| Viscous damping | New hysteretic damping | Coulomb damping | |||||||
| The mechanical model |
.files/image002.gif) |
.files/image004.gif) |
.files/image006.gif) |
||||||
|
The mathematical model
for free vibration |
|
 |
|
||||||
| The amplitude decay |
Exponential decay
|
Geometric decay
|
Linear decay
|
||||||
| Trajectories in the phase plane with various initial states by the Mathmatica | |||||||||
| The damping coefficient | file(avi) |
 YouTube |
file(avi) |
YouTube |
a (a=2) | file(avi) |
YouTube |
||
| 𝜉>1 (𝜉=1.5) | video | video | η>1 (η=1.5) | video | video | video | video | ||
| 𝜉=1 | video | video | η=1 | video | video | ||||
| 𝜉<1 (𝜉=0.3) | video | video | η<1 (η=0.3) | video | video | ||||
| The mechanical model, the displacement history, the velocity history and the trajectories in the phase plane by the Mathmatica | |||||||||
| The damping coefficient | file(avi) |
YouTube |
file(avi) |
YouTube |
a (a=2) | file(avi) |
YouTube |
||
| 𝜉>1 (𝜉=1.5) | initial state=(5, 0) | initial state=(5, 0) | η>1 (η=1.5) | initial state=(-5, 5) | initial state=(-5, 5) | initial state=(18, 0) | initial state=(18, 0) | ||
| 𝜉=1 | initial state=(5, 0) | initial state=(5, 0) | η=1 | initial state=(-5, 5) | initial state=(-5, 5) | ||||
| 𝜉<1 (𝜉=0.3) | initial state=(5, 0) | initial state=(5, 0) | η<1 (η=0.3) | initial state=(5, 0) | initial state=(5, 0) | ||||
.files/image008.gif){kind=small}