阻尼摆运动的系统动力学VENSIM模拟仿真

我就是我 2022-05-16 12:35 227阅读 0赞

阻尼摆运动

以一个在粘稠液体内摆动的摆球为例,示意图如下图。

[![clip\_image002][clip_image002]][clip_image002_clip_image002]

系统动力学流图如下：

[![clip\_image004][clip_image004]][clip_image004_clip_image004]

**具体方程如下：**

(01) AV角速度=

(M质量\*G重力/B阻尼)\*SIN正弦

Units: \*\*undefined\*\*

(02) A摆角= INTEG (

AV角速度,

Units: \*\*undefined\*\*

(03) B阻尼=

Units: \*\*undefined\*\*

(04) FINAL TIME = 400

Units: Month

The final time for the simulation.

(05) G重力=

Units: \*\*undefined\*\*

(06) INITIAL TIME = 0

Units: Month

The initial time for the simulation.

(07) M质量=

Units: \*\*undefined\*\*

(08) SAVEPER =

TIME STEP

Units: Month \[0,?\]

The frequency with which output is stored.

(09) SIN正弦=

sin(A摆角\*6.28/360)

Units: \*\*undefined\*\*

(10) TIME STEP = 1

Units: Month \[0,?\]

The time step for the simulation.

摆角如下：

[![clip\_image006][clip_image006]][clip_image006_clip_image006]

摆角趋于180度，不会发生过摆现象。

[![clip\_image008][clip_image008]][clip_image008_clip_image008]

角速度会逐渐增大，到逐渐减小。

详细请参考：

王其藩，《系统动力学》，上海财经大学，pp:110-112

[clip_image002]: http://hi.csdn.net/attachment/201007/25/0_1280047164UG8f.gif
[clip_image002_clip_image002]: /images/20220516/c555a5a1661846adb34e17e1c51e694e.png
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[clip_image004_clip_image004]: /images/20220516/1d196afad5bd4db186bf9d7270eb7b82.png
[clip_image006]: http://hi.csdn.net/attachment/201007/25/0_12800471653FlZ.gif
[clip_image006_clip_image006]: /images/20220516/0be5b82f6fda489da875d62448057ff6.png
[clip_image008]: http://hi.csdn.net/attachment/201007/25/0_1280047166bVvP.gif
[clip_image008_clip_image008]: /images/20220516/20633dc59bc141389e9e0cf491fba810.png