Nonlinear vibration of Timoshenko FG porous sandwich beams subjected to a harmonic axial load

In this study, the instability and bifurcation diagrams of a functionally graded (FG) porous sandwich beam on an elastic, viscous foundation which is influenced by an axial load, are investigated with an analytical attitude. To do so, the Timoshenko beam theory is utilized to take the shear deformations into account, and the nonlinear Von-Karman approach is adopted to acquire the equations of motion. Then, to turn the partial differential equations (PDEs) into ordinary differential equations (ODEs) in the case of equations of motion, the method of Galerkin is employed, followed by the multiple time scale method to solve the resulting equations. The impact of parameters affecting the response of the beam, including the porosity distribution, porosity coefficient, temperature increments, slenderness, thickness, and damping ratios, are explicitly discussed. It is found that the parameters mentioned above affect the bifurcation points and instability of the sandwich porous beams, some of which, including the effect of temperature and porosity distribution, are less noticeable.