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Investigation into the Dynamic Stability of Nanobeams by Using the Levinson Beam Model
Youqin Huang1, Richeng Huang1, Yonghui Huang1
1Research Centre for Wind Engineering and Engineering Vibration, Guangzhou University, Guangzhou 510006, China.
Materials (Basel, Switzerland)
|May 13, 2023
Summary
This study introduces the Levinson beam theory for analyzing nanobeam dynamic stability, considering shear deformation. It reveals that factors like length and density improve stability, while width and Young
Area of Science:
- Mechanical Engineering
- Nanotechnology
- Materials Science
Background:
- Dynamic stability is crucial for nanobeam mechanical behavior.
- Existing Euler-Bernoulli and Timoshenko theories inadequately account for shear deformation in nanobeams.
- The Levinson beam theory offers a more accurate model for bending and shear interactions in nanobeams, especially those with smaller length/height ratios.
Purpose of the Study:
- To investigate the dynamic stability of nanobeams using the Levinson beam theory.
- To formulate the transverse vibration equation for a Levinson nanobeam embedded in an elastic foundation, incorporating nonlocal effects.
- To derive the governing equation for dynamic stability and analyze the principal instability region (PIR).
Main Methods:
- Formulation of the transverse vibration equation based on Levinson beam theory and nonlocal continuum mechanics.
- Application of Bolotin's method to derive the dynamic stability governing equation.
- Analysis of the principal instability region (PIR) boundaries to assess dynamic stability.
Main Results:
- The study quantifies the impact of various parameters on the PIR width: increases in width, Young's modulus, and size scale parameter lead to wider PIRs (19%, 65%, -9% respectively).
- Conversely, increases in length/height ratio and density result in narrower PIRs (-57%, -20% respectively), indicating improved dynamic stability.
- The local model overestimates the dynamic stability of Levinson nanobeams compared to nonlocal models.
Conclusions:
- Dynamic stability of Levinson nanobeams in elastic foundations is enhanced by increased length and density, and decreased width, height, and Young's modulus.
- These findings are linked to the nanobeam's natural frequency, which governs the PIR width.
- The Levinson beam theory provides a more accurate framework for analyzing nanobeam dynamic stability, especially when shear deformation is significant.
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