Bending of Thermoviscoelastic Functionally Graded Materials Beams

According to the constitutive relation of linear thermovisoelasticity, with the help of Laplace transformation method and the introduction of structure functions and thermal functions, the mathematical model and its corresponding variational principle for thermoviscoelastic FGM beams are set up on the basis of the assumption that plane section remains plane and normal to the beam axis. Using Laplace transformation method, the deflection and the stress distribution are discussed.

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The Effect of Functionally Graded Materials on Temperature during Frictional Heating: Under Uniform Sliding

Materials ◽

10.3390/ma14154285 ◽

2021 ◽

Vol 14 (15) ◽

pp. 4285

Author(s):

Aleksander Yevtushenko ◽

Katarzyna Topczewska ◽

Przemysław Zamojski

Keyword(s):

Mathematical Model ◽

Functionally Graded Materials ◽

Frictional Heating ◽

Ceramic Materials ◽

Functionally Graded ◽

Heating Process ◽

Spatial Distributions ◽

Graded Materials ◽

Exponential Change ◽

The Mathematical Model

The mathematical model of heating process for a friction system made of functionally graded materials (FGMs) was proposed. For this purpose, the boundary-value problem of heat conduction was formulated for two semi-spaces under uniform sliding taking into consideration heating due to friction. Assuming an exponential change in thermal conductivities of the materials, the exact, as well as asymptotic (for small values of time), solutions to this problem were obtained. A numerical analysis was performed for two elements made of ZrO2–Ti-6Al-4V and Al3O2–TiC composites. The influence of the gradient parameters of both materials on the evolution and spatial distributions of the temperature were investigated. The temperatures of the elements made of FGMs were compared with the temperatures found for the homogeneous ceramic materials.

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The Study of the Initial State of Cable-Net Structure Reflector for the FAST

Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2012-70310 ◽

2012 ◽

Author(s):

Yu Liu ◽

Feng Gao

Keyword(s):

Mathematical Model ◽

Variational Principle ◽

Nonlinear Equations ◽

Layer By Layer ◽

Initial State ◽

Main Cable ◽

Highly Nonlinear ◽

Node Location ◽

Set Up ◽

The Mathematical Model

By using the variational principle to set up the mathematical model of the reflector for the FAST, we can get the node location of the cable-net and tension of the main cable by solving highly nonlinear equations of the mathematical model. A new layer-by-layer substitution approach has been proposed for solving the highly nonlinear equations, through the calculation and simulation it verifies the correctness of this method.

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A New Mathematical Model For Heat Radius of Cyclic Superheated Steam Stimulation with Horizontal Wellbore

Mathematical Problems in Engineering ◽

10.1155/2018/7601702 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Congge He ◽

Anzhu Xu ◽

Zifei Fan ◽

Lun Zhao ◽

Bing Bo

Keyword(s):

Mathematical Model ◽

Phase Change ◽

Superheated Steam ◽

Transformation Method ◽

Saturated Steam ◽

Heating Process ◽

Horizontal Wellbore ◽

The Mathematical Model ◽

Laplace Transformation Method ◽

Steam Stimulation

When superheated steam flows along the horizontal wellbore, it may change to saturated steam at some point of the wellbore. In this paper, to accurately predict the heat radius of cyclic superheated steam stimulation with horizontal wellbore, the distribution of thermophysical properties of superheated steam along the horizontal wellbore is considered. The heating process is divided into 4 stages for superheated steam and 3 stages for saturated steam when the phase change undergoes in the wellbore. On this basis, the mathematical model for heat radius of cyclic superheated steam stimulation with horizontal wellbore was established according to energy conservation principle and Laplace transformation method. The calculation result of the new mathematical model is in good agreement with that of the numerical simulation (CMG STARS) for the same parameters from a specific heavy oil reservoir, which verified the correctness of the new mathematical model. The effect of degree of superheat and the cycle of stimulation are analyzed in detail after the new mathematical model is validated. The results show that the heat radius of superheated zone, steam zone, and hot fluid zone all decrease with horizontal well length and increase with the cycle of stimulation. The higher the degree of superheat is, the farther from the heel of the horizontal wellbore the phase change undergoes. Besides, the radius of superheated zone, steam zone, and hot fluid zone increases with the degree of superheat, but the value increases little at steam zone and hot fluid zone.

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Research on Dynamic Balance Method of Precision Centrifuge

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.945-949.777 ◽

2014 ◽

Vol 945-949 ◽

pp. 777-780

Author(s):

Tao Liu ◽

Yong Xu ◽

Bo Yuan Mao

Keyword(s):

Mathematical Model ◽

Balance Control ◽

Dynamic Balance ◽

Dynamic Balancing ◽

Structure Characteristics ◽

Balance System ◽

Simulation Results ◽

Set Up ◽

System Controller ◽

The Mathematical Model

Firstly, according to the structure characteristics of precision centrifuge, the mathematical model of its dynamic balancing system was set up, and the dynamic balancing scheme of double test surfaces, double emendation surfaces were established. Then the dynamic balance system controller of precision centrifuge was designed. Simulation results show that the controller designed can completely meet the requirements of precision centrifuge dynamic balance control system.

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Exact Solutions of a Spatially Dependent Mass Dirac Equation for Coulomb Field plus Tensor Interaction via Laplace Transformation Method

Advances in High Energy Physics ◽

10.1155/2012/873619 ◽

2012 ◽

Vol 2012 ◽

pp. 1-15 ◽

Cited By ~ 11

Author(s):

M. Eshghi ◽

M. Hamzavi ◽

S. M. Ikhdair

Keyword(s):

Dirac Equation ◽

Laplace Transformation ◽

Bound States ◽

Energy Eigenvalue ◽

Coulomb Field ◽

Transformation Method ◽

Arbitrary Spin ◽

Tensor Interaction ◽

Dependent Mass ◽

Laplace Transformation Method

The spatially dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the Laplace transformation method (LTM). Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit and in the absence of tensor interaction (T=0).

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Glass-Alumina Functionally Graded Materials Produced by Plasma Spraying

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.333.227 ◽

2007 ◽

Vol 333 ◽

pp. 227-230

Author(s):

Valeria Cannillo ◽

Luca Lusvarghi ◽

Tiziano Manfredini ◽

M. Montorsi ◽

Cristina Siligardi ◽

...

Keyword(s):

Electron Microscopy ◽

Scanning Electron Microscopy ◽

Plasma Spraying ◽

Functionally Graded Materials ◽

Cross Sections ◽

Functionally Graded ◽

Depth Sensing ◽

Graded Materials ◽

Set Up ◽

Scanning Electron

The present work was focused on glass-alumina functionally graded materials. The samples, produced by plasma spraying, were built as multi-layered systems by depositing several layers of slightly different composition, since their alumina and glass content was progressively changed. After fabricating the graded materials, several, proper characterization techniques were set up to investigate the gradient in composition, microstructure and related performances. A particular attention was paid to the observation of the graded cross sections by scanning electron microscopy, which allowed to visualize directly the graded microstructural changes. The scanning electron microscopy (SEM) inspection was integrated with accurate mechanical measurements, such as systematic depth-sensing Vickers microindentation tests performed on the graded cross sections.

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A new Laplace transformation method for dynamic testing of solar collectors

Renewable Energy ◽

10.1016/j.renene.2014.10.026 ◽

2015 ◽

Vol 75 ◽

pp. 448-458 ◽

Cited By ~ 14

Author(s):

Weiqiang Kong ◽

Bengt Perers ◽

Jianhua Fan ◽

Simon Furbo ◽

Federico Bava

Keyword(s):

Laplace Transformation ◽

Dynamic Testing ◽

Transformation Method ◽

Solar Collectors ◽

Laplace Transformation Method

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Theoretical and Experimental Study of the Dynamics of the Tripod-Ball Sliding Joint With Clearance

Volume 6B: 18th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc2001/vib-21555 ◽

2001 ◽

Author(s):

Jia Xiaohong ◽

Ji Linhong ◽

Jin Dewen ◽

Zhang Jichuan

Keyword(s):

Mathematical Model ◽

Equations Of Motion ◽

Experimental Studies ◽

Active System ◽

New Concepts ◽

Sliding Joint ◽

New Type ◽

Set Up ◽

The Mathematical Model ◽

Kane Method

Abstract Clearance is inevitable in the kinematic joints of mechanisms. In this paper the dynamic behavior of a crank-slider mechanism with clearance in its tripod-ball sliding joint is investigated theoretically and experimentally. The mathematical model of this new-type joint is established, and the new concepts of basal system and active system are put forward. Based on the mode-change criterion established in this paper, the consistent equations of motion in full-scale are derived by using Kane method. The experimental rig was set up to measure the effects of the clearance on the dynamic response. Corresponding experimental studies verify the theoretical results satisfactorily. In addition, due to the nonlinear elements in the improved mathematical model of the joint with clearance, the chaotic responses are found in numerical simulation.

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