1 / 18

Predicting Vibration Frequencies of the Diamond Wafer

Predicting Vibration Frequencies of the Diamond Wafer. Presented by: Austin Antoniou Site: Nuclear Physics Mentor: Dr. Richard Jones. Modes of oscillation. Oscillation on the Z axis Rotation About X Axis Rotation About Y Axis Rotation About Z Axis. y. x. z. Model of the diamond.

dagan
Download Presentation

Predicting Vibration Frequencies of the Diamond Wafer

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Predicting Vibration Frequencies of the Diamond Wafer Presented by: Austin Antoniou Site: Nuclear Physics Mentor: Dr. Richard Jones

  2. Modes of oscillation Oscillation on the Z axis Rotation About X Axis Rotation About Y Axis Rotation About Z Axis y x z

  3. Model of the diamond Wire length=w Tension Forces Diamond length=a Distance between wire joints=s Mass of diamond=m Velocity of a wave traveling on wire=v

  4. Oscillation on the Z axis

  5. Diagram of Z Axis Oscillation

  6. Equation Used for Z axis Oscillation(continued) z(y,t)=A+sin(ky-ωt)+A-sin(ky-ωt) z(0,t)=A+sin(-ωt)+A-sin(ωt) z(0,t)=(-A++A-)sin(ωt) z(y,t)=A[sin(ky)cos(ωt)+cos(ky)sin(ωt)+ sin(ky)cos(ωt)-cos(ky)sin] z(y,t)=2Asin(ky)cos(ωt) Where 2Asin(kw)=z0, A=z0/(2sin(kw)) z’(w,t)=z0kcot(kw)cos(ωt) z’(w,t)=kcot(kw) z’(w,t)=kcot(kw)

  7. Equation Used for Z Axis Oscillation(Continued) z’(w,t)=kcot(kw) This equation can be related to the restoring force: FR= -kFTcot(kw)z FR=(d2z/dt2)m=-kFTcot(kw)z (d2z/dbt2)+[-(kFTcot(kw)/m]z=0 The generic equation used for ω isω2=(K/m) In this case, K is equal to Therefore,

  8. Graph ofω2=ωcot(ω) f(ω) (Rad2/s2) ω (rad/s)

  9. Rotation about the X axis

  10. Diagram of X Axis Rotation

  11. Rotation About the Y Axis

  12. Diagram of Y Axis Rotation

  13. Rotation about the Z axis

  14. Diagram of Z Axis Rotation

  15. Predicted frequencies of the diamond wafer (Hz) (Hz) (Hz) (Hz)

  16. ω2=ωcot(ω) f(ω) (Rad2/s2) ω (rad/s)

  17. What should we make of these calculations? • The higher-frequency oscillations are nearly identical • Mathematically, this is because the slopes of the graphs of the graphs of ω only change slightly from mode to mode • Physically, this is because the system has natural frequencies due to properties such as the length of the wires

  18. Questions?

More Related