Analysis of the Vibration Behaviors of Rotating Composite Nano-Annular Plates Based on Nonlocal Theory and Different Plate Theories

Abstract

Rotating machinery has significant applications in the fields of micro and nano meters, such as nano-turbines, nano-motors, and biomolecular motors, etc. This paper takes rotating nano-annular plates as the research object to analyze their free vibration behaviors. Firstly, based on Kirchhoff plate theory, Mindlin plate theory, and Reddy plate theory, combined with nonlocal constitutive relations, the differential motion equations of rotating functionally graded nano-annular plates in a thermal environment are derived. Subsequently, the numerical method is used to discretize and solve the motion equations. The effects of nonlocal parameter, temperature change, inner and outer radius ratio, and rotational velocity on the vibration frequencies of the nano-annular plates are analyzed through numerical examples. Finally, the relationship between the fundamental frequencies and the thickness-to-radius ratio of the nano-annular plates of clamped inner and outer rings is discussed, and the differences in the calculation results among the three plate theories are compared.

Free vibrations of small-scale plates with complex shape based on the nonlocal elasticity theory

“…Axisymmetric free vibrations of annular and circular Mindlin plates are studied based on the nonlocal continuum theory by Sari [23]. Li et al [24] devoted their work to the research of vibrations of rotating composite nano-annular plates based on Kirchhoff plate theory, Mindlin plate theory, and Reddy plate theory, combined with the nonlocal theory. Shahriari and Shirvani [25] analyzed buckling of skew nanoplates based on nonlocal elasticity theory as well as second-order strain gradient theory.…”