A Nonlinear Eigenvalue Problem for Buckling Analysis of a Graphene Beam

  • Speaker(s)韦东明教授,哈沙克斯坦总统大学
  • DateFrom 2015-10-14 To 2015-10-14
  • Venue北京国际数学研究中心 镜春园78号院 77201教室

题目:A Nonlinear Eigenvalue Problem for Buckling Analysis of a Graphene Beam
摘要:Graphene has been considered to be a wonder structural material for devices in many applications including switches, sensors, loudspeaker and earphones etc. It is recently reported by the Wall Street Daily that “he who controls graphene rules the tech world”. A long list of potential applications and of graphene and the challenges associated with these applications can be found in literature.  This research is focusing on mechanical stability aspect of graphene in the applications such as loudspeaker and earphones and others. The existing continuum based models for buckling analysis of graphene are based on the theory linear elasticity. However, it is demonstrated both theoretically and experimentally that a more accurate continuum model should include third-order elastic stiffness constants and that the constitutive stress-strain law is a quadratic equation.  This nonlinear elastic constitutive law and the Euler-Beam theory for small strains lead us consider a nonlinear and non-homogeneous eigenvalue problem for buckling analysis of a graphene beam with  a parameter depending upon the nonlinear material property.  Existence of eigen-pair solutions to the problem and some properties of the solutions are proved. Next, we consider following model for the graphene beam subject to a nonlinear lateral support. We show the solvability of the second problem by using energy methods and a suitable iteration scheme for a range of lateral support and axial force.