Issue 4
JTAM, Sofia, vol. 46 Issue 4 (2016)

High-Speed Rotor Analytical Dynamics on Flexible Foundation Subjected to Internal and External Excitation

Venelin S. Jivkov1, Evtim V. Zahariev2
1Technical University of Sofia, 8 St. Kliment Ohridski Blvd., 1000 Sofia, Bulgaria
2Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria


The paper presents a geometrical approach to dynamics simulation of a rigid and flexible system, compiled of high speed rotating machine with eccentricity and considerable inertia and mass. The machine is mounted on a vertical flexible pillar with considerable height. The stiffness and damping of the column, as well as, of the rotor bearings and the shaft are taken into account. Non-stationary vibrations and transitional processes are analyzed. The major frequency and modal mode of the flexible column are used for analytical reduction of its mass, stiffness and damping properties. The rotor and the foundation are modelled as rigid bodies, while the flexibility of the bearings is estimated by experiments and the requirements of the manufacturer. The transition effects as a result of limited power are analyzed by asymptotic methods of averaging. Analytical expressions for the amplitudes and unstable vibrations throughout resonance are derived by quasi-static approach increasing and decreasing of the exciting frequency. Analytical functions give the possibility to analyze the influence of the design parameter of many structure applications as wind power generators, gas turbines, turbo-generators, and etc. A numerical procedure is applied to verify the effectiveness and precision of the simulation process. Nonlinear and transitional effects are analyzed and compared to the analytical results. External excitations, as wave propagation and earthquakes, are discussed. Finite elements in relative and absolute coordinates are applied to model the flexible column and the high speed rotating machine. Generalized Newton – Euler dynamics equations are used to derive the precise dynamics equations. Examples of simulation of the system vibrations and nonstationary behaviour are presented.

JTAM, Sofia, vol. 46 Issue 4 pp. 03-18 (2016), [Full Article]

Wave Scattering by Cracks at Macro- and Nano-Scale in Anisotropic Plane by Boundary Integral Equation Method

Petia Dineva1, Tsviatko Rangelov2
1Institute of Mechanics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
2Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria

Elastic wave scattering by cracks at macro- and nano-scale in anisotropic plane under conditions of plane strain is studied in this work. Furthermore, time-harmonic loads due to incident plane longitudinal P- or shear SV- wave are assumed to hold. In a subsequent step, the elastodynamic fundamental solution for general anisotropic continua derived in closed-form via the Radon transform is implemented in a numerical scheme based on the traction boundary integral equation method (BIEM). The surface elasticity effect in the case of nano-crack is taken into consideration via non-classical boundary condition along the crack surface proposed by Gurtin and Murdoch [1]. The numerical results obtained herein reveal substantial differences between anisotropic materials containing a macro- and a nano-crack in terms of their dynamic stress response, where the latter case demonstrates clearly the strong influence of the size-effects. Finally, these types of examples serve to illustrate the present approach and to show its potential for evaluating the stress concentration fields (SCF) inside cracked nanocomposites. The obtained results concern the reliability and safety of the advancing nanomaterials.

JTAM, Sofia, vol. 46 Issue 4 pp. 19-35 (2016), [Full Article]

Static Structural and Modal Analysis Using Isogeometric Analysis

Sangamesh Gondegaon, Hari K. Voruganti
Department of Mechanical Engineering, National Institute of Technology, Warangal, India-506004

Isogeometric Analysis (IGA) is a new analysis method for unification of Computer Aided Design (CAD) and Computer Aided Engineering (CAE). With the use of NURBS basis functions for both modelling and analysis, the bottleneck of meshing is avoided and a seamless integration is achieved. The CAD and computational geometry concepts in IGA are new to the analysis community. Though, there is a steady growth of literature, details of calculations, explanations and examples are not reported. The content of the paper is complimentary to the existing literature and addresses the gaps. It includes summary of the literature, overview of the methodology, step-by-step calculations and Matlab codes for example problems in static structural and modal analysis in 1-D and 2-D. At appropriate places, comparison with the Finite Element Analysis (FEM) is also included, so that those familiar with FEM can appreciate IGA better.

JTAM, Sofia, vol. 46 Issue 4 pp. 36-75 (2016), [Full Article]

Optimization of the Conditions of Convective Drying of Thermosensitive Materials

M. K. Alyzhanov1, M. R. Sikhimbayev2, S. B. Kuzembayev1, K. T. Sherov1, D. R. Sikhimbayeva2, T. A. Khanov2, T. B. Kurmangaliyev3, D. E. Elemes3, B. S. Donenbayev1, M. M. Musaev1, T. M. Buzauova1
1Karaganda State Technical University, 56 B. Mira St., 100027 Karaganda, Kazakhstan
2Karaganda Economic University, 9 Akademicheskaya St., 100009 Karaganda, Kazakhstan
3D. Serikbayev East Kazakhstan State Technical University, 69 Protazanova St., 070004 Ust-Kamenogorsk, Kazakhstan

The article proposes the solution of the problem with the application of thermal vibrations of heat-carrier flow in processes of convective drying, for the purpose of theoretical determination of optimum conditions of short-term excess of handling temperature, that do not influence the decrease of technological characteristics of the thermosensitive materials.

JTAM, Sofia, vol. 46 Issue 4 pp. 76-84 (2016), [Full Article]

Effect of a Convective Boundary Condition on Boundary Layer Slip Flow and Heat Transfer over a Stretching Sheet in View of the Exact Solution

Mona D. Aljoufi, Abdelhalim Ebaid
Department of Mathematics, Faculty of Science, University of Tabuk, P. O. Box 741, Tabuk 71491, Saudi Arabia

The exact solutions of a nonlinear differential equations system, describing the boundary layer flow over a stretching sheet with a convective boundary condition and a slip effect have been obtained in this paper. This problem has been numerically solved by using the shooting method in literature. The aim of the current paper is to check the accuracy of these published numerical results. This goal has been achieved via first obtaining the exact solutions of the governing nonlinear differential equations and then, by comparing them with the approximate numerical results reported in literature. The effects of the physical parameters on the flow field and the temperature distribution have been re-investigated through the new exact solutions. The main advantage of the current paper is the simple computational approach that has been introduced to analyze exactly the present physical problem. This simple analytical approach can be further applied to investigate similar problems. Although no remarkable differences have been detected between the current figures and those obtained in literature, the authors believe that if some numerical calculations were available for the fluid velocity and the temperature in literature then the convergence criteria and the accuracy of the shooting method used in Ref. [15] can be validated in view of the current exact expressions.

JTAM, Sofia, vol. 46 Issue 4 pp. 85-95 (2016), [Full Article]