Effect of the Multi Vibration Absorbers on the Nonlinear FG Beam Under Periodic Load with Various Boundary Conditions

A semi-analytical method is used to study the effects of the multi vibration absorbers on the nonlinear functionally graded (FG) Euler-Bernoulli beam subjected to periodic load. The material properties of the beam are assumed to be continuously graded in the thickness direction. The governing equations of functionally graded beam are obtained based on the Hamilton's principle and these equations are solved by using the Rayleigh-Ritz method. To validate the results, comparisons are made with the available solutions for the natural frequencies of isotropic beam. The effects of the multi vibration absorbers and material parameters on the vibration response of functionally graded beamare investigated. For case study the effect of two symmetrical vibration absorbers is considered, these absorbers are applicable in some of the mechanic systems. In those systems, two absorbers are used close to the beginning and end of the structures instead of using them in the middle of these structures. By considering the industrial applications, it is shown that using the two symmetrical vibration absorbers with lower mass is close to the end of functionally graded beam is better than the middle of one. Also, the effect of different numbers of the vibration absorbers on the nonlinear functionally graded beam with simply supported boundary condition is considered. The results shown that increasing the number of vibration absorbers leads to decreasing the maximum deflection.