Abstract
It is recognized that nanoscale structures exhibit strong surface effects. This article studies axisymmetric bending and free vibration of circular nanoplates with consideration of surface stresses. Using the Gurtin–Murdoch surface elasticity theory and the well-known first-order shear deformation plate theory, a single fourth-order partial differential equation governing axisymmetric bending and free vibration of circular nanoplates is derived. The effect of the surface material properties on the deflection and natural frequencies is analyzed. For a circular nanoplate subjected to a centrally-loaded concentrated force and uniformly distributed loading, explicit expressions for the transverse deflection and its maximum are determined for different boundary conditions. The frequency equations are obtained for the axisymmetric free vibration of free, simply-supported, and clamped circular nanoplates. The natural frequencies and mode shapes are presented. The classical results of Mindlin plates are recovered from the present only if removing the surface effects. The effects of surface properties on the static deflection and natural frequencies are presented graphically.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
