On the thermal vibration analysis of a FG nanotube with deformable boundary effects

Abstract

Purpose: The purpose of this study is to analyze the free lateral vibration behavior of composite nanotubes under thermal environments, considering functionally graded material properties and small-scale effects using strain gradient theory. The study aims to develop a more flexible and accurate vibration model by introducing elastic boundary conditions. Methodology: A novel mechanical model is proposed where boundary supports are represented using elastic springs. Lateral vibrations are modeled with a Fourier sine series representation of displacement, and boundary conditions are implemented via Stokes' transforms to simulate both rigid and deformable supports. The strain gradient theory is employed to capture size-dependent effects. The proposed model's accuracy is verified through comparison with literature and Navier-type solution. Results: Numerical investigations indicate that an increase in temperature change and nanotube length reduces the natural frequencies. Conversely, increasing the material length scale parameter, material grading index, outer-to-inner radius ratio, and boundary spring stiffness leads to higher vibration frequencies. Conclusions: The study provides a comprehensive understanding of the vibrational characteristics of FG nanotubes under thermal effects, especially under various boundary conditions. The results highlight the significance of considering both deformable boundaries and temperature dependence in nanoscale vibration analysis. These insights are valuable for the design of advanced nanodevices such as nanosensors, nanoresonators, and actuators.