Flexural Nonlinear Natural Frequency Analysis of Rotational Functionally Graded Sandwich Rectangular Plates with Uniform and Inhomogeneous Pore Distributions in Thermal Environments

This study investigates the nonlinear dynamic properties of rotating functionally graded sandwich rectangular plates in a thermal environment. The nonlinear vibration equations for a rotating metal-ceramic functionally graded sandwich rectangular plate in a thermal environment are derived using classical thin plate theory and Hamilton’s principle, considering geometric nonlinearity, temperature-dependent material properties, and power law distribution of components through the thickness. With cantilever boundary conditions, the flexural nonlinear differential equations of the rectangular sandwich plate are obtained via the Galerkin method. Since the natural vibration differential equations exhibit nonlinear characteristics, the multiscale method is employed to derive the expression for nonlinear natural frequency. An example analysis reveals how the natural frequency of a functionally graded sandwich rectangular plate varies with rotational speed and temperature. Results show that the nonlinear/linear frequency ratio increases with rotational angular velocity Ω and thickness-to-length ratio h/a, follows a cosine-like periodic pattern with the setting angle, and shows a sharp decrease followed by a rapid increase with increasing width-to-length ratio b/a. The derived analytical solutions for nonlinear frequency provide valuable insights for assessing the dynamic characteristics of functionally graded structures.