FINITE ELEMENT METHOD FOR VISCOELASTIC FRACTIONAL DERIVATIVE MODEL

The finite element method (FEM) for viscoelastic fractional derivative model is presented in this paper. The motion equations are uncoupled with modal analysis method. With Laplace transformation and inverse Laplace transformation, analytical solutions of time domain response and frequency domain response of single degrees-of-freedom are obtained. The time domain response consists of transient response and steady-state response which represent short period damping vibration and long period recovery response, respectively. Take a one-dimensional bar as example, the FEM solution is compared with the analytical one. It is shown that the FEM solution of displacement agrees with analytical one and more elements are required to acquire accurate results of acceleration response in high frequency domain.