The influence of surface effects on axisymmetric vibration of graded porous Mindlin circular nanoplate in a temperature field

Abstract

The surface effect significantly affects the mechanical response of nanoscale materials. In this work, we introduce Gurtin‐Murdoch surface elasticity theory into Mindlin plate theory to study the axisymmetric vibration characteristic of graded porous circular nanoplate in a temperature field. The main structure is a porous graded material with uniform or non‐uniform porosity distribution in its thickness. The numerical shooting technique was applied to solve the governing differential equations derived from Hamilton's principle. Responses for the vibration characteristic of the graded porous nanoplate for both clamped and simply supported boundary conditions were obtained. The numerical results show that when the surface effect is removed, the classical results of Mindlin circular plate will be obtained. Natural frequencies and mode shapes varying with thermal and porosity coefficients were present graphically. And then the effects of surface material properties on the axisymmetric vibration characteristic of the nanoplates were discussed in detail. The parametric study examined the influence of porosity coefficient, porosity distribution mode, surface elastic parameters, and residual surface stress on the vibration characteristics of porous circular nanoplates.