In industrial fields, rotating structures such as, wind turbines, propellers and turbines can undergo significant vibrations up to resonance inducing annoying noises and damaging structures. Therefore, the precise determination of the natural frequencies of these structures is an important step in their design. In applications where the use of light structures is important, the introduction of a viscoelastic material between two elastic layers is widely used to induce a high damping inherent to the resulting multilayer structure. The rigidity of this type of structure depends on the frequency of vibration. According to our knowledge, no prior work has taken into account this dependence between stiffness and frequency in rotating sandwich beams. However, these materials have been widely studied in the case of non-rotating beams. Duigou et al (Iterative algorithms for non-linear eigenvalue problems. Application to vibrations of viscoelastic shells. Comput. Methods Appl. Mech. Engrg. 192, 2003 1323–1335.), for example, solved the complex nonlinear eigenvalue problems of symmetric viscoelastic non-rotating sandwich beams with a frequency-dependent Young's modulus, by coupling the homotopy technique and the asymptotic numerical method (HANM).

In our study, we use the HANM procedure to determine the dynamic parameters of rotating viscoelastic sandwich beams. Our results obtained for viscoelastic sandwich rotating beams with a constant Young's modulus coincide perfectly with those obtained from literature and the software Abaqus. The originality of our work is the consideration of the dependence of Young's modulus on frequency in the study of rotating sandwich beams. To this end, we studied the effect of angular velocity and layer thicknesses on eigenfrequencies and loss factors. Results show that, similarly to the isotropic beams, the sandwich ones gain in rigidity as the angular velocity rises inducing the increase of the eigenfrequencies and the decrease of the loss factors.