Acoustics of wood - ETSAM · Course in Non Destructive Testing of Wood 02 Acoustics – Pág. 2 ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid Madrid, Junio

Course in Non Destructive Testing of Wood 02 Acoustics – Pág. 1ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid Madrid, Junio 2005

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Acoustics of wood

Introduction* Acoustical parameters

* Stress wave propagation in 1D and 3D

* Stress wave velocity, relationship with MOE, MOR, density and fiber length

* Practical application: - evaluation of urban trees, defect detection - wood selection for musical instruments


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Acoustic parameters of wood are:- sound velocity,

- acoustic impedance

- damping, logarithmic decrement

Sound velocity in homogeneous solidsvelocity:

Wave forms: longitudinal (pressure)

transverse (shear)

surface

MOE: modulus of elasticityG : shear modulusν : Poisson ratio

Stress wave is the mixture of the 3 wave forms.

νν

++

=1

12,187,0ts VV

( )( )ννν

ρ 2111

−+−

=MOEVl


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Sonic velocities of orthotropicsolids like wood:

Longitudinal (p) waves: V11, V22, V33

Transverse waves V44 =VRTdeduced from V23 and V32

Figure from V. Bucur: Acoustics of wood

Figure from V. Bucur: Acoustics of wood

Longitudinal velocity surface

Velocity depends on the direction of the propagation.

Velocity of the p waves are the highest


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Hankinson’s formula

0

1

2

3

4

5

0 15 30 45 60 75 90Angle (degree)

Velo

city

(km

/s)

Velocity (km/s)Hankinson

L R

V(α)=V0 V90/(V0 sin(α)n+V90 cos(α)n) n=2

Demonstration:

Material: beech veneer


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Attenuation

figure from F. C. Beall article

Acoustic impedance (z) : z=Vρ

zwood⊥= 0,5 MPa s/m

zwood =2,5 MPa s/m zair =0,4 KPa s/m

Reflection coefficient (R) reflected wave energy/ incident wave energy

Wave propagation is perpendicular to the surface:

q=z1/z2 wood

( )( )2

2

11

+−

=qqR

z1

z2

z1>z2

qwood /air=6000

Rwood/air=0,9993 air


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-1

-0,5

0

0,5

1

1,5

0 1 2 3 4 5 6 7

Time

Ae-λt

A1

A2

T

Damping characterisation by the logarithmic decrement (δ)

δ=ln(A1/A2)=λT

δ=ln(a1/a2)/dt/f

Logarithmic decrement determination

a1

a1: amplitude (black)

a2: amplitude at the delayed spectra (white)

dt: delay

f : frequency

spectra

vibration

a1

a2


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Experimental set-up for

logarithmic decrement determination

Sound propagation around knot


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p-Wave propagation around knot in spruce lumber

Grid size is 10 by 10 mm

Pendulum was used for making uniform start signal


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10


11


12


13


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Amplitude

Time

treshold

starter signal

receiver signal

Measured time depends on the receiver signal level

Determination of the stress wave time


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y = 1,8039x + 6,9R2 = 0,9999

0

100

200

300

400

0 50 100 150 200

dis tance [cm]

time

[ µs]

TOF slope technique for velocity determination

Velocity is determined by the slope.

Accurate test

Stress wave velocity, relationship with MOE, MOR, density and fiber length

MOEdynamic= ρ V2

MOEstatic < MOEdynamic (Reason is creep)

Velocity is a good predictor of MOE

MOE and MOR correlation is rather high (0,7-0,8), so transitive there is correlation between V and MOR ( 0,6 - 0,7)

(correlation coefficients are in the brackets)

Effect of time on MOE determination

y = -0,1988x + 9,5186R2 = 0,9875

8,89,09,29,49,69,8

10,010,210,4

-4 -2 0 2 4

log(characteristic time[s])

MO

E[G

Pa]


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Velocity and densityThere is no correlation between velocity in grain direction and density. Foresters in Australia and Japan are predicting density by stress wave velocity perpendicular to the grain.

Velocity and fiber lengthThere is correlation between fiber length and velocity in fiber direction. Longer fibers resulting higher MOE and MOR.

Velocity and microfibril angleThere is correlation between microfibril angle and velocity in fiber direction. Lower angle results higher velocity and MOE

Practical applications:- Predicting tree stiffness

- Evaluation of urban trees, defect detection


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Stiffness grading of trees by stress wave velocity determination

Director ST300 tool

by Fiber-gen, NZ

Background:

MOE= ρV2

Stiffness grading of trees by stress wave velocity determination

TreeSonic tool by

Fakopp and Weyerhaeuser


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Tree evaluation using the stress wave technique

Sound propagates faster in intact than in decayed wood. By simply hitting on the tree and measuring the radial stress waves velocity, internal defects are detectable. Stress waves are generated by hitting the start transducer using a hammer.

Figure shows the sound propagation in an intact and in a decayed tree.

The principle


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FAKOPP Microsecond Timer

Measurement perpendicular to the grain

Evaluation

The evaluation is rather simple. If the measured velocity is lower than 90% of the velocity in an intact tree, the tree contains an internal defect, in the line between the transducers. Is the deviation is higher the defect size is also higher. The relative velocity change (RVC) is a measure of the defect size.

100*reference

measuredreference

VVV

RVC−

=


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Reference velocity examples:

Tree Radial Tree Radialspecies velocity [m/s] species velocity [m/s]

Poplar 1140 Larch 1490Spruce 1410 Oak 1620Silver fir 1360 Beech 1670Scotch fir 1470 Linden 1650Black fir 1480 Maple 1690

Examples:

We are testing big trees.

Poplar trees in a protected area.


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The extention of the decay is the question.



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A huge plane tree in a play ground

Some defect found by stress wave technique.

Defect was invisible on the outside.


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Acoustic tomography

Using multiple measurements in a plane, 2D imaging of a decay is possible.

Experiment with artificial defect.

Velocity decreases greater than 7% are indicated by bold numbers.


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Self calibration

Self calibration is possible based on the velocity measurement between the neighboring sensors. This direction is near tangential. Wood material close to the bark, between two neighboring sensors is usually healthy, or a defect is visible from outside, like frost vibs. The average of the near tangential velocity data of the healthy sections is the basic reference velocity data.

Ratio of the stress wave velocity measured in different anatomical orientations, relative to the near-tangential direction. Valid for the 6-point setup.


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Acoustic tomographyTypically 6 to 32 acoustic sensors are placed around the tree at the level to be tested. Each sensor is equipped with a spike which is tapped through the bark, into contact with the wood material. A hammer tap on a sensor generates stress waves propagates through the tree, which are received and measured by all the other sensors.

A software takes all of transit time data. Using the distance between sensors, velocity is calculated. The end result is a two dimensional velocity distribution (tomogram) of the tree at the test level.

Decay or cavity appear on the tomogram image.Detecting internal decay by sensors located at the surface is possible, because decay modify the sound propagation.

Sound propagation

Oak disk, grid size is 2 by 2 cm, time resolution is 20 µs.


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Sound propagation in a larch disk

Grid size is 3 by 3 cm, time resolution is 20 µs

20 µs


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40 µs

60 µs


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80 µs

100 µs


30

120 µs

140 µs


31

160 µs

180 µs


32

200 µs

220 µs


33

240 µs

260 µs


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280 µs

300 µs


35

320 µs

340 µs


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360 µs

Acoustic tomography systems:

- PICUS SONIC TOMOGRAPH - ARBOTOM ®- FAKOPP 2D Timer


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PICUS SONIC TOMOGRAPH

Image source is www.tree-test.com

ARBOTOM®

Image source:

www.rinntech.de


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FAKOPP 2D Timer


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Example images:

Linden and

Nut tree


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Evaluation methods

• Relative line velocity decrease• Cell based backprojection• Filtered backprojection

Relative line velocity decrease

1. Calculate reference velocity from the average of line velocities between neighboring sensors.

2. Select a line between any two sensors as a „defect line” if its velocity is lower than 85% of reference velocity

3. Draw a spot where two defect lines intersecting each other.


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Example image,

Relative line velocity decrease method

Cell based backprojection

1. Divide the area into cells.2. The slowness (reciprocal of velocity) of

each cell is calculated by the average of line slownesses intersecting the cell.


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Example image,

Cell based backprojection

Filtered backprojection

• Theoretical basis by J. Radon in 1917• Used in:

- Medicine (CT, NMR)- Geology- Astronomy- Ocean research- Wood NDT- etc.


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• Radon transform of f(x,y):

• Our case:

where ti,j is the time measured between the ith and jth sensorsXj and Xj are the coordinates of the ith and jth sensorsv(x,y) is the velocity at the (x,y) point

We know ti,j and need v(x,y) => INVERSION

• Solution: projection-slice theorem by Bracewell:connection between Radon and Fourier transform

where: : Radon transform: 1-dimensional inverse Fourirer transform: 2-dimensional Fourirer transform

• Discrete version: filtered backprojection algorithm


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Example image,

Filtered backprojection

„3D” test


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Acoustic tomography

demonstration in the arboretum

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Acoustics of wood - ETSAM · Course in Non Destructive Testing of Wood 02 Acoustics – Pág. 2 ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid Madrid, Junio