Non-stationary Response of a Beam for a New Rheological Model

Abstract

The paper is intended to provide the quasi-static and dynamic analysis of beam with fractional order viscoelastic material model, which was derived from integer order description using the Boltzmann superposition principle. The results were obtained for a fractional Zener model by the techniques of Laplace transform and binomial series. An example proves the accuracy of the solution for a simply-supported beam subjected to a uniform distributed load. Theoretical and numerical solutions can be easily extending to the complex structures configurations.