Aerospace Science and Technology 13 (2009) 18–26 www.elsevier.com/locate/aescte Analytical model of sound transmission through orthotropic cylindrical shells with subsonic external flow K. Daneshjou 1 , A. Nouri 2 , R. Talebitooti ∗,2 Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran Received 10 July 2006; received in revised form 10 October 2007; accepted 28 February 2008 Available online 15 March 2008 Abstract Circular thin orthotropic shells have many applications in the aerospace industry such as aircraft, missile and launcher. An analytical study is conducted in this paper to understand the characteristic of sound transmission through an orthotropic cylindrical shell. The shell is assumed to be infinitely long and is subjected to a plane wave with uniform airflow in the external fluid medium. An exact solution is obtained by solving the first-order shear deformation and acoustic wave equations simultaneously. The transmission losses (TLs) obtained from the numerical solution are compared with those of other authors. Additionally, in comparison with the classical thin shell theory (CST), the first-order shear deformation theory (FSDT) calculates with the best degree of accuracy. Numerical results are used to show the effects of fiber direction, geometrical properties, Mach number and material properties.  2008 Elsevier Masson SAS. All rights reserved. Keywords: Wave; Transmission loss; Orthotropic shell; First-order theory 1. Introduction Sound transmission characteristics of structures are needed in the noise control branch. The related analysis usually be- comes a very difficult task because of the complicated inter- actions between the structures and the acoustic media. The general methods for solving the vibro-acoustic problems us- ing numerical procedures are Finite Element Method (FEM), Boundary Element Method (BEM) and Statistical Energy Anal- ysis (SEA) [2]. Noise transmission, measured by transmission loss (TL) through the circular shell, has been studied by Smith [15], White [20], Koval [5,6], Blaise et al. [1] and Kim [7] for isotropic, orthotropic, and laminated fiber-reinforced compos- ite shells. Smith presented a theoretical study of transmission of sound energy through a thin, isotropic elastic cylindrical shell excited by an oblique plane wave. He defined a cross-sectional absorption coefficient that is the ratio of the power absorbed * Corresponding author. Tel.: +0098 21 77452169; fax: +0098 21 22090681. E-mail address: rt_talebi@mail.iust.ac.ir (R. Talebitooti). 1 Professor. 2 PhD Student. to the incident power per unit length. White investigated sound transmission into finite cylindrical shells and found two impor- tant characteristics, the ring frequency (where the wavelength of a longitudinal wave in the material is equal to the circum- ference) and coincidence frequency (where the trace velocity of acoustic wave is equal to the bending-wave velocity in the shell wall). At these two frequencies, the sound transmission through the shell will attain the maximum values. Koval ex- tended Smith’s work to present an analytical model for predict- ing TL for isotropic, orthotropic, and laminated fiber-reinforced composite shells. Due to his work, the significance of the ring and coincidence frequencies was revealed. Blaise et al. then ex- tended Koval’s work to consider an orthotropic shell excited by an oblique plane sound wave with two independent inci- dent angles in order to calculate the diffuse field transmission coefficient. They compared the numerical results with Koval’s and indicated some large differences. Kim calculated the sound transmission through an infinite isotropic cylindrical shell us- ing analytical and experimental model. The incident wave was a plane wave and the inside cavity was assumed to be ane- choic. The shell vibration motions were described by the Love’s equation. Experimental set-up was installed using two pairs of 1270-9638/$ – see front matter  2008 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ast.2008.02.005