Sound transmission into a thick hollow cylinder with the fixed-end boundary condition

In this paper sound transmission through the air filled finite thick cylinders exposed to the different incident acoustic wave is studied. The effect of end boundary conditions on the noise reduction of finite cylinders is evaluated. The uniform incident wave and the wave radiated from monopole and dipole sources are used in this study. Three positions are considered for the dipole source. Every position for the dipole source causes symmetric or antisymmetric pressure distributions on the external surface of the cylinder in tangential or axial direction. For the purpose of sound transmission analysis the linear three-dimensional theory of elasticity utilizing the technique of variables separation for the infinite circular cylinders is used to analyze the vibration of finite circular cylinder. In these analyzes the stress continuity condition on the inner and outer surfaces of the cylinder is satisfied using orthogonalization technique and velocity continuity condition is exactly satisfied on the interfacial surfaces. The sound transmission evaluation is carried out for cylinders with various half-length to outer-radius ratios. The results show that in the case of the fixed-end cylinder, the effect of boundary conditions on the noise reduction can be neglected for the half-length to outer-radius ratio of more than 10. Comparing between the obtained results from different acoustic sources shows that the obtained noise reductions from the uniform acoustic wave are less than those obtained from the monopole and dipole sources.