• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.281-298
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• 2015

In this study, nonlinear transverse vibrations of tensioned Euler-Bernoulli nanobeams are studied. The nonlinear equations of motion including stretching of the neutral axis and axial tension are derived using nonlocal beam theory. Forcing and damping effects are included in the equations. Equation of motion is made dimensionless via dimensionless parameters. A perturbation technique, the multiple scale methods is employed for solving the nonlinear problem. Approximate solutions are applied for the equations of motion. Natural frequencies of the nanobeams for the linear problem are found from the first equation of the perturbation series. From nonlinear term of the perturbation series appear as corrections to the linear problem. The effects of the various axial tension parameters and different nonlocal parameters as well as effects of different boundary conditions on the vibrations are determined. Nonlinear frequencies are estimated; amplitude-phase modulation figures are presented for simple-simple and clamped-clamped cases.

• Computers and Concrete
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• v.30 no.1
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• pp.1-8
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• 2022

The basic purpose of the current study is to compute the numerical analysis of heat source/sink for Darcy-Forchheimer three dimensional nanofluid flow with gyrotactic microorganism by rotatable disk via porous media under the slip conditions. Due to nanoparticles, random and thermophoretic motion phenomenon occurs. The governing mathematical model is handled numerically by shooting method. Additionally, the characteristics of velocities, mass, heat, motile microorganisms and associated parameters are thoroughly analyzed via plots and tables. Different physical parameters like Forchheimer number, slip parameters like velocity, porosity parameter, Prandtl number, Brownian number, thermophoresis parameter, heat sink/source parameter, bioconvected Rayleigh number, buoyancy parameteron dimensionless velocities, temperature. Approximate values of Sherwood microorganism are analyzed.

• Journal of Biomedical Engineering Research
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• v.16 no.1
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• pp.67-76
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• 1995

Explosive evaporative removal process of biological tissue by absorption of a CW laser has been simulated by using gelatin and a multimode Nd: YAG laser. Because the point of maximun temperature of laser-irradiated gelatin exists below the surface due to surface cooling, evaporation at the boiling temperature is made explosively from below the surface. The important parameters of this process are the conduction loss to laser power absorption (defined as the conduction-to-laser power parameter, Nk), the convection heat transfer at the surface to conduction loss (defined as Bi), dimensionless extinction coefficient (defined as BrJ, and dimensionless irradiation time (defined as Fo). Dependence of Fo on Nk and Bi has been observed by experiment, and the results have been compared with the numerical results obtained by solving a 2-dimensional conduction equation. Fo and explosion depth (from the surface to the point of maximun temperature) are increased when Nk and Bi are increased. To find out the minimum laser power for explosive evaporative removal process, steady state analysis has been also made. The limit of Nk to induce evaporative removal, which is proportional to the inverse of the laser power, has been obtained.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.04a
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• pp.266-271
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• 2009

A modeling method for the modal analysis of a multi-packet blade system having a crack undergoing rotational motion is presented in this paper. Each blade is assumed as a slender cantilever beam. The stiffness coupling effects between blades due to the flexibilities of the disc and the shroud are modeled with discrete springs. Hybrid deformation variables are employed to derive the equations of motion. The flexibility due to crack, which is assumed to be open during the vibration, is calculated basing on a fracture mechanics theory. To obtain more general information, the equations of motion are transformed into dimensionless forms in which dimensionless parameters are identified. The effects of the dimensionless parameters related to the angular speed, the depth and location of a crack on the modal characteristics of the system are investigated with some numerical examples.

• Steel and Composite Structures
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• v.20 no.3
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• pp.513-543
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• 2016

Third order shear deformation theory is used to evaluate electro-elastic solution of a sandwich plate with considering functionally graded (FG) core and composite face sheets made of piezoelectric layers. The plate is resting on the Pasternak foundation and subjected to normal pressure. Short circuited condition is applied on the top and bottom of piezoelectric layers. The governing differential equations of the system can be derived using Hamilton's principle and Maxwell's equation. The Navier's type solution for a sandwich rectangular thick plate with all edges simply supported is used. The numerical results are presented in terms of varying the parameters of the problem such as two elastic foundation parameters, thickness ratio ($h_p/2h$), and power law index on the dimensionless deflection, critical buckling load, electric potential function, and the natural frequency of sandwich rectangular thick plate. The results show that the dimensionless natural frequency and critical buckling load diminish with an increase in the power law index, and vice versa for dimensionless deflection and electrical potential function, because of the sandwich thick plate with considering FG core becomes more flexible; while these results are reverse for thickness ratio.

• Journal of Energy Engineering
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• v.4 no.2
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• pp.297-302
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• 1995

Ignition of a reactive solid in a shape of square corner by a hot surface is studied theoretically. Ignition time and the location of ignition point are determined as a function of dimensionless parameters, with the use of the homogeneous model of ignition. The effect of geometry on the ignition of solid fuel results in the local characteristics: the reaction is initiated in a hot point in depth of the substance. It is shown that ignition time is proportional to the dimensionless initial temperature, whereas for the ignition of the semiinfinite body this dependence was quadratic.

• Earthquakes and Structures
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• v.10 no.1
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• pp.91-104
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• 2016

In this paper we investigate the existence of SH-waves in fiber-reinforced layer placed over a heterogeneous elastic half-space. The heterogeneity of the elastic half-space is caused by the exponential variations of density and rigidity. As a special case when both the layers are homogeneous, our derived equation is in agreement with the general equation of Love wave. Numerically, it is observed that the velocity of SH-waves decreases with the increase of heterogeneity and reinforced parameters. The dimensionless phase velocity of SH-waves increases with the decreases of dimensionless wave number and shown through figures.

• Nuclear Engineering and Technology
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• v.39 no.5
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• pp.627-636
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• 2007

The present work is aimed at further discussing the effectiveness of dimensionless parameters recently proposed for the analysis of flow stability in heated channels with supercritical fluids. In this purpose, after presenting the main motivations for the introduction of these parameters in place of previously proposed ones, additional information on the theoretical bases and on the consequences of this development is provided. Stability maps, generated by an in-house program adapted from a previous application to boiling channels, are also shown for different combinations of the operating parameters. The maps are obtained as contour plots of an amplification parameter obtained from numerical discretization and subsequent linearization of governing equations; as such, they provide a quantitatively clear perspective of the effect of different boundary conditions on the stability of heated channels with supercritical fluids. In order to assess the validity of the assumptions at the basis of the in-house model, supporting calculations have been performed making use of the RELAP5/MOD3.3 computer code, detecting the values of the dimensionless parameters at the threshold for the occurrence of instability for a heated channel representative of SCWR proposed core configurations. The obtained results show reasonable agreement with the maps, supporting the applicability of the proposed scaling parameters for describing the dynamic behaviour of heated channels with supercritical fluids.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.83-102
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• 2015

The present paper analyses the radiation effects of mass transfer on steady nonlinear MHD boundary layer flow of a viscous incompressible fluid over a nonlinear porous stretching surface in a porous medium in presence of heat generation. The liquid metal is assumed to be gray, emitting, and absorbing but non-scattering medium. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. The resulting nonlinear ordinary differential equations are solved numerically using Runge-Kutta fourth order method along with shooting technique. Comparison with previously published work is obtained and good agreement is found. The effects of various governing parameters on the liquid metal fluid dimensionless velocity, dimensionless temperature, dimensionless concentration, skin-friction coefficient, Nusselt number and Sherwood number are discussed with the aid of graphs.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.9 no.4
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• pp.859-864
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• 2008

The dynamic interaction between the moving mass and the rotating Timoshenko shaft is investigated. The moving speed of the mass is presented by a constraint equation related to the rotating speed of the shaft. The dimensionless equations of motion for the rotating shaft with a moving mass by using the Timoshenko's beam theory. The dynamic responses of this system are studied. influences of dimensionless parameters such as the rotating speed ratio. the Rayleigh coefficient and the dimensionless axial force are discussed on the transient response and the maximum deflection of the moving system.