Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature

The size-dependent nonlinear free vibration behavior of beam-type porous materials with geometric imperfections is investigated. For porous materials, the even and uneven dispersion patterns are used to model the porous distribution of beam. The Hamilton's principle is utilized to derive the size-dependent nonlinear equations of motion and corresponding boundary conditions based on the Euler-Bernoulli beam model, the von Karman type nonlinearity and the nonlocal strain gradient theory. The approximate analytical solution for the nonlinear free vibration of a hinged-hinged nano/micro beam is deduced by Galerkin's approach and He's variational method. Porous Gold (Au) is chosen as a porous material for a comprehensive parametric study. The material and scaling parameters of Au are determined by fitting the experimental dispersion data of longitudinal and transverse acoustic modes. The effects of the dispersion patterns of porosities, the porous volume fractions, the vibration amplitude and geometric imperfection on the nonlinear vibration characteristics are explored.