Dynamical analysis of the general beam model with singularity function

The aim of this study is to present a general model corresponding to some structural elements such as beam, string, bar and rod. The structural element material may be either elastic or Kelvin-Voigt type visco-elastic. So far, the general models with constant coefficients have considered in the literature. The considered general model is with variable coefficients. For solving general model with variable coefficients, a different solution procedure combining method of multiple scales (MMS) and finite difference method (FDM) are presented. This technique provides an advantage in the numerical solution of the structural element model containing any discontinuity and in its dynamical analysis by perturbation method. Furthermore, two problems including discontinuity are considered to indicate accuracy of the method presented. The comparison of the numerical results obtained from the proposed method and classical method are introduced.