Nonlinear Vibration Behavior of FG Sandwich Beams with Auxetic Porous Copper Core in Thermal Environments

Modeling, analysis, and design are conducted to reveal the nonlinear forced and free vibration behaviors of the functionally graded (FG) sandwich beams with auxetic porous copper core and metal-ceramic facesheets. The copper foams with negative Poisson's ratio (NPR) are designed to be functionally distributed along the structural thickness direction and possess greater relative density in the adjacent sublayers to the facesheets. Meanwhile, the functionally graded material (FGM) facesheets are designed to be metal-rich in the inner surfaces. Through micromechanical modeling and following the Mori-Tanaka model, material properties of FGM facesheets are determined and further taken to be temperature-dependent with the consideration of thermal environments. Nonlinear finite element (FE) simulations are then conducted. From the results of numerical analysis, one can conclude that when compared with the counterpart having a non-auxetic core, the sandwich beam with an auxetic core has lower nonlinear-to-linear frequency ratios of free vibrations and smaller dynamic deflections under a sudden load.