Analysis of wave propagation through functionally graded porous cylindrical structures considering the transfer matrix method

Abstract

This paper presents a study on acoustic wave transmission through functionally graded porous (FGP) cylindrical shells. The mechanical properties of the FGP material, such as porosity, vary continuously along the thickness of the cylinder, considering a power-law distribution profile. According to a laminate model, the structure is assumed to be composed of a finite number of isotropic homogeneous porous sublayers. The extended full method (EFM) is used to describe the displacement and stress variables of each porous sublayer. Next, using the transfer matrix method (TMM), a local transfer matrix is established for each sublayer, which connects the field variables of the inner and outer surfaces of the sublayer. Eventually, the product of these transfer matrices for adjacent sublayers forms the global transfer matrix of the structure. The effects of different structural and environmental properties on sound transmission loss (TL) of the system are studied. The results show that TL is enhanced by increasing porosity of the outer surface of the cylinder, although enhancing the inner porosity adversely affects TL. Finally, it has been proved that by functionally grading a porous cylinder, sound insulation of the structure is improved dramatically in both mass and stiffness-controlled regions.