speed… of what (0)

I conducted some measurements about elastic wave speed.  They are expected to be ground truth against which my finite element code is tested.

Here I have got an ultrasonic transducer (bolted-Langevin type). Cylindrical shape (length: 65mm, radius: 10mm).  The first resonant frequency is 38.8KHz.

A cylindrical rod is attached to the transducer with a grab-screw.  Made of stainless, type 304.  The same radius as the transducer. Length more than 100mm. Its material properties:

  • Young’s modulus (E): 197GPa,
  • Poisson’s ratio (\nu ): 0.3,
  • density (\rho ): 8000Kg/m^3.

AC voltage is applied to the transducer.  Current is measured for various AC frequencies.  When the current hits local peak, the rod ( transducer + stainless rod) is thought to be resonated.

Cutting the stainless rod to several lengths, the 2nd resonance is sought for each length.  Here are some results:

Though it seems like there are a few glitches around length=105mm, I thought these data are good enough for my initial testing purpose.

Since these frequencies are of 2nd mode, wave length \lambda = L (length of transducer + stainless rod).

What about wave velocity.  For frequency f, velocity c = \lambda f. And here is the plot:

This says that wave velocity is not constant but depends on shape, size.  Periodic tables like webelements is implicit about this.  Some of text books  say that speed c = \sqrt{E/\rho} as if it were constant regardless of media shape. More elaborate ones say speed of p-wave c_p = \sqrt{(\lambda + 2\mu)/\rho} and speed of s-wave c_s = \sqrt{\mu/\rho}, where \lambda and \mu are so called Lamé’s parameters. But even these ones sometimes are silent about those properties hold only for infinite, homogeneous, and isotropic media.  Confusing.

About azumih

Computer Programmer
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