Nonlinear vibrations of Timoshenko nanobeam using stress driven nonlocal theory

As properties of nonlinear systems can introduce particular responses not present in linear systems, results from linear models can be inaccurate or misleading. Therefore, studying nonlinear vibrations is of extreme importance in structural vibration analysis. Nonlinear vibrations of a Timoshenko nanobeam were analyzed for the first time using the stress driven nonlocal theory (SDM) and the strain gradient theory (SGT). Nonlinear equations of motion were solved for simply supported- simply supported, clamped-clamped and clamped- simply supported beams using the homotopy analysis method. The results indicated that as the dimensionless characteristic parameter increased, the nonlinear natural frequency increased accordingly. High agreement was observed between the results from a linear frequency of Timoshenko beam model based on the SGT and those from previous research.

Automated summary

Due to the introduction of particular responses not present in linear systems, properties of nonlinear systems can lead to inaccurate or misleading results from linear models. Therefore, studying nonlinear vibrations is crucial in structural vibration analysis. This study utilized the stress driven nonlocal theory (SDM) and the strain gradient theory (SGT) to analyze the nonlinear vibrations of a Timoshenko nanobeam. By solving the nonlinear equations of motion using the homotopy analysis method, it was found that the nonlinear natural frequency increased as the dimensionless characteristic parameter increased. The results also showed a high level of agreement with previous research using a linear frequency of Timoshenko beam model based on the SGT.