Nonlinear vibration of three-phase bidirectional functionally graded sandwich beams with influence of homogenization scheme and partial foundation support

Functionally graded sandwich structures are an advanced class of sandwich structures with material properties varying smoothly in one or more spatial directions. In this work, the effect of the homogenization scheme and partial Pasternak foundation support on nonlinear vibration of bidirectional functionally graded sandwich (BFGSW) beams is studied. The core of the sandwich beams is homogeneous, while the two face layers are made from a three-phase functionally graded material (FGM). Two homogenization schemes, the Voigt model and Maxwell formula, are employed to estimate the effective material properties of the face layers. Based on the refined third-order shear deformation theory, the discrete nonlinear equation of motion is derived with the aid of a two-node beam element, and then solved by a direct iterative procedure. Nonlinear frequencies of the sandwich beams with different boundary conditions are evaluated for various initial vibration amplitudes and foundation parameters. The obtained result reveals that the difference between the nonlinear frequency ratios obtained from the Voigt model and the Maxwell formula is more significant for the beam associated with a higher initial vibration amplitude. The influence of the material distribution and the foundation support on the nonlinear vibration of the sandwich beams is studied in detail and highlighted. © 2022 Elsevier Ltd