Journal of Theoretical and Applied Mechanics, Sofia, vol. 56 Issue 1 (2026)

In this paper, the influence of material composition on free vibration of bidirectional functionally graded beam using a quasi-3D theory is investigated. The material properties are assumed to be graded in both the thickness and longitudinal directions by power gradation laws and four different distribution patterns are considered. Equations of motion based on a quasi-3D model that contains undetermined integral forms and involves few unknowns to derive, are obtained from Hamilton's principle. The problem is solved using the Navier solution for a simply supported beam. The accuracy of the present solution is demonstrated by comparing it with some results available in the literature and a good agreement is showed. The effects of the type of material distribution, power-law indexes, and the aspect ratio on the fundamental frequencies are examined and highlighted.

doi: https://doi.org/10.55787/jtams.2026.1.AI00038

This article presents a study on the behavior of rectangular functionally graded plates under thermo-mechanical bending conditions. The study employs a finite element method to analyze these plates, consisting of functionally graded face sheets and core. Validating the proposed model's accuracy through comparisons with existing literature, the investigation explores the effects of key parameters thermal load, geometric factors, and volume fraction distribution on thermo-mechanical bending behavior. The study includes a thorough parametric analysis to identify significant factors impacting normal stresses and deflection of functionally graded plates. The findings offer valuable insights for designing functionally graded plates subjected to combined thermal and mechanical loads. With its simplicity and potential for future advancements, the suggested method proves highly suitable for addressing these problems.

doi: https://doi.org/10.55787/jtams.2026.1.AI00039

In the present paper, a closed form solution of transverse Stokes rarefied slip fluid flow past axially symmetric bodies is being considered. The transverse Stokes drag is evaluated for axially symmetric bodies in the slip-flow regime and which is valid for Knudsen numbers, Kn ≤ 0.1. The extension of Stokes drag on micro-axially symmetric particles from no-slip boundary conditions to slip boundary conditions has been given. It has been concluded in the end that transverse Stokes drag on the micro-axially symmetric particles is equivalent to Stokes solution for continuum flows multiplied by a rarefaction coefficient which is dependent upon the Knudsen number. The author proposed a new approach of providing analytic closed form drag formula for transverse Stokes slip flow past axially symmetric bodies for rarefied gas.

doi: https://doi.org/10.55787/jtams.2026.1.AI00119

The problem under consideration involves identifying the coefficients of a partial sum of a Fourier series used to approximate the effect of an external periodic force on a Li\'{e}nard oscillator. A method for constructing a nonlinear identifier is proposed, enabling the real-time asymptotical estimation of the oscillator velocity and coefficients of a partial sum of a Fourier series by means of displacement measurements. This method is based on the synthesis of invariant relations that make it possible to interrelate the variables of a special extended dynamic system and determine unknown variables as functions of known ones. The asymptotic convergence of estimates of unknowns to their true values is proven. The results of numerical simulation of the proposed method for the Duffing oscillator are presented.

doi: https://doi.org/10.55787/jtams.2026.1.AI00137

In this paper, the losses of kinetic energy in big band saw machines are examined. Expressions have been obtained to calculate the kinetic energy of the mechanical system in the ideal and the real case. With the help of these expressions, the final dependencies for determining the energy losses for the studied class of machines were obtained. These dependences show the influence of linear and angular inaccuracies, i.e. of the parameters e and α. A number of optimization solutions have been proposed that allow the values of both parameters to be calculated so that energy losses are minimal. The proposed approach can be used in the design of other classes of woodworking machines, as well as in the study of energy losses for this class of machines.

doi: https://doi.org/10.55787/jtams.2026.1.AI00191

Coastal vegetation provides critical wave attenuation for shoreline protection, but existing models are computationally prohibitive or lack educational transparency. We present wave-attenuation-1d, an open-source Python package implementing linearized shallow water equations with vegeta\-tion-induced drag. The model uses fourth-order Runge-Kutta integration on a staggered grid, achieving unconditional stability through implicit treatment of the drag term. Numerical experiments with monochromatic waves through 40-meter vegetation patches demonstrate transmission coefficients from 0.655 (sparse) to 0.010 (dense vegetation), corresponding to 34.5% and 99.0% wave height reductions. While the one-dimensional framework simplifies three-dimensional flows and flexible vegetation dynamics, it provides a computationally efficient baseline for understanding wave-vegetation interactions. The package features standardized NetCDF output and modular architecture, bridging research-grade simulations and accessible educational tools for exploring nature-based coastal protection solutions.

doi: https://doi.org/10.55787/jtams.2026.1.AI00236

This study analyzes the influence of finite-length effects on thermally induced flow in a rarefied monatomic gas between two stationary coaxial cylinders. Using the Direct Simulation Monte Carlo method, thermoacoustic waves induced by a sudden inner-cylinder temperature shock are examined under four axial boundary conditions: diffuse, adiabatic, symmetric, and periodic. Results reveal a transient regime, where thermoacoustic waves propagate and reflect depending on boundary type, and a steady-state regime, where temperature, density, and velocity profiles stabilize. Axial boundaries significantly affect wave dynamics, dissipation, and flow structure, particularly at intermediate and radial positions. The findings emphasize the importance of accurate boundary modeling in rarefied gas dynamics for applications in microscale devices, vacuum systems, and aerospace technologies.

doi: https://doi.org/10.55787/jtams.2026.1.AI00238