Wave attenuation in 1-D viscoelastic periodic structures with thermal effects

The influence of temperature on the unit cell wave attenuation of 1-D viscoelastic periodic structures is important for the design of phononic structures and mechanical metamaterials with desirable properties, considering the damping provided by viscoelasticity. However, the dispersion of evanescent waves in 1-D viscoelastic phononic structures (VPnSs) with thermal effects has not been reported yet. In this study, it is investigated the complex dispersion diagram of 1-D VPnSs considering an isotropic solid (i.e., bulk waves, 3-D model, in plane strain condition) and the standard linear solid model for the viscoelastic effect. The unit cell of the VPnS is composed by steel (elastic material) and epoxy (viscoelastic material). The thermal effect is included in terms of the Young’s modulus (E) with a temperature (T) dependence (i.e., E(T)) for epoxy. It is supposed that the unit cell has a uniform temperature along its dimensions, thus there is no heat flux. The extended plane wave expansion, \(k(\omega ,T)\) $k(\omega ,T)$ approach, where \(\omega\) $\omega$ is the frequency and k is the wave number, is derived to obtain the propagating and evanescent modes of the VPnSs for each value of temperature. The temperature influences significantly the unit cell wave attenuation zones and also the evanescent wave modes. Before the glass transition temperature of the epoxy, the wave modes are shifted for lower frequencies, the attenuation bands are decreased, and the unit cell wave attenuation increases with the rise of temperature. Near the glass transition temperature of the epoxy, the wave dispersion behaviour, depending on the temperature, is very different, whereas after the glass transition temperature of epoxy, the wave dispersion behaviour is close. The relevant results can be used for the wave attenuation design of viscoelastic periodic structures with thermal effects.