Course:PHYS341/2018/Calendar/Lecture 17
Phys341 Lecture 17: Summary and web references
2018.02.09
Textbook 13.1
- 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
- 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
- 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.
- Vibration simulation results – (2,0) bending mode
- Vibration simulation results – (1,1) twisting mode
- Baseball and softball bats: https://html5.dcatalog.com/?docid=c5e57b9f-78f1-41f6-b49b-a83c0136423e#page=36