《5单自由度系统在简谐激励下的受迫振动.pptVIP

The form of this equation is identical to that of Eq., where z replaces x and replaces . the differential equation of motion is Making the substitution Eq. becomes where y = Y has been assumed for the motion of the base. Thus the solution can be immediately written as Response of a damped system under the harmonic motion of the base Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. If the absolute motion x of the mass is desired, we can solve for x = z + y. Using the exponential form of harmonic motion gives Substituting into Eq., we obtain and Response of a damped system under the harmonic motion of the base Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. The steady-state amplitude and phase from this equation are and Response of a damped system under the harmonic motion of the base Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Response of a damped S.D.O.F. system under the harmonic motion of the base Stop here after 100 minutes 幅频特性曲线和相频特性曲线 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 也可以不按相对运动求解（见郑兆昌《机械振动》），而直接求解质量块的绝对运动。此时的运动微分方程为 即相当于质量块受到了两个简谐激励的作用。不 论是利用三角函数关系还是利用复指数函数，所 得结果与上述结果相同。 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2.1.3受迫振动系统力矢量的关系 已知简谐激振力 稳态受迫振动的响应为 现将各力分别用 B、 的旋转矢量表示。 应用达朗贝尔原理，将弹簧质量系统写成 式不仅反映了各力间的相位关系，而且表示着一个力多边形。 惯性力 阻尼力 弹性力 激振力 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. （a）力多边形 (b) z ＜＜1 (c) z = 1 (d) z ＞＞1 2.1.3受迫振动系统力矢量的关系 Evaluation only. Created with Aspose.Slides for .