1 / 30

PHY 7 11 Classical Mechanics and Mathematical Methods 9-9:50 AM MWF Olin 107

PHY 7 11 Classical Mechanics and Mathematical Methods 9-9:50 AM MWF Olin 107 Plan for Lecture 26: Motions of elastic membranes (Chap. 8) Review of standing waves on a string Standing waves on a two dimensional membrane. Boundary value problems. Elastic media in two or more dimensions --.

nyx
Download Presentation

PHY 7 11 Classical Mechanics and Mathematical Methods 9-9:50 AM MWF Olin 107

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. PHY 711 Classical Mechanics and Mathematical Methods • 9-9:50 AM MWF Olin 107 • Plan for Lecture 26: • Motions of elastic membranes (Chap. 8) • Review of standing waves on a string • Standing waves on a two dimensional membrane. • Boundary value problems PHY 711 Fall 2017 -- Lecture 26

  2. PHY 711 Fall 2017 -- Lecture 26

  3. PHY 711 Fall 2017 -- Lecture 26

  4. Elastic media in two or more dimensions -- Review of wave equation in one-dimension – here m(x,t) can describe either a longitudinal or transverse wave. Traveling wave solutions -- PHY 711 Fall 2017 -- Lecture 26

  5. PHY 711 Fall 2017 -- Lecture 26

  6. PHY 711 Fall 2017 -- Lecture 26

  7. Standing wave solutions of wave equation: PHY 711 Fall 2017 -- Lecture 26

  8. PHY 711 Fall 2017 -- Lecture 26

  9. Wave motion on a two-dimensional surface – elastic membrane (transverse wave; linear regime). u(x,y,t) PHY 711 Fall 2017 -- Lecture 26

  10. PHY 711 Fall 2017 -- Lecture 26

  11. PHY 711 Fall 2017 -- Lecture 26

  12. Consider a rectangular boundary: b a PHY 711 Fall 2017 -- Lecture 26

  13. PHY 711 Fall 2017 -- Lecture 26

  14. More general boundary conditions: PHY 711 Fall 2017 -- Lecture 26

  15. Consider a circular boundary: R PHY 711 Fall 2017 -- Lecture 26

  16. Consider circular boundary -- continued PHY 711 Fall 2017 -- Lecture 26

  17. Some properties of Bessel functions PHY 711 Fall 2017 -- Lecture 26

  18. http://dlmf.nist.gov/ PHY 711 Fall 2017 -- Lecture 26

  19. Series expansions of Bessel and Neumann functions PHY 711 Fall 2017 -- Lecture 26

  20. Some properties of Bessel functions -- continued PHY 711 Fall 2017 -- Lecture 26

  21. PHY 711 Fall 2017 -- Lecture 26

  22. PHY 711 Fall 2017 -- Lecture 26

  23. More complicated geometry – annular membrane a b PHY 711 Fall 2017 -- Lecture 26

  24. Consider circular boundary -- continued PHY 711 Fall 2017 -- Lecture 26

  25. Normal modes of an annular membrane -- continued a b PHY 711 Fall 2017 -- Lecture 26

  26. Normal modes of an annular membrane -- continued a b PHY 711 Fall 2017 -- Lecture 26

  27. Normal modes of an annular membrane -- continued a b PHY 711 Fall 2017 -- Lecture 26

  28. Analysis for m=0 and a=0.1, b=0.2: PHY 711 Fall 2017 -- Lecture 26

  29. PHY 711 Fall 2017 -- Lecture 26

  30. a b PHY 711 Fall 2017 -- Lecture 26

More Related