(untitled) (Contemporary Mathematics, 2025)
In this research paper, the focus is on analyzing the free lateral vibration of a nanobeam that has been weakened. The investigation revolves around studying the impact of thermal and magnetic effects on the nanobeam, utilizing both Bernoulli’s beam theory and the nonlocal strain gradient theory (NSGT). Nanostructures hold great significance and find various applications. To derive the governing equations, boundary conditions, and assess the thermal and magnetic influences, Hamilton’s principle is employed. The nanobeam is divided into two parts, with rotational springs connecting them. This model takes into account the additional strain energy caused by cracks, which in turn increases the deflection slope’s discontinuity. The study examines various factors such as crack propagation, crack intensity, thermal and magnetic effects, material length scale parameters, and nonlocal parameters within the non-rheological parameters. A comparative analysis with previous research studies has been conducted, demonstrating a favorable agreement between the findings. The results highlight the significant role played by the aforementioned parameters in the dynamic behavior of the nanobeam. Also, the location and severity of the crack on the nanobeam and its effect on the free vibrations were investigated. The most important application of the conducted research can be used in the construction of drug release systems and stimulate the drugs in a controlled and direct manner at the target site.