Time/wave domain analysis for axially moving pre-stressed nanobeam by wavelet-based spectral element method

• Develop wavelet-based spectral element model for moving pre-stressed nanobeam.
• Process time/wave domain analysis for the moving nanostructure.
• Highlight deficiencies of classical finite element and spectral element methods.
• Study effects of nanobeam moving velocity and pre-stress on vibration and stability.
• Investigate effects of small-scale parameter on vibration and stability.

In this article, a time/wave domain analysis is presented for an axially moving pre-stressed nanobeam by wavelet-based spectral element (WSE) method. WSE scheme is constructed as spectral element method (SEM), except that Daubechies wavelet basis functions are used for transforming governing partial differential equation. These basis functions help to rule out some deficiencies of SEM due to periodicity assumption, especially for time domain analysis. Numerical examples are used for validating the accuracy and efficiency of model. The higher accuracy of WSE approach is then evaluated by comparing its results with those of classical finite element and SEM. The effects of moving nanobeam properties, such as velocity, pretention and nonlocal (small-scale) parameter, on vibration and wave characteristics and dispersion curves are investigated. In addition, the instability of moving nanobeam is studied both analytically and numerically considering divergence and flutter.