Acta Mechanica Sinica

, Volume 12, Issue 3, pp 251–262 | Cite as

The estimate and measurement of longitudinal wave intensity

  • Ming Ruisen


Quasi-longitudinal waves are one type of structural waves, which are important at high frequencies. This paper studies the estimate theory and measurement technique of quasi-longitudinal waves, analyzes the bias error due to the effect of bending waves. In a two-dimensional quasi-longitudinal wave field, the intensity vector is the sum of the effective intensity vector and the intensity variation vector. Its axial component is proportional to two imaginary parts of cross spectral densities and in the measurement, it is measured by a pair of two-transducer arrays. In a onedimensional quasi-longitudinal wave field, the intensity variation is zero, the intensity is proportional to only one imaginary part of a cross spectral density and it can be measured using a two-transducer array. If bending and quasi-longitudinal waves coexist and the contribution from bending waves cannot be eliminated or reduced to a certain extent, the measured quasi-longitudinal wave intensity will contain a large error. The results measured on the three-beam structure show that quasi-longitudinal wave intensity can be accurately measured using the intensity technique when bending waves are negligible in comparison with quasi-longitudinal waves.

Key Words

quasi-longitudinal wave intensity power flow bias error measurement technique 


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  1. 1.
    Noiseux D U. Measurement of power flow in uniform beams and plates.Journal of the Acoustical Society of America, 1970, 47(1): 238–247CrossRefGoogle Scholar
  2. 2.
    Pavic G. Measurement of structure-borne wave intensity, part I: formulation of the methods.Journal of Sound and Vibration, 1976, 49(2): 221–230CrossRefGoogle Scholar
  3. 3.
    Verheij J W. Cross spectral density methods for measuring structure borne power flow on beams and plates.Journal of Sound and Vibration, 1980, 70(1): 133–139CrossRefGoogle Scholar
  4. 4.
    Linjama J, Lahti T. Estimation of bending wave intensity in beams using the frequency response technique.Journal of Sound and Vibration, 1992, 153(1): 21–36MATHCrossRefGoogle Scholar
  5. 5.
    Ming R S. The measurement of structural wave intensity applied to buildings: [Dissertation]. U.K: Heriot-Watt University, 1993Google Scholar
  6. 6.
    Bendat J S, Piersol A G. Random data: analysis and measurement procedures. New York: John Wiley & Sons Inc., 1986Google Scholar
  7. 7.
    Ming Ruisen. Bending wave intensity in a thick beam.Chinese Journal of Acoustics, 1995, 14(3): 265–275Google Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 1996

Authors and Affiliations

  • Ming Ruisen
    • 1
  1. 1.Department of ArchitectureZhejiang UniversityHangzhouChina

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