The relation between resonant frequency and elastic modulus
The relation between resonant frequency and elastic modulus
(OP)
Why the natural resonant frequency of a material is a funtion of elastic modulus?
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The relation between resonant frequency and elastic modulus
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The relation between resonant frequency and elastic modulusThe relation between resonant frequency and elastic modulus(OP)
Why the natural resonant frequency of a material is a funtion of elastic modulus?
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RE: The relation between resonant frequency and elastic modulus
Dig up an engineering textbook, and calculate the natural frequency for a simple beam. The answer should be apparent.
RE: The relation between resonant frequency and elastic modulus
Well Natural Frequency per ASME PTC 19.3 Fig. 1.1 (Equation (1)) w should be rad/s
fn=Kf/U**2 sqrt E/y fn 70 F= Hz 205.3649401
fn is natural frequency of the well at temperature in Hz fn 1050 F= Hz 188.525015
U is the insertion length of the thermowell in inches (was L) U Length= in. 10
E is the modulus of elasticity of the well material at temperature in psi E= psi 28000000
Kf is a well design constant for length and element diameter from table 1.4 Kf= 2.09
y is the specific weight of the well material at temperature, lb/in3 y= lb/in3 0.29
fw is the wake frequency in Hz
Element diameter dia. In 0.25
Well material Type 304 SSt
Obtain E from Metal Properties, y from ASME section VIII
This is in my instructions to self but it looks better in Excel.
John
RE: The relation between resonant frequency and elastic modulus
I think the material crystalline strcture will determine the resonant frequency, since this is related to the Young's modulus and which is dominantely determined by the binding energy of the atomics.
But the resonant frequencies are also related to the geometry and size, etc. of the material specimen.
But these are all the phenonmenom that demonstrate these two are related, I want to get the information about "why they are expressed so", it helps~ :)
RE: The relation between resonant frequency and elastic modulus
The natural frequency is a function of stiffness and mass. No more paramaters apply.
Stiffness however is determined by both shape and modulus of elasticy. Hence, using a material with another modulus will result in a shift in frequency.
RE: The relation between resonant frequency and elastic modulus
You are right about E being a function of the lattice properties, I seem to rememeber you can work out the upper limit of stiffness values for materials by looking at the bond stiffness.
Ah, here we go, Chapter 6 in "Engineering Materials" by Ashby and Jones. Physical basis of Young's modulus.
As to the link between stiffness density and speed of planar vibration in the material then you need to look at the derivation of the single dimension wave equation. http://www.du.edu/~jcalvert/waves/mechwave.htm
Cheers
Greg Locock
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RE: The relation between resonant frequency and elastic modulus
I think I got the relation between these two.
Since the atoms in solid materials are constantly vibrating at very high frequencies and with relatively small amplitudes. And the vibrations of adjacent atoms are coordinating with the atomic bonding. These vibrations are coordinated in such a way that traveling lattice waves are produced, which might be thought the elastic wave or simple sound waves, and that propagates the crystal at the velocity of sound.
These all can help us get the equation.
RE: The relation between resonant frequency and elastic modulus
thread330-87802
Look at Maui's posts. The second one derives modulus.
RE: The relation between resonant frequency and elastic modulus
JMW
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