Issue 3
JTAM, Sofia, vol. 41 Issue 3 (2011)

Free Vibration of Cracked Functionally Graded Beams with Piezoelectric Patches

Rong Zhang
Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, P. R. China


This paper presents a theoretical investigation on free vibrations of cracked functionally graded beams with piezoelectric patches by using Euler–Bernoulli beam theory and the rotational spring model. The electrical potential along the longitudinal direction is also obtained in terms of the Maxwell equation. Different graded properties and support types are discussed, and the location of the crack is found to be important to the natural frequencies. The mode shape of the electrical potential is found to be proportional to the wave number squared, and it is independent of the location and depth of the crack. The results could serve in the approximation methods for dynamic analyses of piezoelectric composite structures with cracks. Key words: piezoelectric patch; functionally graded beam; edge crack; free vibration; mode shape of electrical potential.

JTAM, Sofia, vol. 41 Issue 3 pp. 03-18 (2011), [Full Article]

Maximums and Locations of Normal Shear Stresses in Railway Rail-Wheel Contact

N. Nikolov1, T. Avdjieva2
1Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria
2Faculty of Physics, University of Sofia “St Kliment Ohridski”, 5, J. Bourchier St., 1164 Sofia, Bulgaria

Contact “rail–wheel” under static load 12 tons is numerically investigated applying design of experiments. The maximal normal and shear stresses and their co-ordinates are mathematically modelled depending on ratios of elastic modules and yield strengths of rail and wheel. Significant influence of rail yield strength is established. Low rail yield strengths than 630MPa shift the maximal normal pressure stress from the loading centre and provoke low shear stresses in large material volumes possessing maximums located in depth 4 mm and distance 12–15 mm. High rail yield strengths than 630 MPa concentrate high shear stresses in small material volumes with maximums located close to the rail surface in depth 1.8 mm and distance 6 mm each from one other. The proposed models and diagrams permit easy estimating the contact effects caused by mechanical characteristics; analyzing and predicting micro-crack behaviour; realizing optimal contact by properly chosen mechanical characteristics of both the rail and wheel materials.

JTAM, Sofia, vol. 41 Issue 3 pp. 19-30 (2011), [Full Article]

Coupled Kelvin-Helmholtz and Tearing Mode Instabilities in the Magnetopause Layer

S. Ivanovski1, M. Kartalev2, P. Dobreva2, G. Vatkova2, T. Chernogorova3
1INAF – Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, 80131 Naples, Italy
2Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bontchev St., Bl. 4, 1113 Sofia, Bulgaria
3Sofia University, Faculty of Mathematics and Informatics, 5, James Bourchier Blvd, 1164, Sofia, Bulgaria

We report results from numerical simulations of the coupled Kelvin-Helmholtz (KH) and tearing mode (TM) instability on the dayside magnetopause layer. We use our earlier proposed numerical scheme utilized in time-dependent two-dimensional approach for solving incompressible MHD equations with three dimensional velocity and magnetic field vectors and with magnetic and fluid viscosities included. Numerical tests with different sets of dimensionless input parameters are performed. The focus is on deriving conditions which lead to the development of the most intensive twin-vortex structures of the computed electric current systems. The computational domain in this context is taken to lie on the equatorial magnetopause region. The inferred instabilities could be candidates for causing mechanism of experimentally observed transient events such as the traveling convective vortices, detected in the ionosphere and on the ground.

JTAM, Sofia, vol. 41 Issue 3 pp. 31-42 (2011), [Full Article]

Nonlinear Dynamics and Stability of Thin Films with Insoluble Surfactants

S. Tabakova1,2
1Department of Mechanics, TU – Sofia, branch Plovdiv, 25, Tzanko Djustabanov, BG-4000 Plovdiv, Bulgaria
2Department of Fluid Mechanics, Institute of Mechanics, BAS, Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria

In the present work the dynamics of a surfactant coated free film, laterally bounded by a solid frame, is studied by means of an evolutionary system consisting of three coupled non-linear Partial Differential Equations (PDE) for the film thickness, lateral velocity and insoluble surfactant concentration. A linear stability analysis is implemented numerically by the method of the differential Gauss elimination. It is found that the film is more stable with the increase of the surfactant concentration (related to the Marangoni number) with respect to antisymmetrical disturbances applied to its shape at different combinations of the Reynolds number, theWeber number, the Hamaker constant and the wetting angle. These results are approximately confirmed by the results of the non-linear stability analysis, from which the evolution of the film thickness, lateral velocity and surfactant concentration is found.

JTAM, Sofia, vol. 41 Issue 3 pp. 43-58 (2011), [Full Article]

Solar Wind-Comet Exosphere Interaction. 1. A Single-Fluid Gas-Dynamic Model

V. Keremidarska1, M. Kartalev1, P. Dobreva1, M. Dryer2
1Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria, Geospace Modeling and Forecasting Center – Institute of Mechanics, GIS Foundation, Sofia Bulgaria
2Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville, AL, 35899, USA

The problem of the single-fluid gas-dynamic modelling of the interaction of mass-loaded solar wind with cometary plasma is reexamined. A simple model, based on the Euler equations with added mass-loading, mass-loss and frictional force terms, is utilized. The developed time marching discontinuity-fitting scheme for searching a steadystate solution leads to a self-consistent determination of the shapes and the positions of the outer and the inner shocks and the contact surface. A new for this task grid characteristic numerical scheme is applied. The influence of processes of photoionization, charge exchange, dissociative recombination and ion-neutral frictional force on the interactional regions structure is studied. Positions of the inner shock and the contact surface are obtained under the action of variety of combinations of these processes.

JTAM, Sofia, vol. 41 Issue 3 pp. 59-76 (2011), [Full Article]

Propagation of Waves at an Imperfectly Bonded Interface between Two Monoclinic Thermoelastic Half-Spaces

Joginder Singh1, Baljeet Singh2, Praveen Ailawalia3
1Department of Mathematics, Indo Global College of Engineering, Abhipur, Mohali, India
2Department of Mathematics, Post Graduate Government College, Sector-11, Chandigarh-160011, India
3Department of Mathematics, RIMT Institute of Engineering and Technology, Mandi Govindgarh, Punjab, India

An imperfectly bonded interface between two monoclinic thermoelastic half-spaces is chosen to study the reflection and transmission of plane waves in context of generalized thermoelasticity. Six relations between amplitudes of incident, reflected and transmitted quasi-P (qP) waves, quasi thermal (qT ) waves and quasi-SV (qSV ) waves are obtained. Some particular cases are obtained which agree with earlier well established results. A procedure for computing reflected and refracted angles is derived for a given incident wave, where the angles of reflection are found not equal to the angles of incident waves in a monoclinic thermoelastic medium.

JTAM, Sofia, vol. 41 Issue 3 pp. 77-92 (2011), [Full Article]