Nonlinear vibration analysis of FGER sandwich beams

This paper tackles amplitude-dependent dynamic characteristics of functionally graded electrorheological (FGER) sandwich beams. Nonlinear characteristics of the electrorheological fluid (ERF) layer is introduced and modeled by an exponential function. In addition, considering geometrical nonlinearity and assuming continuous variation for functionally graded material (FGM) properties through the layers thickness, the nonlinear governing equations for free vibration of the FGER beam are derived by means of the finite element method (FEM). The developed governing equations are solved using a combined modal-recursive approach and verified by related studies in the literature. Further numerical investigations are conducted for the validated FGER beam model, where the trends of dynamic characteristics of the beam vs. vibration amplitude are studied. Nonlinear fundamental frequency and modal loss factor ratio are extracted in different boundary conditions, applied electric fields, FGM volume fraction indices and thickness ratios.