Determination of the modulus of elasticity of prismatic bars by longitudinal vibration Laboratory practice
Instructions

Principle
Dynamic longitudinal modulus of elasticity (MOE) of homogenius prismatic bars is given by the following term:

where: is the density and is the velocity of sound. A precise sound velocity determination is given by longitudinal vibration:

where is the length of the beams, is the longitudinal vibration frequency.


Material and dimensions
Material is basically any solid material. Recommended length minimum 0,5m and minimum 5 times of the width of the bar. We can test shorter beams, but high frequency respond microphone is required, like dynamic microphone. This case the minimum length goes down to 0,3m.

Setup
Using the following setup determination of the longitudinal vibration frequency is easy:


The test bar is supported by two rubber strips. End of the bar is hit by hammer. There is a microphone at the opposite end.

Test procedure
Please hit the end of the bar. Direction of hit is longitudinal. Weigh of the hammer is 0,5-5% of the weight of the sample. Material of the hammer head is steel or hard wood (hard type). A perfect hit is speedy and the hammer spring back from the bar.
Settings of the FFT software: Frequency range: 11025 (or 5512) Hz, Trigger level 5% but in noisy environment higher trigger level is recommended.
Typically more the one peak is observed. Selecting of the longitudinal vibration frequency please predict the longitudinal frequency of dry wood samples by the following term:


where the is the length in m and the predicted frequency is given in Hz. The actual frequency will be in the range of predicted frequency +/-20%. For wet wood samples please use 1600 instead of 2500.
Equipment list
Balance 				Measuring tape and/or caliper
Rubber strips			Soft and hard hammers
Samples				PC with sound card, microphone and FFT software


Example spectra: Length=0,5m, longitudinal vibration frequency = 4954Hz.
Velocity = 4954m/s. Material: Robinia pseudoacacia, dimensions: 13 x 70 x 500mm



Determination of the modulus of elasticity of prismatic bars by bending vibration Laboratory practice
Instructions

Principle
Dynamic bending modulus of elasticity (MOE) of homogenius prismatic bars is given by the following term, where the effect of the shear is neglected:
where is bending vibration frequency, n is the mode number, support condition is free
 , n is mode number, but
  is the mass of the bar
  is the length of the bar
  is the inertia, where a is the width and b is the thickness of the bar
Effect of shear is minor if the length of the bar is higher than 30 times of the thickness.
When the length is shorter, the obtained result is lower than the correct one.
Perfect solution provided by Timoshenko equation. Another practice deals with this problem.

Material and dimensions
Material is basically any solid material. Recommended length is at least 30 times of the thickness of the bar. Slender beam is recommended.


Setup
Using the following setup determination of the bending vibration frequency is easy:


The test bar is supported by two rubber strips at 0,223L locations from the end. Center of the bar is hit by hammer, where a microphone picks up the vibration signal.

Test procedure
Please hit the center of the bar. Weigh of the hammer is 0,5-5% of the weight of the sample. Material of the hammer head is rubber (soft type). Settings of the FFT software: Frequency range: 1102 Hz, Trigger level 5% but in noisy environment higher level is recommended.
The tallest peak is belongs to the bending vibration, mode number 1.
For testing higher modes please place rubber supports at nodal points and the maximum amplitude locations are the hit and microphone locations. The following figure shows the nodal locations at the first 4 modes:


The nodal locations, bending of uniform cross-section bar, free support condition. 
Equipment list
Balance 				Measuring tape and/or caliper
Rubber strips			Soft and hard hammers
Samples				PC with sound card, microphone and FFT software

Example spectra: Bending vibration, mode no. 1. Frequency=263,6Hz
Material: Robinia pseudoacacia, dimensions: 13 x 70 x 500mm

Determination of the shear modulus of prismatic bars by torsional vibration Laboratory practice
Instructions

Principle
Dynamic shear modulus (G) of homogenius prismatic bars is given by the following term:

where is torsional vibration frequency, n is the mode number,
 , n is mode number, but
  is the density of the bar
  is the length of the bar
  is the inertia, where a and b are the cross-sectional dimensions
  where a>=b and c is given in the following table

a/b

1

1.25

1.5

1.75

2

2.5

3

4

5

10

20

C

0.141

0.172

0.196

0.214

0.229

0.249

0.263

0.281

0.291

0.312

0.323



Material and dimensions
Material is basically any solid material. Recommended length is at least 30 cm. Ratio between with/thickness is at least 2 or higher.

Setup
Using the following setup determination of the bending vibration frequency is possible:


The test bar is supported by a rubber strips at the center of the bar and two small rubber support is placed at the ends according to the figure above. Hit location marked by a circle close to the corner. Microphone location is another corner.

Test procedure
Please hit the bar close to the corner. Weigh of the hammer is 0,5-5% of the weight of the sample. Material of the hammer head is depends on the frequency. For low frequency please use soft, for high frequency please use hard hammer. Settings of the FFT software: Frequency range: depends on dimensions, Trigger level 5% but in noisy environment higher level is recommended.
Identification of torsional peaks is not easy. Typically bending and torsional peaks appears together. First determine the bending frequencies and deselect those peaks. The remaining are the torsional peaks. The torsional peaks are almost “equidistant” peaks, ratio between 1, 2 and 3 modes are 1, 2 and 3. In practice +/-10 percent deviation is possible. Please use mode number 1 data in the evaluation.
Equipment list
Balance 				Measuring tape and/or caliper
Rubber strips			Soft and hard hammers
Samples				PC with sound card, microphone and FFT software

Bending (B1, B2 and B3) and torsional (T1, T2 and T3) vibration of a bar. Material: Robinia pseudoacacia, dimensions: 13 x 70 x 500mm