Strange sound, annoying sound

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Strange sound, annoying sound
Lecture

• Department of Computer Science
• MIKI, Yasushi

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Annoying sound
?Scratching a window glass with nails
?Scratching a blackboard
?Rubbing expanded polystyrene
Frictional sound
Stringed instruments (violin, etc.)
Naki-suna (Creaking of Sand Layer)
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Mechanism of generating frictional vibration
Stick-Slip phenomenon
object
Spring 1
wall
Spring 2
Frictional force
pull
Damper 1
platform
Damper 2
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Mechanism of generating frictional vibration
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Solution of a differential equation
s1, r1
s2, r2
M1
v
M2
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Change of periods due to the maximum static
frictional force
?Max. static frictional force
Time???
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Change of periods
? ? ? ? ? ? ? ?
Abrupt change of period due to a small change of
frictional force
? ? ?
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Change of frictional force
Change randomly
Pressing force of a nail to the board
Random
Abrupt change of period of vibration
Change of pulling velocity
Scratching velocity of a nail
Change randomly
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Solution of the equation
s1, r1
s2, r2
M1
mmax
v
M2
Add randomness here!
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Annoying sound, is it chaos?
Chaos
Logistic mapping
Frictional vibration
f(x) c x (1 - x)
Logistic map
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Annoying sound and logistic mapping
f(x) c x (1 - x)
c 3.65
c 3.5
c 3.2
Repeating the mapping f(x), x has the period of
2-point periodicity (left), 4-point periodicity
(middle), and becomes aperiodic (right), due to
the value c.
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Annoying sound and logistic mapping
f(x) c x (1 - x)
Change of periodicity due to the value c. Lets
hear the sounds!
Low speed reproduction
High speed reproduction
4.0
3.5
c 3.0
Increasing the value of c according to time.
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Annoying sound and logistic mapping
f(x) c x (1 - x)
We can produce such a sound
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We can recognize the annoying sound as a chaotic
vibration,
but
What makes us feel such an annoying impression.
unpleasant
?
uncomfortable