Applications of the Complex Modulation Transfer Function on SEAsystems
(1999) Abstract
 The SEA coupling and dissipation loss factors are determined insitu from Complex Modulation Transfer Functions, CMTF:s, based on measured impulseresponses. A quotient of CMTF:s is leastsquare curvefitted to a SEA model and the SEA loss factors are determined from the results of the curvefit.
A two subsystem SEA model with timevarying power is considered. In the frequency domain, powerenergy transfer functions can be formed. In a powerenergy transfer function in the model with two poles and one zero, the zero and one pole are almost equal, if the coupling is weak. When trying to determine the poles and the zero from the CMTF curve one then runs into problems since the zero is so close to the pole. The situation... (More)  The SEA coupling and dissipation loss factors are determined insitu from Complex Modulation Transfer Functions, CMTF:s, based on measured impulseresponses. A quotient of CMTF:s is leastsquare curvefitted to a SEA model and the SEA loss factors are determined from the results of the curvefit.
A two subsystem SEA model with timevarying power is considered. In the frequency domain, powerenergy transfer functions can be formed. In a powerenergy transfer function in the model with two poles and one zero, the zero and one pole are almost equal, if the coupling is weak. When trying to determine the poles and the zero from the CMTF curve one then runs into problems since the zero is so close to the pole. The situation with one pole is easier to handle. Therefore instead a quotient of two SEA powerenergy transfer functions with the same input power was taken. The result is a model with one pole leading to a robust evaluation of the loss factors. The result is the quotient of the two subsystem energies where the input power does not enter and thus need not be known. The virtual boundary condition using this new transfer function model is given by putting the denominator energy equal to zero, meaning that the corresponding subsystem is energy earthed.
Even for SEA models with more than two subsystems, a model with one pole can be derived.
In the physical system the power can be timevaried by letting the system excitation signal consist of random noise modulated with a deterministic timevarying function. However, since the ensemble average of the squared response is proportional to the squared impulseresponse convolved with the squared modulating function, random excitation is avoided and replaced by impulseresponse measurements. The Fourier transform of the lowpass filtered squared impulse response is the CMTF.
A CMTF curve for a short distance between source and observation position does not show simple lowpass character, but has a "floor". A model for the modulation transfer function could therefore consist of a modulation frequencyindependent part diminishing with source distance and originating from the direct field and a lowpass character sourcedistance independent part originating from the reverberant field. At a certain distance from the source the magnitudes of the two parts are equal. The distance is here called the modulation direct field radius in analogy with the ordinary direct field radius. The modulation direct field radius is monotonically increasing with the modulation frequency. Thus the distance affected by the direct field is larger for the modulation than for the nonmodulated, stationary, case.
Experiments were carried out on two plates connected at a point by a spring and in two rooms divided by a wall. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/40190
 author
 Lundberg, KarlOla ^{LU}
 supervisor
 opponent

 Ljunggren, Sten, Professor in Building Acoustics, Dept. of Building Sciences, KTH
 organization
 publishing date
 1999
 type
 Thesis
 publication status
 published
 subject
 keywords
 vacuum technology, hydraulics, Mechanical engineering, modulated noise, insitu, modulation transfer function, loss factor, SEA, vibration and acoustic engineering, Maskinteknik, hydraulik, vakuumteknik, vibrationer, akustik
 pages
 89 pages
 publisher
 Dept. of Engineering Acoustics, LTH, Lund University, P.O.B. 118 SE221 00 Lund Sweden,
 defense location
 Hörsal V:D, Vhuset, John Ericssons väg 1 Lund
 defense date
 20000114 10:15:00
 external identifiers

 other:ISRN: LUTVDG/TVBA99/1008SE
 ISBN
 9178740339
 language
 English
 LU publication?
 yes
 id
 69a4675d12014e9da53ffa9690fdd45c (old id 40190)
 date added to LUP
 20160401 15:24:50
 date last changed
 20181121 20:34:17
@phdthesis{69a4675d12014e9da53ffa9690fdd45c, abstract = {{The SEA coupling and dissipation loss factors are determined insitu from Complex Modulation Transfer Functions, CMTF:s, based on measured impulseresponses. A quotient of CMTF:s is leastsquare curvefitted to a SEA model and the SEA loss factors are determined from the results of the curvefit.<br/><br> <br/><br> A two subsystem SEA model with timevarying power is considered. In the frequency domain, powerenergy transfer functions can be formed. In a powerenergy transfer function in the model with two poles and one zero, the zero and one pole are almost equal, if the coupling is weak. When trying to determine the poles and the zero from the CMTF curve one then runs into problems since the zero is so close to the pole. The situation with one pole is easier to handle. Therefore instead a quotient of two SEA powerenergy transfer functions with the same input power was taken. The result is a model with one pole leading to a robust evaluation of the loss factors. The result is the quotient of the two subsystem energies where the input power does not enter and thus need not be known. The virtual boundary condition using this new transfer function model is given by putting the denominator energy equal to zero, meaning that the corresponding subsystem is energy earthed.<br/><br> <br/><br> Even for SEA models with more than two subsystems, a model with one pole can be derived.<br/><br> <br/><br> In the physical system the power can be timevaried by letting the system excitation signal consist of random noise modulated with a deterministic timevarying function. However, since the ensemble average of the squared response is proportional to the squared impulseresponse convolved with the squared modulating function, random excitation is avoided and replaced by impulseresponse measurements. The Fourier transform of the lowpass filtered squared impulse response is the CMTF.<br/><br> <br/><br> A CMTF curve for a short distance between source and observation position does not show simple lowpass character, but has a "floor". A model for the modulation transfer function could therefore consist of a modulation frequencyindependent part diminishing with source distance and originating from the direct field and a lowpass character sourcedistance independent part originating from the reverberant field. At a certain distance from the source the magnitudes of the two parts are equal. The distance is here called the modulation direct field radius in analogy with the ordinary direct field radius. The modulation direct field radius is monotonically increasing with the modulation frequency. Thus the distance affected by the direct field is larger for the modulation than for the nonmodulated, stationary, case.<br/><br> <br/><br> Experiments were carried out on two plates connected at a point by a spring and in two rooms divided by a wall.}}, author = {{Lundberg, KarlOla}}, isbn = {{9178740339}}, keywords = {{vacuum technology; hydraulics; Mechanical engineering; modulated noise; insitu; modulation transfer function; loss factor; SEA; vibration and acoustic engineering; Maskinteknik; hydraulik; vakuumteknik; vibrationer; akustik}}, language = {{eng}}, publisher = {{Dept. of Engineering Acoustics, LTH, Lund University, P.O.B. 118 SE221 00 Lund Sweden,}}, school = {{Lund University}}, title = {{Applications of the Complex Modulation Transfer Function on SEAsystems}}, year = {{1999}}, }