Bending Waves Propagating in a Bar with Periodically Nonuniform Material Properties

재질이 주기적으로 불균일한 보에서 전파하는 굽힘 탄성파

  • Published : 2000.08.01


A bar with periodically nonuniform material properties is selected as a one-dimensional model of a flat-panel speaker. This paper describes a theoretical approach to the bending waves propagating i n the nonuniform bar. The phase speed of the wave is obtained using perturbation techniques for small amplitude, sinusoidal modulation of the flexural rigidity and mass density. It is shown that the wave speed is decreased due to the nonuniformity of the material properties by the amount proportional to the square of the modulation amplitude. The resonance occurring when the wavelength is half of the period of the material properties is analyzed by the method of multiple scales. It is also shown that the wave speed at the resonance mode is decreased by the amount proportional to the modulation amplitude but the wave of this mode does not propagate far enough due to attenuation.


Bending Wave;Wave Speed;Flat-Panel Speaker;Perturbation Technique;Multiple-Scale Method


  1. 김정호, 김준태, 김진오, 민진기, 1997, '진동/음향 해석에 의한 스피커의 음향특성 연구,' 대한기계학회논문집(A), 제21권, 제10호, pp. 1742-1756
  2. 김준태, 김정호, 김진오, 1998, '직접방사형 스피커의 음향특성 해석 및 설계,' 한국소음진동공학회지, 제8권, 제2호, pp. 274-282
  3. 김진오, 문병환, 김준태, 1999, '재질이 주기적으로 불균일한 보의 굽힘 진동 해석,' 한국음향학회지, 제18권, 제3호, pp. 73-78
  4. Nayfeh, A. H., 1981, Introduction to Perturbation Techniques, John Wiley & Sons, New York, pp. 418-426
  5. Meirovitch, L., 1986, Elements of Vibration Analysis, 2nd ed., McGraw-Hill, New York, p. 222
  6. Harris, N. and Hawksford, M. O., 1997, 'The Distributed-Mode Loudspeaker as a Broad-Band Acoustic Radiator,' Audio Engineering Society 103rd Convention Preprint 4526 (D-6)
  7. Colloms, M., 1997, High Performance Loud-speakers, 5th ed., John Wiley & Sons, New York, pp. 39-50
  8. Williams, F. W., Wanxie, Z., and Bennett, P. N., 1993, 'Computation of the Eigenvalues of Wave Propagation in Periodic Substructural Systems,' ASME Journal of Vibration and Acoustics, Vol. 115, pp. 422-426
  9. Hawwa, M. A. and Nayfeh, A. H., 1997, 'Flexural Wave Propagation in a Fluid-Loaded Elastic Plate with Periodically Varying Rigidity,' ASME Journal of Vibration and Acoustics, Vol. 119, pp. 415-419
  10. Sen Gupta, G., 1970, 'Natural Flexural Waves and the Normal Modes of Periodically Supported Beams and Plates,' Journal of Sound and Vibrations, Vol. 13, pp. 89-101
  11. Mead, D. J., 1970, 'Free Wave Propagation in Periodically Supported Infinite Beams,' Journal of Sound and Vibration, Vol. 11, pp. 181-197