Issue 2
JTAM, Sofia, vol. 52 Issue 2 (2022)

AXIAL BUCKLING ANALYSIS OF FUNCTIONALLY GRADED PLATES (AL/AL2O3) USING NAVIER METHOD

Bouderba Bachir1, Berrabah Hamza Madjid2
1Department of Science and Technology, Mechanical Engineering Materials and Structures Laboratory, Ahmed Ben Yahia Al-Wancharissi University – Tissemsilt, Tissemsilt, Algeria
2Department of Civil Engineering, Mechanical Engineering Materials and Structures Laboratory, Ahmed Zabana University – Relizane, Relizane, Algeria


In the present paper, exact solution of the axial buckling analysis to the functionally graded materials plates (Al/Al2O3) is studied. Using a four variable refined plate theory, both a quadratic variation of the transverse shear strains across the thickness and the zero traction boundary conditions on the top and bottom surfaces of the plate is satisfied without using shear correction factors, from the principle of minimum total potential energy, we obtain the governing equations. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. Numerical examples on the buckling analysis of functionally graded plate demonstrate the accuracy of the present approach.

JTAM, Sofia, vol. 52 Issue 2 pp. 103-117 (2022), [Full Article]

THE APPLICATION OF THE HODOGRAPH METHOD TO FREE SURFACE FLOW PROBLEM

May Manal Bounif, Abdelkader Gasmi
Laboratory of Pure and Applied Mathematics, Faculty of Mathematics and Informatics, University of M'sila, Algeria

The problem of the steady two-dimensional free-surface flow of a fluid under a sluice gate is considered. The hodograph method is used to solve this problem analytically for different values of the inclination angle of the gate wall. The obtained results agree with the experimental and numerical results given by Birkhoff & Zarantonello and Gasmi & Mekias respectively.

JTAM, Sofia, vol. 52 Issue 2 pp. 118-128 (2022), [Full Article]

A METHOD FOR THE SOLUTION OF UNIFORM TORSION OF CARTESIAN ORTHOTROPIC BAR

István Ecsedi, Attila Baksa
Institute of Applied Mechanics, University of Miskolc, H-3515 Miskolc, Miskolc-Egyetemváros, Hungary

The object of this paper is the Saint-Venant torsion of homogeneous orthotropic bar with solid cross section. The solution of the uniform torsion of orthotropic bar with a suitable coordinate transformation is reduced to the solution of the torsion problem of an isotropic solid cross section. Both the torsion function and Prandtl's stress function formulations are used. A new method is given to determine the shape of orthotropic cross section which has the maximal torsional rigidity for a given cross sectional area.

JTAM, Sofia, vol. 52 Issue 2 pp. 129-143 (2022), [Full Article]

AXIAL TRANSONIC COMPRESSOR STALL MECHANISM WITH DIFFERENT ROTATIONAL SPEEDS

Naseem Ahmad1,2, Qun Zheng2, Li Hefei2, Ghulam Ishaque2
1Department of Mechanical Engineering, Institute of Space Technology, Islamabad 44000, Pakistan
2College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China

In the current research work multi passage, steady RANS, and URANS simulations were carried out on NASA rotor 37 to investigate the stall mechanism of the axial transonic compressor with three rotational speeds. 100%, 80%, and 60% rotational speeds were selected to examine the behavior of the rotating stall. The basic flow mechanism was achieved by examining the blade passage field thoroughly. The interaction between the shockwave and TLV produced blockage, which led to rotating stall for 100% and 80% rotational speeds. The spilled flow at the leading edge, which was caused by the TLV was the main reason for the rotating stall at 60% of rotational speed.

JTAM, Sofia, vol. 52 Issue 2 pp. 144-163 (2022), [Full Article]

STABILITY OF THE COUPLED LIQUID-ELASTIC BOTTOM OSCILLATIONS IN A RECTANGULAR TANK

Yuri Kononov1, Oleksandr Lymar2
1Institute of applied mathematics and mechanics, National Academy of Sciences of Ukraine, Sloviansk, Ukraine
2Mykolaiv National Agrarian University, Mykolaiv, Ukraine

Eigenoscillations of the elastic bottom of a rigid (two-dimensional) rectangular tank with an ideal incompressible liquid with irrotational flows, which completely fills it, are were investigated. The elastic bottom is a clamped thin rectangular plate subject to tensile or compressive forces in its middle surface. It is shown that the frequency equation is divided into two equations describing symmetric (even) and antisymmetric (odd) frequencies, and can be written in a single form for these frequencies. For even and odd frequencies, an approximate formula is obtained, from which approximate conditions follow for stability of coupled vibrations of an elastic basis and a liquid. Exact stability conditions are obtained. The stability conditions of the static approach coincide with the exact stability conditions of the dynamic approach. It is shown that the approximate value of the critical bending stiffness for asymmetric frequencies is 0.952 times lower, and for symmetric frequencies – 0.930 times.

JTAM, Sofia, vol. 52 Issue 2 pp. 164-178 (2022), [Full Article]

BOUNDARY LAYER FLOW OF A CONDUCTING HYPERBOLIC NANOFLUID OVER A STRETCHING SURFACE WITH CHEMICAL REACTION AND HEAT SOURCE/SINK

S. Venkateswarlu1, S.V.K. Varma2, R.V.M.S.S Kiran Kumar3
1Department of Mathematics, Vikrama Simhapuri University~College, Kavali-524201, A.P, India
2Department of Mathematics, School of Applied Sciences, REVA University, Bengaluru-560064, Karnataka, India
3Government Polytechnic College, Anantapur-515002, A.P, India

In this article, a steady incompressible stagnation point flow of a conductive hyperbolic radiative nano-liquid past a stretching surface is investigated. The effects of heat generation/absorption and first-order destructive chemical reactions are considered. The Buongiorno's nanofluid model is used to study the combined effects of thermophoresis and Brownian motion. The governing higher order non-linear partial differential equations (PDE's) are transformed to a set of ordinary differential equations (ODE's) by applying suitable similarity relations. The resulting ordinary differential equations are numerically solved with the help of a boundary value problem default solver in MATLAB bvp4c tool. The attitude of fluid velocity, temperature and concentration on various flow quantities are analyzed through tables and figures. From the outcomes, we observed that for raising the values of Weissenberg's number the fluid velocity is diminished.

JTAM, Sofia, vol. 52 Issue 2 pp. 179-196 (2022), [Full Article]