Flutter and divergence instability of rectangular plates under nonconservative forces considering surface elasticity

• Published in: International journal of mechanical sciences Vol. 149; pp. 254 - 261
• Main Authors: Xiao, Q.-X., Li, X.-F.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2018
• Subjects: Flutter instability; Follower force; Rectangular plate; Surface elasticity; Rectangular plate; Follower force; Flutter instability; Surface elasticity
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2018.09.052

•Dynamic stability of thin rectangular nanoplates considering surface elasticity.•Transition from divergence instability to flutter instability.•Effects of surface stress and surface mass on the natural frequencies and buckling loads.•The load–frequency interaction for tangency coefficients of subtangential follower forces. [Display omitted] Nanomaterials are widely used in engineering applications. For nanostructures, surface effects usually have a significant impact on the mechanical properties of micro/nano materials and structures. This paper investigates the dynamic stability of a thin rectangular plate with surface effects under a nonconservative force. Based on the Kirchhoff plate theory incorporating surface elasticity, Hamilton’s principle is employed to derive a governing partial differential equation subject to appropriate boundary conditions. A characteristic equation describing the load–frequency interaction curves is obtained. The load–frequency interaction curves are displayed graphically for various tangency coefficients. The effects of surface stress and surface mass on the frequencies and buckling loads are highlighted. Surface effects on the transition from divergence instability to flutter instability are analyzed. The surface stress and surface mass play a crucial role in affecting flutter loads of nanostructural instability. The obtained results are of benefit to safety design of micro/nano scale plates subjected to compressive loading and generalized follower force in nonconservative systems.