vault backup: 2025-09-18 08:08:58

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书籍/力学书籍/力学/Dynamics of Structures (Ray Clough, Joseph Penzien) (Z-Library)/auto/Dynamics of Structures (Ray Clough, Joseph Penzien) (Z-Library).md

@@ -511,10 +511,10 @@ Inertial forces which resist accelerations of the structure in this way are the
 以这种方式抵抗结构加速度的惯性力是结构动力学问题最重要的区别特征。通常，如果惯性力占结构内部弹性力平衡的总载荷的很大一部分，那么在求解问题时必须考虑其动力学特性。另一方面，如果运动非常缓慢，以至于惯性力可以忽略不计，那么即使载荷和响应可能随时间变化，也可以通过静力结构分析程序对任何所需时刻的响应进行分析。
 # 1-4 METHODS OF DISCRETIZATION  
 
-# Lumped-Mass Procedure  
+## Lumped-Mass Procedure集中质量法  
 
 An analysis of the dynamic system in Fig. $1{-}2b$ is obviously made complicated by the fact that the inertial forces result from structural time-varying displacements which in turn are influenced by the magnitudes of inertial forces. This closed cycle of cause and effect can be attacked directly only by formulating the problem in terms of differential equations. Furthermore, because the mass of the beam is distributed continuously along its length, the displacements and accelerations must be defined for each point along the axis if the inertial forces are to be completely defined. In this case, the analysis must be formulated in terms of partial differential equations because position along the span as well as time must be taken as independent variables.  
-
+对图 $1{-}2b$ 中动态系统的分析，显然因惯性力源于结构的时变位移，而这些位移又受到惯性力大小的影响这一事实而变得复杂。这种因果关系的闭环，只能通过用微分方程来表述问题才能直接解决。此外，由于梁的质量沿其长度连续分布，如果要完全定义惯性力，就必须为沿轴线上的每个点定义位移和加速度。在这种情况下，分析必须用偏微分方程来表述，因为沿展向的位置和时间都必须作为自变量。
 ![](5b5fdcb154e29001df240e2ab229061f5cc678705056dab6a6bf695812120d4c.jpg)  
 FIGURE 1-2 Basic difference between static and dynamic loads: (a) static loading; (b) dynamic loading.  
 
@@ -522,28 +522,34 @@ However, if one assumes the mass of the beam to be concentrated at discrete poin
 
 The number of displacement components which must be considered in order to represent the effects of all significant inertial forces of a structure may be termed the number of dynamic degrees of freedom of the structure. For example, if the three masses in the system of Fig. 1-3 are fully concentrated and are constrained so that the corresponding mass points translate only in a vertical direction, this would be called a three-degree-of-freedom (3 DOF) system. On the other hand, if these masses are not fully concentrated so that they possess finite rotational inertia, the rotational displacements of the three points will also have to be considered, in which case the system has 6 DOF. If axial distortions of the beam are significant, translation displacements parallel with the beam axis will also result giving the system 9 DOF. More generally, if the structure can deform in three-dimensional space, each mass will have 6 DOF; then the system will have 18 DOF. However, if the masses are fully concentrated so that no rotational inertia is present, the three-dimensional system will then have 9 DOF. On the basis of these considerations, it is clear that a system with continuously distributed mass, as in Fig. $1{-}2b$ , has an infinite number of degrees of freedom.  
 
-# Generalized Displacements  
+然而，如果假设梁的质量集中在如图1-3所示的离散点上，分析问题将大大简化，因为惯性力只在这些质点处产生。在这种情况下，只需要定义这些离散位置的位移和加速度。
+
+为了表示结构所有显著惯性力的影响而必须考虑的位移分量数量，可以称为结构的动力自由度数量。例如，如果图1-3系统中的三个质量完全集中，并且受到约束，使得相应的质点只在垂直方向上平移，这将被称作一个三自由度（3 DOF）系统。另一方面，如果这些质量不是完全集中的，以至于它们具有有限的转动惯量，这三个点的转动位移也必须考虑，在这种情况下，系统有6个自由度。如果梁的轴向变形显著，沿梁轴线平行的平移位移也将产生，使系统具有9个自由度。更一般地，如果结构可以在三维空间中变形，每个质量将有6个自由度；那么系统将有18个自由度。然而，如果质量完全集中，以至于没有转动惯量，那么三维系统将有9个自由度。基于这些考虑，显然，如图1-2b所示的质量连续分布的系统具有无限个自由度。
+## Generalized Displacements  
 
 The lumped-mass idealization described above provides a simple means of limiting the number of degrees of freedom that must be considered in conducting a dynamic analysis of an arbitrary structural system. The lumping procedure is most effective in treating systems in which a large proportion of the total mass actually is concentrated at a few discrete points. Then the mass of the structure which supports these concentrations can be included in the lumps, allowing the structure itself to be considered weightless.  
 
 However, in cases where the mass of the system is quite uniformly distributed throughout, an alternative approach to limiting the number of degrees of freedom may be preferable. This procedure is based on the assumption that the deflected shape of the structure can be expressed as the sum of a series of specified displacement patterns; these patterns then become the displacement coordinates of the structure. A simple example of this approach is the trigonometric-series representation of the deflection of a simple beam. In this case, the deflection shape may be expressed as the sum of independent sine-wave contributions, as shown in Fig. 1-4, or in mathematical form,  
+上述描述的集中质量理想化提供了一种简单的方法，用于限制在对任意结构系统进行动力分析时必须考虑的自由度数量。集中质量程序在处理总质量的很大一部分实际集中在少数离散点的系统中最为有效。然后，支撑这些集中质量的结构质量可以包含在集中质量中，从而使结构本身可以被视为无质量的。
 
+然而，在系统质量相当均匀分布的情况下，限制自由度数量的另一种方法可能更可取。该程序基于这样的假设：结构的变形形状可以表示为一系列指定位移模式的总和；这些模式随后成为结构的位移坐标。这种方法的一个简单例子是简单梁变形的三角级数表示。在这种情况下，变形形状可以表示为独立的正弦波贡献的总和，如图1-4所示，或以数学形式表示，
 $$
 v(x)=\sum_{n=1}^{\infty}b_{n}\;\sin{\frac{n\pi x}{L}}
 $$  
 
 In general, any arbitrary shape compatible with the prescribed support conditions of the simple beam can be represented by this infinite series of sine-wave components. The amplitudes of the sine-wave shapes may be considered to be the displacement coordinates of the system, and the infinite number of degrees of freedom of the actual beam are represented by the infinite number of terms included in the series. The advantage of this approach is that a good approximation to the actual beam shape can be achieved by a truncated series of sine-wave components; thus a 3 DOF approximation would contain only three terms in the series, etc.  
-
+一般而言，任何与简支梁规定的支撑条件兼容的任意形状都可以通过这种无限的弦波分量序列来表示。弦波形状的振幅可以被认为是系统的位移坐标，并且实际梁的无限数量自由度由序列中包含的无限项来表示。这种方法的优点是，通过截断的弦波分量序列可以实现对实际梁形状的良好近似；因此，一个3自由度近似将只包含序列中的三项，等等。
 ![](0da72b8cfd678d5bbc10ab5bc08dfb5d10fd6fc48239f554bbc9f23715cd62ed.jpg)  
 FIGURE 1-4 Sine-series representation of simple beam deflection.  
 
 This concept can be further generalized by recognizing that the sine-wave shapes used as the assumed displacement patterns were an arbitrary choice in this example. In general, any shapes $\psi_{n}(x)$ which are compatible with the prescribed geometric-support conditions and which maintain the necessary continuity of internal displacements may be assumed. Thus a generalized expression for the displacements of any onedimensional structure might be written  
-
+这一概念可以通过认识到在本例中用作假定位移模式的正弦波形状是一个任意选择来进一步推广。通常，任何与规定的几何支撑条件兼容并保持内部位移必要连续性的形状 $\psi_{n}(x)$ 都可以假定。因此，任何一维结构位移的广义表达式可以写成
 $$
 v(x)=\sum_{n}Z_{n}\psi_{n}(x)
 $$  
 
 For any assumed set of displacement functions $\psi(x)$ , the resulting shape of the structure depends upon the amplitude terms $Z_{n}$ , which will be referred to as generalized coordinates. The number of assumed shape patterns represents the number of degrees of freedom considered in this form of idealization. In general, better accuracy can be achieved in a dynamic analysis for a given number of degrees of freedom by using the shape-function method of idealization rather than the lumpedmass approach. However, it also should be recognized that greater computational effort is required for each degree of freedom when such generalized coordinates are employed.  
+对于任何假定的位移函数 $\psi(x)$，结构的最终形状取决于振幅项 $Z_{n}$，**这些振幅项将被称作广义坐标**。假定形状模式的数量代表了这种理想化形式中考虑的自由度数量。通常，在给定自由度数量的情况下，通过使用理想化的形状函数法而不是集中质量法，可以在动态分析中获得更高的精度。然而，也应该认识到，当采用这种广义坐标时，每个自由度需要更大的计算量。
 
 # The Finite-Element Concept