Nonlinear forced vibration investigation of the sandwich porous FGM beams with viscoelastic core layer

In the present investigation, nonlinear forced vibration analyses of porous functionally graded material viscoelastic sandwich beams are studied. The analytical formulation takes into account normal and shear strains in the core layer by employing the higher-order Zig-Zag theories. The sandwich structure consists of FGM faces that exhibit porosities, while the core layer is composed of viscoelastic material. The proposed model is developed in the frequency domain, by incorporating the material properties of the viscoelastic material through complex numbers. The introducing of the geometric nonlinearity effect results in a sixth-order frequency-amplitude equation, affected by numerous intricate coefficients. This equation was resolved using the balanced harmonic method in conjunction with a one-mode Galerkin's method to predict damping and frequency response curves. These latters are presented and discussed for several geometrical and mechanical sandwich beams configuration. The parametric study is specifically aimed at delineating the influence of the FGM parameters of the face sheets, particularly, the power-law index and the porosity parameter on the response curves and the variation of the nonlinear loss factor with the amplitude of vibration.