Issue 3
JTAM, Sofia, vol. 55 Issue 3 (2025)

COMPARATIVE ANALYSIS OF THE NUMERICAL METHODS FOR INVESTIGATING MAGNETIC MOMENT PRECESSION IN φ0-JOSEPHSON JUNCTIONS

P. Atanasova1,2, E. Dieva1
1Faculty of Mathematics and Informatics, University of Plovdiv, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
2Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria


The Josephson junction, a fascinating element in superconductivity, is a cornerstone of quantum computer hardware. Analyzing this object requires solving differential equations, often beyond the scope of analytical solutions. This article focuses on a model of the φ0-Josephson junction, which describes the magnetic moment precession. A critical aspect of this investigation is addressing system stiffness, a common challenge in numerical simulations. Various numerical methods are rigorously compared to evaluate their efficiency. The study highlights the key contributions to identifying effective numerical methods for accurately solving stiff systems of the junction model and demonstrating their applicability to previously inaccessible parameter regimes. This paper presents the first use of certain methods for this model, achieving higher accuracy and effectively managing stiffness.

JTAM, Sofia, vol. 55 Issue 3 pp. 263-277 (2025), [Full Article]

THERMAL AGING EFFECT ON MECHANICAL PROPERTIES OF 30% GLASS FIBER REINFORCED POLYAMIDE 11

Nikolay Georgiev, Krasimir Staykov, Damyan Ganchev
Faculty of Mechanical Engineering, Technical University of Sofia, Bulgaria

This study investigates the effects of artificial thermal aging on the mechanical properties of 30% glass fiber-reinforced Polyamide 11 (PA11-GF30). Tensile and compression tests were conducted on specimens aged at 125°C, 150°C, and 175°C for up to 4152 hours. The results indicate a progressive decline in mechanical properties, with tensile strength decreasing from an initial 104.6 MPa to 92.63 MPa (12.4% reduction) at 125°C, 73.96 MPa (34.3% reduction) at 150°C, and 74.36 MPa (33.8% reduction) at 175°C. Similarly, compressive strength declined from 135.59 MPa to 122.81 MPa (9.4% reduction) at 125°C, 124.28 MPa (8.3% reduction) at 150°C, and 104.76 MPa (22.7% reduction) at 175°C. Notably, an initial strengthening phase was observed due to post-crystallization, particularly at lower temperatures. Elongation at break exhibited a sharp decline, confirming the transition from ductile to brittle behavior, with samples at 150°C and 175°C reaching the 5% brittleness threshold after 2016 hours and 1344 hours, respectively. These findings provide critical insights for the design and application of PA11-GF30 in high-temperature environments, supporting its use in automotive, aerospace, and industrial sectors requiring durable polymer-based components.

JTAM, Sofia, vol. 55 Issue 3 pp. 278-288 (2025), [Full Article]

NUMERICAL STUDY OF PRESSURE FIELD UNDER VARIOUS REGIME FLOW INSIDE RECESS OF AN ORIFICE COMPENSATED HYDROSTATIC BEARING

Slimane Ghouas1, Faiza Ghezali2, Ahmed Bouzidane3, Tayeb Yahiaoui1, Thomas Marc4
1Laboratory of Aeronautics and Propulsion Systems, Faculty of Mechanics, University of Science and Technology of Oran - Mohammed Boudiaf, B.O. Box 1505, El-M'Naouer, 31000, Oran, Algeria
2Structural and Solid Mechanics Laboratory, Department of Mechanical Engineering, Djillali Liabes's University of Sidi Bel Abbés, BP 89 BEN mhidi, Sidi-Bel-Abbés (22000), Algeria
3Research Laboratory of Industrial Technologies, Department of Mechanical Engineering, University Tiaret, BP 78 City/Province, Tiaret 14000, Algeria
4Department of Mechanical Engineering, École de Technologie Supérieure, 1100 Notre-Dame Street West, Montreal, Quebec, (H3C 1K3), Canada

This research investigates the effects of regime flow in recess on the pressure distribution within a hydrostatic bearing flat pad supplied by an orifice restrictor. The validation of the findings is conducted using Reynolds' analytical method, which demonstrates a strong correlation with computational fluid dynamics (CFD) simulations, particularly when the Reynolds number in the recess is maintained below 1000. The simulations were carried out using the SST-kω turbulence model. The results reveal that a reduction in viscosity has a pronounced effect on lubrication efficiency. Furthermore, it was observed that deeper recesses yield a more uniform pressure distribution in contrast to shallower recesses, and an increase in the eccentricity ratio results in the presence of the Rayleigh step throughout the entire pressure supply spectrum.

JTAM, Sofia, vol. 55 Issue 3 pp. 289-301 (2025), [Full Article]

ON VIBRO-ACOUSTIC RADIATION OF AN UNDERWATER SHELL CABIN: A REFINED BEM METHOD AND COMPARISON WITH EXPERIMENT

Zhenxing Yu1, Peng Li2, Kuai Liao2
1School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu, 610031, P.R. China
2Nuclear Power Institute of China, Chengdu, 610041, P.R. China

This paper introduces a refined Boundary Element Method (BEM) and its application in analyzing the propagation of shell vibration noise within the surrounding water. This method discretizes the structural boundary utilizing constant quadrilateral elements, facilitating the computation of singular integrals. Additionally, incorporating the CHIEF method ensures the uniqueness of the solution in Conventional Boundary Integral Equations (CBIE) under low-frequency vibration conditions. This method is used to analyze the sound radiation of the cylindrical shell experimental model, and the correctness of it is proved by comparing it with the FEM numerical simulation and experimental data. On this basis, a further examination of the model's acoustic radiation efficiency and modal behavior is conducted.

JTAM, Sofia, vol. 55 Issue 3 pp. 302-324 (2025), [Full Article]

DYNAMICS OF AXIALLY MOVING PLATES IMMERSED IN FLUID SUBJECTED TO FOLLOWER FORCE

Hong Ying Li, Qin Jing Ji, Ming Yao Zhang, Jian Li
Key Laboratory of Structural Dynamics of Liaoning Province, College of Sciences, Northeastern University, Shenyang 110819, China

The dynamics is investigated for an axially moving immersed plate subjected to time-dependent tension and follower force. The study is focused on simultaneous resonant cases i.e. principal parametric resonance and subharmonic resonance. Based on von Kármán plate theory and D'Alambert's principle, the vibration equations of the plate are derived. Employing the method of multiple scales, simultaneous resonance is discussed. Stability of periodic solutions of the system is examined by Lyapunov's stability theory. By analyzing the influence of follower load amplitude and tuning parameter on the steady-state periodic motion of simultaneous resonances, the system displays complex and variable dynamical behaviors. Furthermore, the approximate analytical results are verified by using the Runge-Kutta method.

JTAM, Sofia, vol. 55 Issue 3 pp. 325-342 (2025), [Full Article]

SH WAVE SCATTERING BY A NANOCRACK IN A GRADED PIEZOELECTRIC HALF-PLANE WITH NANORELIEF

Tsviatko V. Rangelov1, Petia S. Dineva2
1Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria
2Institute of Mechanics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria

The study focuses on an exponentially graded piezoelectric (PEM) half-plane featuring a nanorelief along its surface boundary, which also includes a blunt nanocrack. The system is subjected to anti-plane time-harmonic elastic SH waves propagating at an incident angle in the nano half-plane. The model integrates the continuum mechanics approach with the Gurtin-Murdoch surface elasticity model. An efficient, non-hypersingular traction boundary integral equation method (BIEM) is developed, verified, and applied in simulation studies. This method is based on an analytically derived Green`s function for a graded PEM half-plane. A parametric study illustrates the significant influence of factors such as material gradient magnitude, surface elasticity, nanorelief and nanocrack characteristics on the generalized stress concentration factors (GSCFs).

JTAM, Sofia, vol. 55 Issue 3 pp. 343-370 (2025), [Full Article]

A GENERAL ANALYTICAL STABILITY ANALYSIS OF THE MATHIEU-HILL EQUATION

Mehmet Pakdemirli
Department of Mechanical Engineering, Manisa Celal Bayar University, Manisa, Turkey

A general Mathieu-Hill equation is considered. The periodic function of the equation consists of series of cosine functions with arbitrary number of elements. Stability analysis is performed via the strained parameters method, a perturbation technique. Stability branches are calculated approximately up to second order for the first, second and general n'th regions for an arbitrary number of elements m. Hence, the analysis presents a general solution for any n'th stability region with arbitrarily large m number of elements which cannot be traced in the past literature. The first three stability regions are plotted for a special problem having three parametric excitation terms. Numerical simulations of sample stable, and unstable solutions are given. As with all classical perturbation methods, the analytical solutions for stability branches are compatible with the real stability branches if the perturbation parameter is not large. For large perturbation parameters, the real stability branches and the approximate analytical ones diverge from each other making the approximate stability branches not reliable. This general approach in which there are infinite number of parametric excitations and general solutions for any stability branches is the main contribution of this work to the literature. The work has the potential of application to a wide range of problems modeled by the Mathieu-Hill equations. The general formulas derived are applied to a specific rotating blade vibration problem arising in rotor dynamics and turbomachinery. A study that results in a stability map for the shaft/blade design and operational parameters is extremely valuable for designers, diagnostics, and maintenance engineers. The system contains a number of even frequency parametric excitations. Special solutions of the previous results and the reduction of the general solutions presented here to this specific problem are compatible within the range of order of magnitudes considered.

JTAM, Sofia, vol. 55 Issue 3 pp. 371-384 (2025), [Full Article]