Motivated by the limitations of classical models in capturing the behavior of materials at the micro/nanoscales, this work proposes an analytical formulation for thermoelastic damping (TED) in circular cross-sectional micro/nanobeams with size-dependent mechanics and heat transfer. This model incorporates small-scale effect through the modified couple stress theory (MCST) for mechanics and the Moore-Gibson-Thompson (MGT) model for heat conduction. To accomplish this objective, the initial step involves introducing the general equations of the MCST and MGT model. Following the establishment of the MGT model, the temperature variations throughout the beam are obtained by solving the heat equation. Additionally, by implementing the principles of the MCST, the model incorporates size-dependent constitutive relations. Finally, the research employs the energy dissipation (ED) approach to render a mathematical expression for TED in tiny beams with circular cross section. This relation, expressed as an infinite series, accounts for size-dependent effects by incorporating the MCST and MGT model. In the section dedicated to numerical results, the initial step involves verifying the accuracy of the proposed model through a validation study. Next, the section showcases various numerical results, focusing on how the MCST and MGT model affect the temperature distribution and TED value. The acquired results underscore that the influence of the MCST and MGT model on the amount of TED in small-sized circular cross-sectional beams cannot be disregarded.

The main objective of this paper is to examine the stability and convergence of the Laplace-Adomian algorithm to approximate solutions of the pantograph-type differential equations with multiple delays. This is done by comparatively investigating it with other methods.

A study was conducted to examine the effects of two-step fuel injection on a modified four-cylinder engine that was converted from port to direct injection. The primary fuel source utilized was hydrogen-enriched compressed natural gas (HCNG), which replaced the conventional gasoline. In the initial phase of the procedure, compressed natural gas (CNG) was introduced into the intake manifold at a concentration of 10 % by mass, relative to the total fuel mixture. The remaining 90 % of the fuel consisted of HCNG, which was injected directly into the cylinders. The injection of compressed natural gas (CNG) commenced at 160° before top dead center (BTDC) with a 20° stroke duration. The HCNG fuel was injected in a two-step process. In the initial phase, HCNG was injected at 130° BTDC with a 50° stroke duration, with a stepwise increase from 0 % to 40 %.