Incorporating the Havriliak-Negami model in wave propagation through polymeric viscoelastic core in a laminated sandwich cylinder

摘要

This paper presents the fundamental problem of three-dimensional acoustic wave transmission through a sandwich structure with viscoelastic core excited by an obliquely plane wave. The structure consists of a functionally graded shell as an outer layer, an isotropic layer as an inner layer and also a viscoelastic core. This work considers Havriliak-Negami model for description of complex modulus of viscoelastic core. The Havriliak-Negami model is a new mathematical method for the simulation of polymeric relaxation behavior in the frequency domain. In this model, both of complex Young's and shear moduli are frequency dependent. Moreover, considering the effective roles of shear deformation and rotary inertia, dynamic governing equations of the functionally graded cylinder, viscoelastic core and isotropic shell are derived within the frameworks of the three-dimensional theory of elasticity. Furthermore, analytical model of acoustic wave transmission based on transfer matrix method is composed of a set of fluid and structural equations which taking into account the frequency dependency of mechanical characterization for the viscoelastic core. A good agreement can be observed, comparing the present results with those of other authors. Besides, the results show that a double-walled cylinder with viscoelastic core has a better acoustic insulation in comparison with isotropic shell with the same mass. Contrary to elastic material, by thickening the viscoelastic layer, sound transmission loss decreases in mass-controlled region due to shear deformation and rotary inertia. It has been also proved that polymer with a larger loss factor has good performance in energy dissipation.