Finite Element Analysis of Sound Transmission Loss in One-Dimensional Solids

S. D. Yu, J. G. Kawall

Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada.

DOI: 10.4236/oja.2013.34017                

Abstract

A higher-order acoustic-displacement based finite element procedure is presented in this paper to investigate one-dimensional sound propagation through a solid and the associated transmission loss. The acoustic system consists of columns of standard air and a solid, with the upstream column of air subjected to a sinusoidal sound source. The longitudinal wave propagation in each medium is modeled using three-node finite elements. At the interfaces between the air and the solid medium, the continuity in acoustic displacements and the force equilibrium conditions are enforced. The Lagrange multipliers method is utilized to assemble the global equations of motion for the acoustic system. Numerical results obtained for various test cases using the procedure described in the paper are in excellent agreement with the analytical solutions and other independent solutions available in the literature.

Keywords

Finite Element Method; Sound Transmission Loss

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	G. M. L. Gladwell, “A Variational Formulation of Damped Acousto-Structural Vibration Problems,” Journal of Sound and Vibration, Vol. 4, 1966, pp. 172-186.
[2]	A. Craggs, “A Finite Element Method for Damped Acoustic Systems: An Application to Evaluate the Performance of Reactive Mufflers,” Journal of Sound and Vibration, Vol. 48, No. 3, 1976, pp. 377-392.
[3]	A. Craggs, “Coupling of Finite Element Acoustic Absorption Models,” Journal of Sound and Vibration, Vol. 66, No. 4, 1979, pp. 605-613.
[4]	Y. J. Kang and J. S. Bolton, “Finite Element Modeling of Isotropic Elastic Porous Materials Coupled with Acoustical Finite Elements,” Journal of Acoustic Society of America, Vol. 98, No. 1, 1995, pp. 635-643.
[5]	B. Tabarrok and F. P. J. Rimrott, “Variational Methods and Complementary Formulations in Dynamics,” Kluwer Academic Publishers, Kluwer, 1994.
[6]	P. M. Morse and K. U. Ingard, “Theoretical Acoustics,” Elsevier, New York, 1968.
[7]	A. Craggs, “A Finite Element Model for Rigid Porous Absorbing Materials,” Journal of Sound and Vibration, Vol. 61, No. 1, 1978, pp. 101-111.
[8]	M. J. Crocker, “Handbook of Acoustics,” John Wiley & Sons, Inc., New York, 1998.