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Vibration of a composite elastic beam on an inhomogeneous elastic foundation

Sahin Onur

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 2

107--119

EN

The lowest vibration modes of a composite beam resting on an inhomogeneous elastic foundation in the case of a clamped-free boundary condition are investigated. It is observed that the relation between the frequency and foundation constant has an effect on the valid solution of the problem. An asymptotic procedure is employed to derive the eigenfrequencies as well as the eigenforms revealing that only under certain conditions on the ratios of material parameters. Numerical illustrations are presented to confirm that the obtained asymptotic frequencies agree well with the exact frequencies in the lowest frequency range. Comparisons of asymptotic and exact displacements are also presented and a remarkable agreement is observed for high-contrast beam components.

2

Transient heat and mass transfer of hydromagnetic effects on the flow past a porous medium with movable vertical permeablesheet

Okedoye A. M., Salawu S. O.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 4

175--190

EN

An unsteady flow of heat and species transport through a porous medium in an infinite movable vertical permeable flat surface is considered. The hydromagnetic chemical reactive fluid flow is stimulated by the thermal and solutant convection, and propelled by the movement of the surface. The formulated nonlinear flow equations in time space are solved analytically by asymptotic expansions to obtain solutions for the flow momentum, energy and chemical concentration for various thermo-physical parameters. The existence of flow characteristic is defined with the assistance of the flow parameters. In the study, the impact of some pertinent flow terms is reported and discussed. The study revealed that the species boundary layer increases with a generative chemical reaction and decreases with a destructive chemical reaction. Also, arise in the generative species reaction term reduces the flow momentum for the cooling surface. The impact of other flow governing parameters is displayed graphically as well as the fluid wall friction, wall energy and species gradients. The results of this study are important in chemical thermal engineering for monitoring processes to avoid solution blow up.

3

Some reliability issues of the corrugated i-beam girder

Sokołowski D, Kamiński M.

Engineering Transactions

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2015

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Vol. 63, iss. 3

297--315

EN

The main aim of this paper is reliability analysis of the corrugated-web I-girder carried out to verify its susceptibility to the random corrosion of the web and to make a comparison of the results of the first and of the second order reliability analysis. The methodology implemented in the study is based on the stochastic finite element method related to the generalized stochastic perturbation technique, where a discretization of the entire structure is carried out with four-node quadrilateral shell finite elements. This is numerically implemented using the FEM engineering system ROBOT and computer algebra system MAPLE, where all probabilistic procedures are programmed. The perturbation-based results are compared with these coming from the Monte-Carlo simulation and with an analytical solution obtained via symbolic integration carried out in MAPLE also. The indices of reliability are determined for the maximum deflections of the beam as the function of an input coefficient of variation of the web’s thickness whose meaning is the extent of a corrosion process.

4

Approximate analytical solutions to thermo-poro-elastic equations

Yurusoy M., Pakdemirli M., Noyan O. F.

International Journal of Applied Mechanics and Engineering

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2004

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Vol. 9, no 1

181-187

EN

Thermo-poro-elastic equations describing the pressure and temperature diffusion from a deep layer of high temperature and pressure to a fluid saturated porous permeable layer are considered. The coupled partial differential system is transformed into an ordinary differential system via similarity transformations. Approximate analytical solutions to the ordinary differential system are found using perturbation methods and the criteria for validity of the solutions are established. Series solutions of the ordinary differential system are also given. Perturbation solutions and series solutions are contrasted with numerical solutions. When the criteria are met, perturbation solutions and numerical solutions are in good agreement. In contrast, the series solutions have a limited range of applicability.

5

Anharmonic polarization of ferroelectric ceramics in alternating field. I. Large damping

Aleksiejuk M., Knyazev M. A.

Journal of Technical Physics

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2002

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Vol. 43, no 3

257-263

EN

Polarization of ferroelectric ceramics in an alternating electric field with frequency UJ in a case when damping is large is considered. For the two-type of ions phenomenological model of ferroelectrics which includes only two types of ions of the crystalic lattice, the nonlinear anharmonic equation for polarization is considered. By perturbation method the solution of this equation in the first order in anharmonicity coefficient is constructed. It is shown that an additional oscillations of polarisation with frequency omega/2 and phase shift between real and imaginary components of polarization appeared.