries, the sub-grid stress is determined by a wall model in which the wall shear stress is directly calculated from the Lagrangian force on the immersed boundary. A coupling mathematical model of the transition process for a model Francis turbine comprising turbulent flow and rotating rigid guide vanes is established. The spatiotemporal distributions of pressure, velocity, vorticity and turbulent quantity are gained with the transient process; the drag and lift coefficients as well as other forces (moments) are also obtained as functions of the attack angle. At the same time, analysis is conducted of the characteristics of pressure pulsation, velocity stripes and vortex structure at some key parts of flowing passage. The coupling relations among the turbulent flow, the dynamical force (moment) response of blade and the rotating of guide vane are also obtained.

Key Words
immersed boundary method; velocity correction; large eddy simulation; turbulent flow; transition process; hydraulic turbine

Address
Wen-Quan Wang and Yan Yan: Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming 650500, China


Abstract
Longitudinal fracture in a functionally graded beam configuration was studied analytically with taking into account the non-linear behavior of the material. A cantilever beam with two longitudinal cracks located symmetrically with respect to the centroid was analyzed. The material was functionally graded along the beam width as well as along the beam length. The fracture was studied in terms of the strain energy release rate. The influence of material gradient, crack location along the beam width, crack length and material non-linearity on the fracture behavior was investigated. It was shown that the analytical solution derived is very useful for parametric analyses of the non-linear longitudinal fracture behavior. It was found that by using appropriate material gradients in width and length directions of the beam, the strain energy release rate can be reduced significantly. Thus, the results obtained in the present paper may be applied for optimization of functionally graded beam structure with respect to the longitudinal fracture performance.

Key Words
functionally graded beam; fracture; material non-linearity; analytical solution

Address
Victor I. Rizov: Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 - Sofia, Bulgaria


Abstract
The study deals with physical modeling of a typical three storeyed building frame supported by a pile group of four piles (2x2) embedded in cohesive soil mass using three dimensional finite element analysis. For the purpose of modeling, the elements such as beams, slabs and columns, of the superstructure frame; and that of the pile foundation such as pile and pile cap are descretized using twenty noded isoparametric continuum elements. The interface between the pile and the soil is idealized using sixteen node isoparametric surface element. The soil elements are modeled using eight nodes, nine nodes and twelve node continuum elements. The present study considers the linear elastic behaviour of the elements of superstructure and substructure (i.e., foundation). The soil is assumed to behave non-linear. The parametric study is carried out for studying the effect of soil- structure interaction on response of the frame on the premise of sub-structure approach. The frame is analyzed initially without considering the effect of the foundation (non-interaction analysis) and then, the pile foundation is evaluated independently to obtain the equivalent stiffness; and these values are used in the interaction analysis. The spacing between the piles in a group is varied to evaluate its effect on the interactive behaviour of frame in the context of two embedment depth ratios. The response of the frame included the horizontal displacement at the level of each storey, shear force in beams, axial force in columns along with the bending moments in beams and columns. The effect of the soil- structure interaction is observed to be significant for the configuration of the pile groups and in the context of non-linear behaviour of soil.

Key Words
soil-structure interaction; pile spacing; embedment depth; pile diameter; storey displacement; bending moment; shear force; axial force

Address
S. A. Rasal and H. S. Chore: Department of Civil Engineering, Datta Meghe College of Engineering, Sector-3, Airoli, Navi Mumbai-400708, India
V. A. Sawant: Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee-247667, India

Abstract
The moving load causes the occurrence of vibrations in civil engineering structures such as bridges, railway lines, bridge cranes and others. A novel engineering method for separation of the variables in the differential equation of the elastic line of Bernoulli-Euler beam has been developed. The method can be utilized in engineering structures, leading to \"a beam under moving load model\" with generalized boundary conditions. This method has been implemented for analytical study of the dynamic response of the metal structure of a single girder bridge crane due to the telpher movement along the bridge girder. The modeled system includes: a crane bridge girder; a telpher, moving with a constant horizontal velocity; a load, elastically fixed to the telpher. The forced vibrations with their own frequencies and with a forced frequency, due to the telpher movement, have been analyzed. The loading resulting from the telpher uniform movement along the bridge girder is cyclical, which is a prerequisite for nucleation and propagation of fatigue cracks. The concept of \"dynamic coefficient\" has been introduced, which is defined as a ratio of the dynamic deflection of the bridge girder due to forced vibrations, to the static one. This ratio has been compared with the known from the literature empirical dynamic coefficient, which is due to the telpher track unevenness. The introduced dynamic coefficient shows larger values and has to be taken into account for engineering calculations of the bridge crane metal structure. In order to verify the degree of approximation, the obtained results have been compared with FEM outcomes. An additional comparison has been made with the exact solution, proposed by Timoshenko, for the case of simply supported beam subjected to a moving force. The comparisons show a good agreement.

Key Words
engineering structures; dynamic response; forced vibrations; bridge crane

Address
Jordan T. Maximov and Vladimir P. Dunchev: Department of Applied Mechanics, Technical University of Gabrovo, 5300 Gabrovo, Bulgaria


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