An efficient method to model the time-domain behavior of viscoelastically damped systems based on an improved fractional derivative model

Viscoelastic materials are widely used as an efficient passive control technique to mitigate undesirable vibration and noise in many engineering fields. However, the damping properties of these materials are strongly influenced by operational and environmental factors, such as excitation frequency and operating temperature, leading to some difficulty during the finite element modelling of engineering systems containing these materials, especially for transient analysis. Thus, it is proposed herein an improved fractional derivative model to be combined with the finite element method in a straightforward way to describe the frequency- and temperature-dependent behavior of viscoelastic materials. As an academic application, the influence of the temperature on the transient responses of a viscoelastic sandwich beam subjected to some types of excitations is addressed. Moreover, the parameters of the viscoelastic model are obtained by curve-fitting for each operating temperature and the resulting equations of motion of the viscoelastic system in the time-domain are solved by using the Newmark integration scheme. Through this improved fractional derivative model, the time-domain responses of the viscoelastic sandwich beam are evaluated for several operating temperatures and compared with the corresponding obtained by the open literature to demonstrate the main features and capabilities of the proposed method.