Animation of three damping models (2017)

 

  Viscous damping New hysteretic damping  Coulomb damping
The mechanical model
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) 描述: \\140.121.146.149\web\new.gifYouTube   file(avi) 描述: \\140.121.146.149\web\new.gifYouTube a (a=2) file(avi) 描述: \\140.121.146.149\web\new.gifYouTube
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) 描述: \\140.121.146.149\web\new.gifYouTube   file(avi) 描述: \\140.121.146.149\web\new.gifYouTube a (a=2) file(avi) 描述: \\140.121.146.149\web\new.gifYouTube
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, 3.53)

initial state=(-5, 3)

initial state=(-5, 5)

initial state=(-5, 3.53)

initial state=(-5, 3)

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)

                             ※the nature frequency

                            ※ latest update:2017/12/8