Method of images for the harmonic response of beams and rectangular plates

Gunda, Rajendra; Vijayakar, Sandeep; Singh, Rajendra

doi:10.1006/jsvi.1995.0418

Cited by 26 publications

(30 citation statements)

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“…For an observation point located on the plate, the result observed corresponds to interference between the direct wave and the multiple reflected waves. According to this reasoning, also defended by other authors [6][7][8] the free space Green function is still valid in a plate of finite dimension but an additional correction term must be added in order to both satisfy the inhomogeneous plate equation and the boundary conditions. Therefore, in the absence of any external source to the plate, it is reasonable to write the Green function of the plate as follows:…”

Section: Frequency Response Of a Circular Array Of Point Receiversmentioning

confidence: 87%

Measurement of thickness or plate velocity using ambient vibrations

Ing

Etaix

Leblanc

et al. 2010

The Journal of the Acoustical Society of America

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Abstract:Assuming the Green's function is linear with respect to the boundary conditions, it is demonstrated that flexural waves detected by a point receiver and a circular array of point receivers centered on the previous receiver are proportional regardless location of the source and geometry of the plate. Therefore determination of plate velocity or thickness is done from the measurement of ambient vibrations without using any emitter. Experimental results obtained with a plate of non regular geometry excited with a single transducer or a remote loudspeaker are shown to verify the theoretical approach.

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Section: Frequency Response Of a Circular Array Of Point Receiversmentioning

confidence: 87%

Measurement of thickness or plate velocity using ambient vibrations

Ing

Etaix

Leblanc

et al. 2010

The Journal of the Acoustical Society of America

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show abstract

“…For a finite plate, the Green's function can be approximated by means of the image source method [6,10]. The image source method is basically a methodology to enforce the boundary conditions that should be satisfied at the edges of the finite plate.…”

Section: Green's Functions Of a Point Excited Platementioning

confidence: 99%

“…Depending on the magnitude of all image sources F , certain boundary conditions can be satisfied along the edge of the plate. In papers from Gunda the procedure is outlined for several types of boundary conditions [6,8]. Consider the measured out-of-plane displacement w(x j , y j , ω) of an harmonically excited, finite plate, at discrete measurement positions (x j , y j ), j = 1...M , on the plate surface.…”

Section: Green's Functions Of a Point Excited Platementioning

confidence: 99%

“…Such a model is much better suited to represent the vibrational field of a point excited plate, especially in the higher frequency range, as the accuracy of the image source method is known to increase with frequency and damping [6]. Indeed, Cuenca and Simon [7] estimated the material properties of a point excited plate (with free boundary conditions) on the basis of a point mobility measurement, fitting the point mobility measurement data on to the image source method model.…”

Section: Introductionmentioning

confidence: 99%

“…Using the image source method to theoretically describe the wave field of a plate with a boundary condition which is different from a simply supported or roller boundary condition, is a difficult task (albeit not impossible, see [6,8]). Moreover, in practice the reflection coefficients deviate from the theoretical prediction, because of non-modelled dissipation effects, introducing an uncertainty in the theoretical models.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimation of plate material properties by means of a complex wavenumber fit using Hankel's functions and the image source method

Roozen

Leclère

Ege

et al. 2017

Journal of Sound and Vibration

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This paper presents a new wave fitting approach to estimate the frequency dependent material properties of thin isotropic plate structures from an experimentally obtained vibrational field, exciting the plate at a single point. The method projects the measurement data on to an analytical image source model, in which Hankel's functions are used for a description of the wave fields emanating from the point of excitation, including the reflected wave fields from the edges of the finite plate. By minimizing the error between the projected field and the measured field, varying the complex wave number and the source strengths of the image sources, an optimum fit is searched for. Thus the source strengths of the image sources do not need to be determined theoretically, but are estimated from the fit on to the experimental data instead (thus avoiding difficulties in theoretically assessing the reflection coefficient of the edges of the plate). The approach uses a complex wavenumber fit, enabling the determination of the dynamic stiffness of the plate structure and its damping properties as function of frequency. The method is especially suited for plates with a sufficient amount of damping, excited at high frequencies.

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Estimation of Vibrational Power in Built-Up Systems Involving Box-Like Structures, Part 1: Uniform Force Distribution

Fulford

Petersson

2000

Journal of Sound and Vibration

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Method of images for the harmonic response of beams and rectangular plates

Cited by 26 publications

References 0 publications

Measurement of thickness or plate velocity using ambient vibrations

Measurement of thickness or plate velocity using ambient vibrations

Estimation of plate material properties by means of a complex wavenumber fit using Hankel's functions and the image source method

Estimation of Vibrational Power in Built-Up Systems Involving Box-Like Structures, Part 1: Uniform Force Distribution

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