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@ -465,7 +465,7 @@ $\rho_{x y}$ correlation coefficient $\sigma$ normal stress $\sigma_{x}$ standar
$\phi_{n},\phi_{n}(x)$ nth mode shape $\phi$ mode shape matrix $\psi,\,\psi_{n}$ generalized displacement functions $\pmb{\psi}_{n}$ generalized displacement vector $\Psi$ matrix of assumed made shapes $\omega,\omega_{n}$ undamped natural circular frequencies
$\omega_{D},\omega_{D n}$ damped natural circular frequencies $\overline{{\omega}}$ circular frequency of harmonic forcing function $\chi(x)$ load distribution
# OVERVIEWOFSTRUCTURALDYNAMICS
# Chap 1 OVERVIEWOFSTRUCTURALDYNAMICS
# 1-1 FUNDAMENTAL OBJECTIVE OF STRUCTURAL DYNAMICS ANALYSIS
@ -477,17 +477,26 @@ Two basically different approaches are available for evaluating structural respo
In general, structural response to any dynamic loading is expressed basically in terms of the displacements of the structure. Thus, a deterministic analysis leads directly to displacement time-histories corresponding to the prescribed loading history; other related response quantities, such as stresses, strains, internal forces, etc., are usually obtained as a secondary phase of the analysis. On the other hand, a nondeterministic analysis provides only statistical information about the displacements resulting from the statistically defined loading; corresponding information on the related response quantities are then generated using independent nondeterministic analysis procedures.
本书的主要目的是介绍分析方法,用于确定任何给定类型的结构在承受任意动态载荷时产生的应力和变形。从某种意义上说,这一目标可被视为标准结构分析方法的延伸,这些方法通常只关注静态载荷,而本书则允许同时考虑动态载荷。在此背景下,静态载荷条件可被视为动态载荷的一种特殊形式。然而,在线性结构分析中,区分施加载荷的静态和动态分量,分别评估每种载荷的响应,然后叠加这两个响应分量以获得它们的总效应,是比较方便的。这样处理时,静态和动态分析方法在本质上是根本不同的。
为了本次介绍的目的,“动态”一词可以简单地定义为随时间变化的;因此,动态载荷是指其大小、方向和/或位置随时间变化的任何载荷。同样地,结构对动态载荷的响应,即由此产生的应力和变形,也是随时间变化的,或者说是动态的。
评估结构对动态载荷响应的两种基本不同方法是:确定性方法和非确定性方法。在任何给定情况下选择使用哪种方法取决于载荷的定义方式。如果载荷的时间变化是完全已知的,即使它可能具有高度振荡或不规则的特性,在本文中,它将被称作预设动态载荷;并且任何指定结构系统对预设动态载荷响应的分析被定义为确定性分析。另一方面,如果时间变化不完全已知但可以在统计意义上定义,这种载荷被称为随机动态载荷;并且其相应的响应分析被定义为非确定性分析。本文的重点是发展确定性动态分析方法;然而,第四部分致力于介绍非确定性分析方法,第五部分包含一章,讨论非确定性分析方法在地震工程领域的应用。
通常,结构对任何动态载荷的响应基本上以结构位移的形式表达。因此,确定性分析直接得出与预设载荷历史相对应的位移时程;其他相关的响应量,如应力、应变、内力等,通常作为分析的次要阶段获得。另一方面,非确定性分析仅提供由统计定义的载荷引起的位移的统计信息;然后使用独立的非确定性分析程序生成有关相关响应量的相应信息。
# 1-2 TYPES OF PRESCRIBED LOADINGS
Almost any type of structural system may be subjected to one form or another of dynamic loading during its lifetime. From an analytical standpoint, it is convenient to divide prescribed or deterministic loadings into two basic categories, periodic and nonperiodic. Some typical forms of prescribed loadings and examples of situations in which such loadings might be developed are shown in Fig. 1-1.
As indicated in this figure, a periodic loading exhibits the same time variation successively for a large number of cycles. The simplest periodic loading has the sinusoidal variation shown in Fig. 1-1a, which is termed simple harmonic; loadings of this type are characteristic of unbalanced-mass effects in rotating machinery. Other forms of periodic loading, e.g., those caused by hydrodynamic pressures generated by a propeller at the stern of a ship or by inertial effects in reciprocating machinery, frequently are more complex. However, by means of a Fourier analysis any periodic loading can be represented as the sum of a series of simple harmonic components; thus, in principle, the analysis of response to any periodic loading follows the same general procedure.
几乎任何类型的结构系统在其使用寿命期间都可能承受某种形式的动力载荷。从分析的角度来看将规定性载荷或确定性载荷分为周期性载荷和非周期性载荷两大基本类别是很方便的。规定性载荷的一些典型形式以及可能产生此类载荷的典型情况如图1-1所示。
如图所示周期性载荷在连续多个周期内表现出相同的时间变化。最简单的周期性载荷具有图1-1a所示的正弦变化称为简谐载荷这类载荷是旋转机械中不平衡质量效应的特征。其他形式的周期性载荷例如由船舶尾部螺旋桨产生的水动力压力或往复式机械中的惯性效应引起的载荷通常更为复杂。然而通过傅里叶分析任何周期性载荷都可以表示为一系列简谐分量的和因此原则上任何周期性载荷的响应分析都遵循相同的通用程序。
![](37e0f32d397ac8880649e94902667146bc0f04d3f3df423c13253a100ab25bb3.jpg)
FIGURE 1-1 Characteristics and sources of typical dynamic loadings: (a) simple harmonic; $(b)$ complex; (c) impulsive; (d) long-duration.
Nonperiodic loadings may be either short-duration impulsive loadings or longduration general forms of loads. A blast or explosion is a typical source of impulsive load; for such short-duration loads, special simplified forms of analysis may be employed. On the other hand, a general, long-duration loading such as might result from an earthquake can be treated only by completely general dynamic-analysis procedures.
非周期性载荷可以是短时冲击载荷,也可以是长时一般形式载荷。爆炸是冲击载荷的典型来源;对于这种短时载荷,可以采用特殊的简化分析方法。另一方面,例如地震引起的一般长时载荷,只能通过完全通用的动力分析程序来处理。
# 1-3 ESSENTIAL CHARACTERISTICS OF A DYNAMIC PROBLEM
A structural-dynamic problem differs from its static-loading counterpart in two important respects. The first difference to be noted, by definition, is the time-varying nature of the dynamic problem. Because both loading and response vary with time, it is evident that a dynamic problem does not have a single solution, as a static problem does; instead the analyst must establish a succession of solutions corresponding to all times of interest in the response history. Thus a dynamic analysis is clearly more complex and time-consuming than a static analysis.
@ -495,7 +504,11 @@ A structural-dynamic problem differs from its static-loading counterpart in two
The second and more fundamental distinction between static and dynamic problems is illustrated in Fig. 1-2. If a simple beam is subjected to a static load $p$ , as shown in Fig. $1\!-\!2a$ , its internal moments and shears and deflected shape depend only upon this load and they can be computed by established principles of force equilibrium. On the other hand, if the load $p(t)$ is applied dynamically, as shown in Fig. $1\!-\!2b$ , the resulting displacements of the beam depend not only upon this load but also upon inertial forces which oppose the accelerations producing them. Thus the corresponding internal moments and shears in the beam must equilibrate not only the externally applied force $p(t)$ but also the inertial forces resulting from the accelerations of the beam.
Inertial forces which resist accelerations of the structure in this way are the most important distinguishing characteristic of a structural-dynamics problem. In general, if the inertial forces represent a significant portion of the total load equilibrated by the internal elastic forces of the structure, then the dynamic character of the problem must be accounted for in its solution. On the other hand, if the motions are so slow that the inertial forces are negligibly small, the analysis of response for any desired instant of time may be made by static structural-analysis procedures even though the load and response may be time-varying.
结构动力学问题与其静载荷问题在两个重要方面有所不同。首先要注意的区别,根据定义,是动力学问题随时间变化的特性。由于载荷和响应都随时间变化,因此很明显,动力学问题不像静力学问题那样只有一个解;相反,分析人员必须建立一系列对应于响应历史中所有感兴趣时间的解。因此,动力学分析显然比静力学分析更复杂、更耗时。
静力学问题和动力学问题之间的第二个也是更根本的区别如图1-2所示。如果一个简支梁承受静载荷 $p$ ,如图 $1\!-\!2a$ 所示,其内力矩、剪力和变形形状仅取决于此载荷,并且可以通过已建立的力平衡原理计算。另一方面,如果载荷 $p(t)$ 以动力学方式施加,如图 $1\!-\!2b$ 所示,梁产生的位移不仅取决于此载荷,还取决于抵抗产生这些加速度的惯性力。因此,梁中相应的内力矩和剪力不仅必须平衡外部施加的力 $p(t)$ ,还必须平衡由梁的加速度产生的惯性力。
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

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学部E06 07 可再生与交叉
不支持特别基础的方法研究
聚焦一个点,深入,保持一个基金体量
工程背后的科学问题
题目上把核心点放出来
基金最重要的
- 题目
- 摘要
- 立项依据
重要问题里找创新点
先思考题目和摘要
反复凝练
调研 迅速集中到研究的小点

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1-2分钟发言材料围绕自身工作及发展谈感想谈计划
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我现在工作的重心都在发电机组多体动力学求解器开发,部分气动、多体、控制、水动多模块的耦合工作,虽然我一直在风电行业,但是多体动力学这块我也是从头开始
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