## 1 Introduction  
Viscoelasticity regards the study of materials exhibiting a time dependence behavior. The knowledge of the viscoelastic properties of these materials is at the basis of a correct analysis of structures, where the viscoelastic materials are employed, especially when dealing with dynamic phenomena and vibrations. Materials with viscoelastic behavior are widely employed in many different applications starting from biological tissues, such as the disks in the human spine [1] and skin tissue [2; 3], up to civil and industrial systems such as elastomers. As regards the latter field of study, tall buildings are damped with viscoelastic materials to avoid instabilities and to face vibration problems caused by wind or earthquakes [4; 5]. Viscoelastic dampers have long been used in the control of vibration and noise in aerospace structures and industrial machines. In many mechanical systems, such materials are widespread and used for damping and insulation scope [6], i.e., they are used in automobile bumpers, machine insulation, to protect computer drives from mechanical shocks and are also used in shoe insoles to reduce impact transmitted to the person and to increase comfort. Moreover, materials that behave elastically at room temperature often show significant viscoelastic properties when heated. In addition, tires are made of different polymers and elastomers with peculiar viscoelastic properties responsible for many tire/road interaction phenomena that affect vehicle dynamics in term of safety and performance. Friction performance [7; 8], rolling resistance and wear are some examples of events in which the viscoelasticity of the tread plays a fundamental role. The characterization of these materials involves two main phases: experimental tests and analytical modelling. A good understanding of the dynamical behavior of structures where viscoelastic materials are used is strictly dependent on their rheological properties and on some of their geometric parameters. These characteristics in turn depend on the temperature and on the induced excitation frequency quantities. Material models and simulation tools become fundamental to understand and to reduce uncertainties during the earliest phases of the material development, optimizing the design of composite and multi-layered material components and the manufacturing process. Furthermore, the possibility to employ realistic models of materials allows to make reliable predictions of the behavior of existing components as well as for those in the process of development. To define a constitutive law for linear viscoelasticity, at least three different common approaches can be adopted: integral models, linear differential models and fractional derivative models. The basic foundation of linear viscoelasticity theory is the Boltzmann's superposition principle according to which every loading step makes an independent and additive contribution to the final state [9]. This idea can be used to formulate an integral representation of linear viscoelasticity. Nevertheless, a more convenient and widespread way to describe the linear viscoelasticity is the differential approach, where a combination of mechanical elements, ideal springs and dashpot, are used to describe the rheological properties. On one hand, spring is a perfect elastic element, following [PERSON]'s law and behaving like an elastic solid; on the other hand, dashpot is a perfect viscous element, following [PERSON]'s Law. The methodology links stress and strain through linear differential equation. The simplest and most famous models currently employed are the Maxwell model, Kelvin-Voigt model and Zener model. However, Maxwell model fails in reproduction of the creep phenomenon and Kelvin-Voigt model fails in the description of the relaxation behavior [10].