Auxetic metamaterial pre-twisted helical nanobeams: vibrational characteristics

The current investigation pertains to the vibrational characteristics of an out-of-plane helical nanobeam composed of auxetic material. This study marks the first instance of such an analysis. The Frenet-triad is a mathematical tool utilized to account for the impact of curvature, allowing for the dynamic alteration of the coordinate system and the precise definition of the location vector. In order to examine this model, the governing equations are formulated utilizing Timoshenko’s beam theory and Eringen’s nonlocal elasticity theory and applying Hamilton’s principle. The generalized differential quadrature method (GDQM) is employed to solve the governing equations under various boundary conditions. The present study validates the precision and effectiveness of the existing model through a comparison between the outcomes obtained from the simplified approach and the benchmark results reported in the literature. The findings reveal satisfactory level of conformity between the two sets of results. Ultimately, the numerical outcomes are derived with a focus on exploring the impact of various factors such as inclination angle, auxetic rib length, curvatures, tortuosity, and pre-twists on the helical nanobeam. The findings of this work may be used as a benchmark for further investigations in designing the micro and nanosprings. Besides, one of the most important applications of the current study is in the bio section in designing and investigation of DNA structure.