<title>Predicting and measuring flexural power flow in plates</title>

Abstract

Structural power flow is an alternative way of analyzing vibrations, where, differently from traditional techniques, the emphasis is put on the active part of the vibration energy instead of the total. The active vibration energy is directly related to the injection and dissipation of energy in the structure and can, therefore, be a valuable tool for solving vibroacoustical problems. However, measuring the active part of the vibration energy in the presence of a highly reverberant field is often impractical. This paper presents an experimental method especially adapted for the computation of structural power flow using spatially dense vibration data measured with scanning laser Doppler vibrometers. In the proposed method, an operational deflection shape measured over the surface of the structure is curve-fitted using a two-dimensional discrete Fourier series approximation. This approximation minimizes the effects of spatial leakage. From the wavenumber-frequency domain data thus obtained, it is straightforward to compute the spatial derivatives that are necessary to determine the structural power flow. An example consisting of a rectangular aluminum plate supported by four rubber mounts and excited by an electrodynamic shaker is used to appraise the proposed method. Both numerically simulated data and experimental data are used. keywords: structural power flow, vibration intensity, laser vibrometers, plate structures, operational deflection shapes 0-81 94-2264-9/96/$6.OO SPIE Vol. 2868 / 149 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/04/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx =0 if in which case it can be shown that V x (wVw*) =0 . With this assumption, Eqs. (10) may be rewritten as: SPIE Vol. 2868 / 151 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/04/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

Characterisation of a dissipative assembly using structural intensity measurements and energy conservation equation

“…The application of SFT on truncated signals amplifies the components of high wavenumbers, which brings large contributions of the high wavenumber components to the results, especially in the case of calculating the high-order derivatives of the velocity. For a plate-like structure, the boundary conditions lead to an error of wraparound on the wavenumber spectrum [14]. The wraparound error can sometimes be reduced by zero padding method (surrounding the plate data by a band of zeros).…”

Detecting closing delaminations in laminated composite plates using nonlinear structural intensity and time reversal mirrors

“…However, in practical applications the stress field is not readily available and must be extracted using alternative techniques. In this paper, we use a finite difference (FD) based technique that allows estimation of the components of the intensity starting from acceleration cross spectra [24,26]. We select this technique because it is suitable for both the numerical and experimental estimates of SI.…”

“…We report a numerical investigation on the use of NSI to identify and localize a hidden closing delamination in laminated plates. First, we introduce a finite difference (FD) technique to estimate the NSI on a composite thin plate [24][25][26] based only on acceleration input data. Plates with different levels of orthotropy are studied to understand the effect of the preferential directions of energy propagation on the damage sensitivity.…”

<title>Characterization of a dissipative assembly by structural intensity using optical measurements</title>

“…(13) into account, the relationship between the dissipated power and the density of total energy is defined by the following equation L Ly JWdIS(x,y)dy = w Je(x,y)dy = coE(x) (14) where E (x) = Je(x, y)dy is the density of the total energy integrated in y direction (in Jim). By taking Eq.…”