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1

Nonlinear free vibration and transient responses of porous functionally graded magneto-electro-elastic plates

Sh Esayas L., Kattimani Subhaschandra, Vinyas M.

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 1

art. no. e38, 2022

EN

The geometrically nonlinear free vibration and transient response of porous functionally graded magneto-electro-elastic (PFG-MEE) plates are studied based on the first-order shear deformation (FSDT) theory, von Karman's nonlinear strain–displacement relations along with modified power law. With Hamilton's theory, the coupled equations of motion are obtained and analyzed by adapting finite element methods (FEM). Moreover, using Newmark's, Picard's, and Newton–Raphson methods, a porous FG-MEE plate's nonlinear and transient response is analyzed using MATLAB software. After validating the present study, the influence of porosity distribution, porosity index, boundary conditions, aspect ratios, and thickness to length ratios on the nonlinear frequency ratio and nonlinear transient response of porous FG-MEE plate is investigated. It is revealed that geometric parameters, porosity index, boundary conditions, and form of porosity distribution significantly influence the nonlinear frequency ratio and nonlinear transient deflections of porous FG-MEE plates.

2

Effect of kerr foundation and in-plane forces on free vibration of fgm nanobeams with diverse distribution of porosity

Jankowski Piotr

Acta Mechanica et Automatica

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2020

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Vol. 14, no. 3

135--143

EN

In the present paper, the effect of diverse distribution of functionally graded porous material and Kerr elastic foundation on natu-ral vibrations of nanobeams subjected to in-plane forces is investigated based on the nonlocal strain gradient theory. The displacement field of the nanobeam satisfies assumptions of Reddy higher-order shear deformation beam theory. All the displacements gradients are assumed to be small, then the components of the Green-Lagrange strain tensor are linear and infinitesimal. The constitutive relations for functionally graded (FG) porous material are expressed by nonlocal and length scale parameters and power-law variation of material pa-rameters in conjunction with cosine functions. It created possibility to investigate an effect of functionally graded materials with diverse dis-tribution of porosity and volume of voids on mechanics of structures in nano scale. The Hamilton’s variational principle is utilized to derive governing equations of motion of the FG porous nanobeam. Analytical solution to formulated boundary value problem is obtained in closed-form by using Navier solution technique. Validation of obtained results and parametric study are presented in tabular and graphical form. Influence of axial tensile/compressive forces and three different types of porosity distribution as well as stiffness of Kerr foundation on natural frequencies of functionally graded nanobeam is comprehensively studied.

3

The results of consolidation of sinters being deformed under complex loading condition

Rosiak M.

Archives of Metallurgy and Materials

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2013

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Vol. 58, iss. 4

1197--1206

EN

The paper deals with the analysis of the possible application of deformation to sinters under uniaxial compression combined with oscillatory torsion. The main problem of the technology relating to the manufacturing of heavy duty machine components using metal powders is associated with the difficulty to obtain sufficiently high, homogeneously distributed densities across the product volume. The tests were carried out using a test stand allowing the deformation under uniaxial compression combined with torsion. The sintered test specimens were made from the NC 100.24 iron powder. The fabricated sintered test specimens were subject to deformation under the uniaxial compression combined with oscillatory torsion, at three different torsion angle values α = ±30; ±50; ±70. respectively. In order to investigate the effect of different torsion frequencies, each test was made at each torsion angle α for at three different frequencies f = 1 Hz; 0.71Hz; 0.32Hz, respectively, and at the same compression velocity. The results obtained allow to conclude that the application of the combined uniaxial compression and oscillatory torsion (for the preset value of draft) during the tests permitted to obtain the average density of the sinters greater than that obtainable in the case of only unconstrained uniaxial compression. The effect of increased density was enhanced by both the additional torsion-induced deformation, and the tangential stress which would promote the closing of pores.

PL

W pracy analizowano możliwość zastosowania odkształcania spieków w warunkach jednoosiowego ściskania z równoczesnym oscylacyjnym skręcaniem. Głównym problemem technologii wytwarzania elementów maszyn z proszków metali, pracujących w warunkach wysokich obciążeń, jest uzyskiwanie dużej gęstości przy jednorodnym jej rozkładzie w objętości wyrobu. Próby przeprowadzono na stanowisku, pozwalającym na odkształcanie w warunkach jednoosiowego ściskania z równoczesnym skręcaniem. Wsad do wykonania próbek spiekanych stanowił proszek żelaza NC 100.24. Uzyskane próbki spiekane odkształcano w próbie jednoosiowego ściskania z równoczesnym oscylacyjnym skręcaniem w trzech wariantach kąta skręcenia α =±30; ±50; ±70. Dla uwzględnienia wpływu częstotliwości skręceń, dla każdego wariantu kąta skręcenia α, próby realizowano w trzech wariantach częstotliwości f = 1Hz; 0,71 Hz; 0,32Hz i przy jednakowej prędkości ściskania. Uzyskane wyniki pozwoliły stwierdzić, że zastosowanie w czasie próby jednoosiowego ściskania (do zadanej wielkości gniotu) równoczesnego skręcania oscylacyjnego, pozwala uzyskać średnią gęstość spieku większą niż w przypadku zastosowania tylko jednoosiowego ściskania swobodnego. Elementem sprzyjającym wzrostowi gęstości jest dodatkowe odkształcenie wywołane skręcaniem oraz naprężenie styczne sprzyjające efektywniejszemu zamykaniu porów.