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Defect detection and localization in orthotropic wood slabs by inversion of dynamic surface displacements
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10.1121/1.2945706
/content/asa/journal/jasa/124/2/10.1121/1.2945706
http://aip.metastore.ingenta.com/content/asa/journal/jasa/124/2/10.1121/1.2945706

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Wooden plate and Cartesian axis system. The and axes are along the wood tangential and radial growth ring directions, and the axis along the longitudinal or fiber direction. The defect is in the form of a rectangular inclusion centered midway through the slab depth. Also shown are three independent shakers used to excite the slab.

Image of FIG. 2.
FIG. 2.

Calculated color-coded surface displacement at 5 and when the shaker in the lower left position is excited at each frequency. Positive and negative relative phases are indicated by red to yellow and dark to light blue, respectively.

Image of FIG. 3.
FIG. 3.

Result of applying weak flexural wave inversion operator (WFWI) developed for the isotropic case, Eq. (5), to the displacement data (lower left driver excited) at each frequency for both the homogeneous wooden slab and the flawed wooden slab. The magnitude of the inversion in units of is color coded from blue to red.

Image of FIG. 4.
FIG. 4.

Result of applying the weak flexural wave inversion operator (WFWI) developed for the orthotropic case, Eq. (11), to the displacement data at each frequency for the homogeneous wooden slab to obtain the three stiffness parameters , , and . The magnitude of the inversion in units of the respective values is color coded from blue to red. The three artifacts seen in each figure are due to the presence of the shakers.

Image of FIG. 5.
FIG. 5.

Result of applying the weak flexural wave inversion operator (WFWI) developed for the orthotropic case, Eq. (11), to the displacement data at each frequency for the flawed wooden slab to obtain the three stiffness parameters , , and . The magnitude of the inversion in units of the respective values is color coded from blue to red. The three artifacts again seen in each figure are due to the presence of the shakers. The defect which is located in the upper left of the wooden slab can be seen in each display.

Image of FIG. 6.
FIG. 6.

Result of applying the GFM operator developed for the orthotropic case, Eq. (12), to the displacement data at each frequency for the homogeneous and flawed wooden slab when the driver in the lower left is excited. The resulting generalized force values are shown color coded from blue to red. The operator defined in Eq. (12) has been determined inserting the values for , , and that were used in the forward finite-element calculation of displacements. The highlight seen in each figure in the lower left is due to the presence of the shaker. The inclusion located in the upper left of the flawed wooden slab can be seen best in the result.

Image of FIG. 7.
FIG. 7.

Result of applying the GFM operator developed for the orthotropic case, Eq. (12), to the displacement data at each frequency for the homogeneous and flawed wooden slab when the driver in the lower left is excited. The resulting generalized force values are shown color coded from blue to red. The operator defined in Eq. (12) has been determined inserting the values for , , and that were obtained by applying the inversion operator to the displacement data. The highlight seen in each figure in the lower left is due to the presence of the shaker. The inclusion located in the upper left of the flawed wooden slab can be clearly seen at both frequencies.

Tables

Generic image for table
TABLE I.

Nine independent stiffness matrix elements for Douglas fir .

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/content/asa/journal/jasa/124/2/10.1121/1.2945706
2008-08-01
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Defect detection and localization in orthotropic wood slabs by inversion of dynamic surface displacements
http://aip.metastore.ingenta.com/content/asa/journal/jasa/124/2/10.1121/1.2945706
10.1121/1.2945706
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