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Enhancing the Study of Waves in Metals Using Computational Analysis

Enhancing the Study of Waves in Metals Using Computational Analysis. Michael B. Ottinger Missouri Western State University Mark A. Johnson Missouri State University American Association of Physics Teachers Monday, January 21, 2008. Outline.

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Enhancing the Study of Waves in Metals Using Computational Analysis

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  1. Enhancing the Study of Waves in Metals Using Computational Analysis Michael B. Ottinger Missouri Western State University Mark A. Johnson Missouri State University American Association of Physics Teachers Monday, January 21, 2008

  2. Outline • History of Problem and Description of Experiment to be Modeled • Modeling Technique Used • Data from Computer Model • Conclusions

  3. Experiment Engineering Project: • Use sound wave reflection in a metal to determine locations of cracks and irregularities in the metal. • Analyze shape of reflected wave to determine properties of irregularity

  4. Preliminary Design • 1.0 Inch x 3.0 Inch x 3.0 Inch Aluminum Block • Compression Transducer (1.0 cm diameter) placed at bottom center of block. • Emits short compression pulse • Measures reflected compression waves • Oscilloscope displays compression waves as a function of time

  5. Experimental Data Anomalous Waves Initial Wave Reflected Compression Waves

  6. Theory of Anomalous Wave • Transducer is picking up a shear wave created as the compression wave reflects off top surface • Compression Wave Speed: • Shear Wave Speed: • Time for Compression Wave to Reach Transducer: • Time for Shear Wave to Reach Transducer:

  7. Creation of Shear Wave

  8. Questions • Is this theory valid? Does reflection off a free surface produce a shear wave? • If there is a shear wave, how does the compression transducer detect the shear wave?

  9. Computer Modeling • PHY 410 – Selected Topics in Physics “Computational Physics” • Teaches basic algorithms to model complex physics phenomena.

  10. Modeling Technique • Finite Element: • Cylindrical Symmetry R=1.5 inches H = 1.0 inches • Two-Dimensional Array of Concentric Rings (nr=1500 nz=1000) • Displacements: • Radial: dr(i,j) Axial: dz(i,j) • Euler-Cromer Method • az(i,j)=Fij/mij • vz(i,j,t)=vz(i,j),t-1)+az(i,j)*dt • dz(I,j,t)=dz(I,j,t-1)+vz(I,j,t)*dt

  11. Equations of Motion • Compression Force: Young’s Modulus (Y) • Shear Force: Shear Modulus (S) • Bulk Force: Poisson’s Relation

  12. Compression Acceleration

  13. Shear Acceleration

  14. Poisson Acceleration

  15. Initial Wave Generation • Compression Transducer : Circular w/ D = 1.0 cm • Create two periods of compression acceleration with f=100 ns • For r<0.50 cm and t<200ns, az(0,r)=A cos (2pt/100 ns)

  16. Data Analysis • Observation of dz(0,0.2cm) as a function of time: Reflected Compression Wave Initial Wave Anomalous Wave

  17. Initial Compression/Shear Wavest=500, 1500, 2500, 3500 ns

  18. Reflected Compression/Shear WavesT=6500, 8500, 10000 & 13000 ns

  19. Compression and Shear at Surface Shear Wave Arriving at Transducer Creates a Compression Wave

  20. Conclusions • Simulation shows that a shear wave is produced as the compression wave enters the metal • Shear waves are produced at each surface as the compression wave reflects • At the surface the shear wave creates a compression oscillation that is detected by the transducer • Poisson’s Relation enables the creation of the shear from compression and compression from shear. (Data not shown).

  21. Future Research • Analyze the reflected wave forms from the compression and shear waves to see how a compression transducer can be used to analyze shear waves • Use Computer Simulation to analyze reflected wave forms from cracks and other deformities in metal.

  22. Questions?

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