SS-V：6010 简支薄方板 - 周期性强迫振动响应

测试编号 VD02 查看受周期性强迫振动的简支方板的瞬态响应。

定义

简支 10×10×0.05 m 的简支薄方板在均匀压力 P=100 Pa 的作用下，随时间呈如下函数变化。

P=100*( sin( ω∗t )−sin( 3ω∗t ) ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGqbGaeyypa0JaaGymaiaaicdacaaIWaGaaiOkamaabmaabaGa ci4CaiaacMgacaGGUbWaaeWaaeaacqaHjpWDcqGHxiIkcaWG0baaca GLOaGaayzkaaGaeyOeI0Iaci4CaiaacMgacaGGUbWaaeWaaeaacaaI ZaGaeqyYdCNaey4fIOIaamiDaaGaayjkaiaawMcaaaGaayjkaiaawM caaaaa@50CE@

其中，
ω = 2 ∗ P I ∗ f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacqaHjpWDcqGH9aqpcaaIYaGaey4fIOIaamiuaiaadMeacqGHxiIk caWGMbaaaa@40B2@
f = 1.2 H z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGMbGaeyypa0JaaGymaiaac6cacaaIYaGaamisaiaadQhaaaa@3E9D@
激励频率。

采用十六 (16) 个模式来准确估算动力学解，所有模式均假定有 2% 的模态阻尼。

材料属性为：
属性
值
弹性模量
2.e+11 Pa
泊松比
0.3
密度
8.e+3 kg/m3

结果

方板被模拟成一个 3D 实体。为了施加铰支座，在板的平面中间处创建了载荷线 (Figure 1)。为了根据上述公式模拟周期性载荷变化，向方板施加了两个压力载荷。
  • P = 100 ∗ sin ( ω ∗ t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGqbGaeyypa0JaaGymaiaaicdacaaIWaGaey4fIOIaci4Caiaa cMgacaGGUbWaaeWaaeaacqaHjpWDcqGHxiIkcaWG0baacaGLOaGaay zkaaaaaa@45C6@ 施加于方板的顶面，以及
  • P = − 100 ∗ sin ( 3 ω ∗ t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGqbGaeyypa0JaeyOeI0IaaGymaiaaicdacaaIWaGaey4fIOIa ci4CaiaacMgacaGGUbWaaeWaaeaacaaIZaGaeqyYdCNaey4fIOIaam iDaaGaayjkaiaawMcaaaaa@4770@ 施加于方板的底面
图 1.


下表包含动力学解的稳定状态部分的典型值 (Figure 2)。
偏移 Y，mm 曲面应力，MPa
-2.886 2.062 SimSolid，实体模型
-2.863 2.018 参考，薄方板
图 2.


1 Test 13P from NAFEMS Publication R0016, “Selected Benchmarks for Forced Vibration”（强迫振动的选定基准） J. Maguire, D.J.Dawswell, L. Gould