Course:PHYS341/2018/Calendar/Lecture 17

Phys341 Lecture 17: Summary and web references

2018.02.09

Textbook 13.1

1. Plates and Membranes
   • Everything vibrates
   • Not just simple structures like strings and air columns
   • And everything that vibrates, radiates sound
   • Next up: two-dimensional objects
   • Plates (stiff without tension)
   • Membranes (under tension, not stiff)
   • Real musical instruments tend to be constructed of plates and membranes
   • Plates → soundboxes (any string instrument)
   • Membranes → drums
2. A wooden plate
   • Consider a thin plate of sitka spruce
   • The finest of acoustic woods, from Haida Gwaii
   • 350 x 72 x 4 mm, quarter sawn (we’ll get into wood grain later)
   • Excellent for sound boards
3. Vibrations of a plate
   • A long narrow plate (called a bar) vibrates differently from a string
   • It is stiff (a string is floppy)
   • It does not need to held tightly to vibrate (or at all, except for gravity)
   • Consider the free vibrations (i.e. lightly held) of the wooden plate
   • These we can simulate in a commercial “finite-element” (FE) code like SolidWorks
   • The FE code is very complex; it takes into account the mass and stiffness of the wood (which is different in different directions due to the grain)
   • The results show all the basic features of plate vibrations
   • Unlike strings, the thicker the plate, the higher the frequency. The mass increases with thickness, but the stiffness rises even faster.
4. Vibration simulation results – (2,0) bending mode
5. Vibration simulation results – (1,1) twisting mode
6. Baseball and softball bats: https://html5.dcatalog.com/?docid=c5e57b9f-78f1-41f6-b49b-a83c0136423e#page=36