Issue 2
JTAM, Sofia, vol. 35 Issue 2 (2005)

Simulation and Solution of the Classical Mechanics Mechanical and Mathematical Vibration Models on a Higher Order Dimensional Space

Y. Ts. Tsankov, Al. B. Kazakoff
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria


The objective of the work presented in this paper is an attempt at presenting and solving the known from the classical mechanics two-dimensional plane single mass mechanical and mathematical vibration models in a higher order dimensional space. A characterisation of the Riemannian Manifolds is performed for this purpose by means of curvature operators. The computer codes Mathematica and MATLAB are used in the numerical simulation. The object of a higher order dimensional space is a sphere, and motion transformation is performed onto it. The system motion is investigated in a qualitative aspect in time and frequency domain.

JTAM, Sofia, vol. 35 Issue 2 pp. 01 (2005)

Analytical Modelling for Bend Stress Relaxation Tests Facilitating the Identification of Creep Parameters

N. Georgiev, C. Kouyumdjiev
Department of Technical Mechanics, “Angel Kanchev” University of Rousse, 8, Studentska Str., 7017 Rousse, Bulgaria

Bend stress relaxation tests are routinely used to study the creep behaviour of various materials usually by qualitative comparisons of experimental data. Two approaches: analytical and numerical allowing more profound quantitative description of these processes were proposed in ref. [4]. A generalization of the analytical model [4] valid for the general case of nonlinear stress distribution is developed in the present paper. It is shown that this model gives the same results as more complete numerical model [4] keeping the advantages of the closed form solution. Furthermore it is an effective basis for further development of methods of identifying materials creep parameters by using bend stress relaxation tests.

JTAM, Sofia, vol. 35 Issue 2 pp. 02 (2005)
BIEM for 3D Wave Propagation in a Laterally Varying Media

P. Dineva1, V. Saykov2
1Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, Sofia 1113, Bulgaria
2Department of Computer Sciences, New Bulgarian University, 21, Montevideo Str., Sofia 1618, Bulgaria

It is proposed three-dimensional mechanical model describing seismic wave propagation in a laterally varying media. 3D boundary-integral equation method (BIEM) is created and accompanied software is developed for synthesis of theoretical seismograms on the free surface of a local finite seismic region situated in a half-space and excited by incident seismic waves. Validation study that estimates the accuracy of the method is done by solution of the test example for wave propagation in an elastic isotropic cube placed in a half–space with mechanical properties equal to these of the soil in the half-space. Parametric study revealing the influence of the properties of both the incident seismic wave and the inhomogeneity of the soil half-space on the 3D seismic signal at the free surface of the considered local seismic region is presented. It is shown by the obtained numerical results that the difference between the amplitudes of the seismograms obtained without and with existence of the heterogeneity–the finite elastic cube, that simulates the local finite geological region, can change strongly the seismic signal.

JTAM, Sofia, vol. 35 Issue 2 pp. 03 (2005)
Application of the Classical Linear Elastic Beam Theory for Analysis of the Mode III Crack Propagation in Composite Materials

Angel Mladensky, Victor Rizov
University of Architecture, Civil Engineering and Geodesy, 1, Chr. Smirnensky Blvd., 1046 Sofia, Bulgaria

In the present study, the object of investigation is the Mode III crack propagation in an unidirectional fibre reinforced composite beam. The crack propagates longitudinally to the beam axis, parallel to the reinforcing fibers. An analytical solution of the problem for determination of the strain energy release rate is obtained. For this purpose the values of the crack front internal forces are used. The solution is obtained on the basis of the linear elastic fracture mechanics. The accuracy of the formula obtained is confirmed by comparison with a finite element solution. A parametrical investigation of crack position influence on strain energy release rate is also carried out.

JTAM, Sofia, vol. 35 Issue 2 pp. 04 (2005)
Three Point Bend Test of Sub-Size Charpy Specimens for Fracture Toughness Evaluation

G. Kortenski
Institute of Metal Science, Bulgarian Academy of Sciences, 67, Shipchensky Prohod Str., 1574 Sofia, Bulgaria

A preliminary study is done to qualify a fracture toughness procedure for miniature Charpy specimens (3 × 4 × 27 mm) loaded in three point bending. Several aspects are investigated such as: determination of reference temperature T0, fracture toughness of steels in transition regime and master curve approach. Results obtained on a test case of 24 specimens are very satisfactory.

JTAM, Sofia, vol. 35 Issue 2 pp. 05 (2005)
On Correlations and Fractal Characteristics of Time Series

Nikolay K. Vitanov1, Kenshi Sakai2, Elka D. Yankulova3
1Institute of Mechanics, Bulgarian Academy of Sciences, Akad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
2Tokyo University of Agriculture and Technology, 3-5-8, Saiwai-cho, Fuchu-shi, Tokyo, 183-8509, Japan
3Faculty of Biology, "St. Kliment Ohridski" University of Sofia, 8, Dragan Tsankov Blvd., 1162 Sofia, Bulgaria

Correlation analysis is convenient and frequently used tool for investigation of time series from complex systems. Recently new methods such as the multifractal detrended fluctuation analysis (MFDFA) and the wavelet transform modulus maximum method (WTMM) have been developed. By means of these methods (i) we can investigate long-range correlations in time series, and (ii) we can calculate fractal spectra of these time series. But opposite to the classical tool for correlation analysis - the autocorrelation function, the newly developed tools are not applicable to all kinds of time series. The inappropriate application of MFDFA or WTMM leads to wrong results and conclusions. In this article we discuss the opportunities and risks connected to the application of the MFDFA method to time series from a random number generator and to experimentally measured time series (i) for accelerations of an agricultural tractor, and (ii) for the heartbeat activity of Drosophila melanogaster. Our main goal is to emphasize on what can be done and what cannot be done by the MFDFA as tool for investigation of time series.

JTAM, Sofia, vol. 35 Issue 2 pp. 06 (2005)
An Approach for Gait Symmetry Assessment

L. Angelova, Y. Toshev
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria

Quantifying asymmetries in gait patterns it is the first step in trying to define what degree of asymmetry is acceptable in patient’s gait patterns during the rehabilitation process. The present study concerns the application of a dynamic symmetry criterion based on a subdivision of the double support phases at the instantaneous time point of gait cycle when both left and right vertical ground reactions are equal. This special gait asymmetry characteristic for a group of normal subjects compared to a group of THR (total hip replacement) patients is evaluated. The results showed the approach was encouraging to provide useful insights into the effect of joint replacement on a patient walking ability and it could be a base to develop a biofeedback to train patients.

JTAM, Sofia, vol. 35 Issue 2 pp. 07 (2005)