Mode localization phenomenon in microbeams due to surface roughness

TL;DR

This study investigates how surface roughness affects the vibration modes of microbeams, revealing phenomena like mode localization and zero-frequency modes, with implications for microbeam design and analysis.

Contribution

A novel model for microbeams with surface roughness is developed, analyzing its impact on natural frequencies and mode shapes across different boundary conditions.

Findings

Surface roughness can induce zero-frequency modes.

Surface roughness may cause mode localization.

Mode localization correlates with increased natural frequency.

Abstract

This is the first study on the mode localization phenomenon in microbeams due to surface roughness. A new model for microbeams with rough surfaces is developed. The natural frequencies and mode shapes of cantilever, simple supported, and clamped-clamped microbeams are determined depending on the beam surface roughness. A parametric study is presented demonstrating two prospects: surface roughness may lead to a zero-frequency mode or a mode localization. As for the first prospect, it is demonstrated that surface roughness may add more softness to a specific mode of vibration and reduce its natural frequency causing a rigid-body mode. As for the second prospect, surface roughness may inhibit the propagation of vibration energy throughout the beam length leading to a mode localization. It is revealed that a mode localization is accompanied with an increase in the natural frequency of the microbeam. It is revealed that the description of the beam vibration according to one of these two prospects depends on the beam size, parameters of the surface roughness, and the boundary conditions.