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CONTENTS
Volume 6, Number 3, May 2019
 

Abstract
In this work, a novel first-order shear deformation beam theory is applied to explore the vibration and buckling characteristics of thick functionally graded beams. The material properties are assumed to vary across the thickness direction in a graded form and are estimated by a power-law model. A Fourier series-based solution procedure is implemented to solve the governing equation derived from Hamilton\'s principle. The obtained results of natural frequencies and buckling loads of functionally graded beam are checked with those supplied in the literature and demonstrate good achievement. Influences of several parameters such as power law index, beam geometrical parameters, modulus ratio and axial load on dynamic and buckling behaviors of FGP beams are all discussed.

Key Words
vibration; buckling; functionally graded beams; refined first shear deformation theory, coupled effect

Address
Ahmed Bekhadda, Abdelmadjid Cheikh, Ismail Bensaid,
Abdelhamid Hadjoui: IS2M Laboratory, Faculty of Technology, Mechanical engineering Department, University Abou Beckr Belkaid (UABT), Tlemcen, Algeria

Ahmed A. Daikh: Mechanics of structures and solids Laboratory, Department of Mechanical Engineering,
Faculty of Technology, PO Box 89, University of Sidi Bel Abbes, Algeria

Abstract
Current investigation deals with the thermal stability characteristics of carbon nanotube reinforced composite beams (CNTRC) on elastic foundation and subjected to external uniform temperature rise loading. The single-walled carbon nanotubes (SWCNTs) are supposed to have a distribution as being uniform or functionally graded form. The material properties of the matrix as well as reinforcements are presumed to be temperature dependent and evaluated through the extended rule of mixture which incorporates efficiency parameters to capture the size dependency of the nanocomposite properties. The governing differential equations are achieved based on the minimum total potential energy principle and Euler-Bernoulli beam model. The obtained results are checked with the available data in the literature. Numerical results are supplied to examine the effects of numerous parameters including length to thickness ratio, elastic foundations, temperature change, and nanotube volume fraction on the thermal stability behaviors of FG-CNT beams.

Key Words
FG-CNT beams; thermal buckling; elastic foundation; thermal effects

Address
Ismail Bensaid: IS2M Laboratory, Faculty of Technology, Department of Mechanical Engineering, University Abou Beckr Belkaid (UABT), Tlemcen, Algeria

Bachir Kerboua: Mechanical Engineering Department, University Abou Beckr Belkaid (UABT), Tlemcen, Algeria

Abstract
A spike attached to a blunt nosed body significantly alters its flow field and influences the aerodynamic coefficients at hypersonic speed. The basic body is an axisymmetric, with a hemisphere nose followed by a cylindrical portion. Five different types of spikes, namely, conical aerospike, hemisphere aerospike, flat-face aerospike, hemisphere aerodisk and flat-face aerodisk are attached to the basic body in order to assess the aerodynamic characteristic. The spiked blunt body without the aerospike or aerodisk has been set to be a basic model. The coefficients of drag, lift and pitching moment were measured with and without blunt spike body for the length-to-diameter ratio (L/D) of 0.5, 1.0, 1.5 and 2.0, at Mach 6 and angle of attack up to 8 degrees using a strain gauge balance. The measured forces and moment data are employed to determine the relative performance of the aerodynamic with respect to the basic model. A maximum of 77 percent drag reduction was achieved with hemisphere aerospike of L/D = 2.0. The comparison of aerodynamic coefficients between the basic model and the spiked blunt body reveals that the aerodynamic drag and pitching moment coefficients decrease with increasing the L/D ratio and angle of attack but the lift coefficient has increasing characteristics.

Key Words
aerodynamics coefficients; aerospike; aerodisk; blunt body; fluid dynamics; hypersonic flow; pitching moment; shock wave; space vehicle

Address
R. Kalimuthu: Vikram Saarabhai Space Centre, Trivandrum 695022, India

R. C. Mehta: Department of Aeronautical Engineering, Noorul Islam Centre for Higher Education,
Kumaracoil 629180, India

E. Rathakrishnan: Department of Aerospace Engineering, Indian Institute of Technology, Kanpur 208016, India

Abstract
This study develops a dual purpose: i) evaluating the effects of two different Mars atmosphere models (NASA Glenn and GRAM-2001) on aerodynamics of a capsule (Pathfinder) entering the Mars atmosphere, ii) verifying the feasibility of evaluating the ambient density and pressure by means of the methods by McLaughlin and Cassanto, respectively and therefore to re-build the values provided by the models. The method by McLaughlin relies on the evaluation of the capsule drag coefficient, the method by Cassanto relies on the measurement of pressure at a point on the capsule surface in aerodynamic shadow. The study has been carried out computationally by means of: i) a code integrating the equations of dynamics of the capsule for the computation of the entry trajectory, ii) a DSMC code for the solution of the flow field around the capsule in the altitude interval 50-100 km. The models show consistent differences at altitudes higher than about 40 km. It seems that the GRAM-2001 model is more reliable than the NASA Glenn model. In fact, the NASA Glenn model produces, at high altitude, temperatures that seem to be too low compared with those from the GRAM-2001 model and correspondingly very different aerodynamic conditions in terms of Mach, Reynolds and Knudsen numbers. This produces pretty different capsule drag coefficients by the two models as well as pressure on its surface, making not feasible neither the method by McLaughlin nor that by Cassanto, until a single, reliable model of the Mars atmosphere is not established. The present study verified that the implementation of the Cassanto method in Mars atmosphere should rely (such as it is currently) on pressure obtained experimentally in ground facilities.

Key Words
Mars atmosphere models; pathfinder capsule; computation of entry trajectory; methods evaluating ambient density and pressure; DSMC method

Address
Gennaro Zuppardi: Department of Industrial Engineering – Aerospace Division, University of Naples \"Federico II\", Piazzale Tecchio, 80 – 80125 Naples, Italy

Abstract
Numerical study of the flutter of a plate on a viscoelastic foundation is carried out in the paper. Critical velocity of the flutter of a plate on an elastic and viscoelastic foundation is determined. The mathematical model for the investigation of viscoelastic plates is based on the Marguerre\'s theory applied to the study of the problems of strength, rigidity and stability of thin-walled structures such as aircraft wings. Aerodynamic pressure is determined in accordance with the A.A. Ilyushin\'s piston theory. Using the Bubnov - Galerkin method, the basic resolving systems of nonlinear integro-differential equations (IDE) are obtained. At wide ranges of geometric and physical parameters of viscoelastic plates, their influence on the flutter velocity has been studied in detail.

Key Words
mathematical modeling; numerical algorithms; supersonic flutter; viscoelastic foundation

Address
Bakhtiyar Alimovich Khudayarov: Department of Higher Mathematics, Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Tashkent, 100000, Uzbekistan


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