BULGARIAN ACADEMY OF SCIENCES NATIONAL COMMITTEE OF THEORETICAL AND APPLIED MECHANICS Journal of Theoretical and Applied MechanicsPrint
ISSN: 0861-6663 Online ISSN: 1314-8710 |

Journal of Theoretical and Applied Mechanics, Sofia, vol.

**54**Issue 3 (2024)#### Table of contents

**EFFECT OF TEMPERATURE DEPENDENT VISCOSITY ON THERMAL INSTABILITY OF OLDROYDIAN VISCOELASTIC FLUID LAYER SATURATING POROUS MEDIUM**

Joginder Singh Dhiman

^{1}, Praveen K. Sharma

^{2}, Khushboo Gupta

^{1}

^{1}

*Himachal Pradesh University, Department of Mathematics & Statistics, Shimla, India, 171005*

^{2}

*Himachal Pradesh University, University Institute of Technology (UIT), Shimla, India, 171005*

The effect of temperature-dependent viscosity on the onset of
thermal convection in a viscoelastic fluid-saturating porous medium is studied
for different cases of combination of rigid and dynamically free boundaries,
Darcy-Brinkman-Oldroyd model is considered to investigate the rheological
behaviour of the fluid. A necessary condition for the existence of overstability
is derived, analytically. The values of critical Darcy-Rayleigh numbers for
both stationary and oscillatory convection with linear and exponential viscosity
variations (i.e. temperature-dependent viscosity) are computed numerically,
using the Galerkin technique. The effects of rheological parameters, modified
Darcy number, wave number and variable viscosity parameter on the stability
of the system are computed numerically and depicted graphically for each case
of combinations of boundary conditions. It is observed that the viscoelastic
parameters; stress relaxation time and strain retardation time do not affect the
onset of stationary convection, whereas the stress relaxation time has destabilizing
effect and strain retardation time has stabilizing effect on the onset of oscillatory
convection. It is also found that the temperature-dependent viscosity
and modified Darcy number have a stabilizing effect on the onset of stationary
as well as oscillatory convection for each case of boundary conditions.

JTAM, Sofia, vol. **54**Issue 3 pp. 255-277 (2024), [

**Full Article**]

**TIME-DEPENDENT DELAMINATION OF MULTILAYERED INHOMOGENEOUS BEAM LOADED IN PURE TORSION: AN ANALYTICAL SOLUTION**

V. Rizov

^{}

*Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 - Sofia Bulgaria*

The multilayered inhomogeneous beam configuration considered
in this paper exhibits delamination fracture that is time-dependent due to the
viscoelastic behaviour. Besides, the two external torsion moments applied on
the beam vary smoothly with time. The beam has a rectangular cross-section.
The layers of the beam are continuously inhomogeneous in longitudinal direction.
The two crack arms are loaded in pure torsion. A solution of the
strain energy release rate for the delamination is derived by analyzing the timedependent
strain energy stored in the beam structure. An alternative method
based on the analysis of the beam compliances under the two torsion moments
is applied in order to verify the solution of the strain energy release rate.

JTAM, Sofia, vol. **54**Issue 3 pp. 278-291 (2024), [

**Full Article**]

**TRANSVERSE CRACK AND MASS UNBALANCE INTERACTION IN A SPINNING ROTOR: A THEORETICAL STUDY**

Nabam Teyi

^{}, Sandeep Singh

^{}

*Department of Mechanical Engineering, North Eastern Regional Institute of Science and Technology, Nirjuli, Arunachal Pradesh, India – 791109*

This paper investigates the response of a cracked rotor to varying
angles between the crack front and the unbalanced force vector caused by
changing centrifugal forces. A rotor with a switching crack is first mathematically
represented, and then the response is generated using SIMULINK. At
varied angles, the combined effect of crack and imbalance is observed. Maximum
and minimum rotor deflection values are depicted on the orbit plots,
and their difference with respect to the angles are noted. For various harmonics
and vibration amplitudes, a full-spectrum Fast Fourier Transform (FFT) is
conducted. Using FFT plots, the critical amplitude of vibrations for each variable
angle is determined, and observations are given. This report finishes with
some concluding remarks.

JTAM, Sofia, vol. **54**Issue 3 pp. 292-307 (2024), [

**Full Article**]

**EFFECT OF THE INFLUENCE OF THE DIFFERENT CORROSION LEVEL ON THE REPAIR EFFICIENCY OF MARINE AND OFFSHORE STRUCTURES BY BONDED COMPOSITE**

B. Belarbi

^{1}, M.S. Bennouna

^{2,3}, K. Sadek

^{2}, B. Aour

^{2}, E. Abdelouahed

^{2}, B.A. Bachir Bouiadjra

^{4}, A. Talha

^{5}

^{1}

*University of Tlemcen, Algeria*

^{2}

*LABAB Laboratory, National Polytechnic School Maurice Audin, Oran, 31000, Algeria*

^{3}

*Applied Science Faculty, Kasdi Merbah University, Waregla 30000, Algeria*

^{4}

*LMPM Laboratory, University of Sidi Bel Abbes 22000, Algeria*

^{5}

*Lille Mechanics Unit, University of Lille, (UML, EA 7512), University of Lille, 59655 Villeneuve d’Ascq, France*

In this research paper, we examined the effectiveness of repairing
corroded marine structures using bonded composites through finite element
analysis (FEM) to evaluate the J Integral. Our focus is to provide an overview
of the behavior of a cracked and corroded plate repaired with a boron patch
and bonded with (Araldite 2015). To obtain optimized results, we studied the
effects of eight corrosion levels under different loading and temperature conditions.
The selected temperatures were

JTAM, Sofia, vol. *T*= 80°C and room temperature*T*= 25°C. The structure is under different mechanical loading of amplitude*F*= 220, 240, 260, 280, 300, 320, 340, 360 MPa.The analysis shows that increasing loading and corrosion levels result an increase in J Integral. The detachment of patches was evaluated under high loading (*F*= 360 MPa) for corrosion level*a*= 4.0 mm/year.**54**Issue 3 pp. 308-322 (2024), [

**Full Article**]

**GENERATING NON-MONOPHONIC MUSIC WITH VARIATIONAL AUTOENCODER: A CASE STUDY**

Ivan K. Yanakiev

^{}

*Institue of Mechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria*

The paper proposes an approach for generating musical pieces
based on the Variational Auto Encoder (VAE) and realized in the MATLAB
framework. In the work the architecture of the used VAE is described and also
its training with dataset from the MAESTRO MIDI Dataset. The aim of the
work is to study to what extent the used VAE is suitable for learning and representing
musical structure. The resulting pieces show some features of musical
structure on a mid-term temporal scale. It is concluded that the model successfully
represents traits of general musical structure on the broader timescale
as well as some short-scale musical figures. However, it fails to account for
time-related musical structure of the long-term musical architectonics.

JTAM, Sofia, vol. **54**Issue 3 pp. 323-338 (2024), [

**Full Article**]

**NUMERICAL STUDY OF 2D STEADY FLUID FLOW IN LID-DRIVEN RECTANGULAR DOMAIN WITH TEMPERATURE EFFECT USING HYBRID FINITE VOLUME METHOD**

V. Ambethkar

^{}, Jyoti

^{}

*Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi-110007, India*

This paper investigates the numerical simulation for the two dimensional
(2D) steady fluid flow by using hybrid finite volume method in the
lid-driven rectangular domain. The top wall is moving with a constant speed
in the positive horizontal direction and other walls are in rest. Different constant
temperature are applied to the top and bottom wall and left and right walls
are thermally insulated. The dimensionless governing equations are discritized
using the hybrid scheme of finite volume method. The SIMPLE algorithm is
used to compute the numerical solution of the flow variables such as

JTAM, Sofia, vol. *u*-velocity,*v*-velocity, pressure (*p*) and temperature (θ).*u*-velocity is maximum on the top wall and it is decreasing as we go down till the geometric center.*v*-velocity is maximum near the top left corner and minimum near the top right corner of the domain. Pressure contour graph shows the maximum pressure near the top right corner and minimum near top left corner. Temperature contour graph shows the maximum temperature on the bottom wall and it will decrease as we goes towards the top wall.**54**Issue 3 pp. 339-355 (2024), [

**Full Article**]

**ANALYTICAL STUDY OF PARALLEL PLATE FLOW OF A NEWTONIAN FLUID WITH SPATIAL VARIATIONS IN VISCOSITY**

Mehmet Pakdemirli

^{}

*Mechanical Engineering Department, Manisa Celal Bayar University, 45140, Muradiye, Yunusemre, Manisa, Turkey*

One dimensional Newtonian fluid flow between fixed parallel
plates is considered. The viscosity is not constant but changes with the spatial
variable of height. Two different classes of problems are treated: 1) Continuous
changes in the viscosity, 2) Discontinuous changes in the viscosity. In the
first class, general integral form solutions are given first and then, for the four
different viscosity functions, the velocities and the discharges are calculated.
For the second class of discontinuous changes, two problems are solved: 1)
Two different immiscible fluids one laying on top of the other, 2) An intermediate
high viscosity fluid lubricated by a low viscosity thin layer fluid at the
boundaries. Velocity profiles and discharges are calculated for both cases. It is
found that spatial viscosity variations have substantial effects on the velocity
profiles and discharges and cannot be ignored for a precise treatment.

JTAM, Sofia, vol. **54**Issue 3 pp. 356-365 (2024), [

**Full Article**]