Nonlinear dynamic analysis of viscoelastic beams using a fractional rheological model

- Quasi-static analysis, classical and fractional dynamic analysis of viscoelastic beam is presented.
- Plots of the relaxation modulus for different values of fractional derivative order are provided.
- Galerkin's method, Laplace transforms, Bessel functions and binomial series are used in paper.
- An example shows how existence of fractional derivative influences the structure response.
- Study allows researchers to choose a mathematical model to fit an experimental model.

The paper presents quasi-static analysis, classical and fractional dynamic analysis of a simply supported viscoelastic beam subjected to uniformly distributed load, where the Riemann-Liouville fractional derivative is of the order ν ∈ (0, 1). A comparative study of the results obtained for a classical and fractional Zener model using the techniques of Laplace transform, Bessel functions theory and binomial series is achieved. The graphic representations show how the existence of fractional derivative in the selected rheological model influences the dynamic response of the structure. This paper provides a theoretical basis for researchers who want to choose a mathematical model that will precisely fit with a particular experimental model.