Sound transmission across orthotropic cylindrical shells using third-order shear deformation theory

Abstract

The objective of this paper is representation of an analytical solution to calculate transmission loss (TL) of an arbitrarily thick cylindrically orthotropic shell, immersed in a fluid medium with a uniform external airflow and contains internal fluids. The shell is assumed to be infinitely long and is excited by an oblique plane wave. The displacements are expanded as cubic functions of the thickness coordinate to present an analytical solution based on Third-order Shear Deformation Theory (TSDT). Equations of motion of the shell are then obtained using virtual work method. By solving shell vibration as well as acoustic wave equations simultaneously, the exact solution for TL is obtained. Predictions with the presented models are compared with those of previous models (CST and FSDT) for thin shells. Similar results are achieved as the effects of shear and rotation on TL are not noticeable in a thin shell. However, the model introduced here exhibits more accurate results for thick shells where the shear and rotation effects become more significant in lower R/h ratios. Additionally, the effects of related parameters on TL such as material and geometrical properties are discussed.

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“…Huang et al (2005) investigated the free vibration behaviour of orthotropic rectangular plates with varying thickness under general boundary conditions. Shojaeefard et al (2014) presented an analytical solution for calculating the sound transmission loss of thick orthotropic cylindrical shell using third order shear deformation theory (TSDT).…”

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“…The sound insulation performance of an infinite multilayered cylindrical shell including orthotropic skins and a polymeric core is investigated in Magniez et al's [57] study by using the FSDT and three-dimensional theory. Shojaeefard et al [58] analytically developed the research on sound propagation through orthotropic cylindrical shells by utilizing the third-order shear deformation theories. Qu et al [59] in their paper proposed semi-analytical procedures for modeling a coupled structure including submerged spherical cylindrical shells reinforced with circumferential rings and longitudinal stringers to evaluate the vibration and acoustic response of such a structure.…”