Nonlinear vibration analysis of FGER sandwich beams

• In this paper nonlinear FE modeling and dynamic characteristics of the FGER sandwich beams are studied.
• The nonlinear frequency dependent viscoelastic layer is modeled by an exponential function by assuming relevant hysteresis loop.
• FGM layers are modeled considering geometrical nonlinearity, and the properties are assumed to vary through the layer thickness.
• The nonlinear governing equations for free vibration of the FGER beam are derived with finite element method based on energy method.
• Combined modal-recursive approach is utilized to manage the solution of the nonlinear model.

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.