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1、随机振动(PSD)分析第1页/共35页主要内容主要内容定义和目的Workbench随机振动分析功能分析流程第2页/共35页随机振动分析随机振动分析定义和目的什么是随机振动分析基于概率的谱分析.典型应用如火箭发射时结构承受的载荷谱，每次发射的谱不同，但统计规律相同.Reference:Random vibrations in mechanical systems by Crandall&Mark第3页/共35页和确定性谱分析不同，随机振动不能用瞬态动力学分析代替.应用基于概率的功率谱密度分析，分析载荷作用过程中的统计规律Image from“Random Vibrations Theory an
2、d Practice”by Wirsching,Paez and Ortiz.随机振动分析随机振动分析定义和目的第4页/共35页什么是PSD?PSD是激励和响应的方差随频率的变化。PSD曲线围成的面积是响应的方差.PSD的单位是 方差/Hz(如加速度功率谱的单位是G2/Hz).PSD可以是位移、速度、加速度、力或压力.随机振动分析随机振动分析定义和目的第5页/共35页输入:结构的自然频率和阵型功率谱密度曲线输出:1s位移和应力（用于疲劳分析）.随机振动分析随机振动分析定义和目的第6页/共35页载荷:单点激励得到结果:相对或绝对的1s 输出整体结构的结果，可以进行云图显示.1s位移,速度或加速度
3、后处理:1s 可以进行云图显示.随机振动分析随机振动分析Workbench随机振动功能第7页/共35页Model:输电铁架Analysis:地面激励PSD分析.Steps:进行模态和随机振动分析，并显示结果.随机振动分析随机振动分析随机振动分析流程第8页/共35页打开,.Browse to file if not in list随机振动分析随机振动分析随机振动分析流程第9页/共35页打开分析向导随机振动分析随机振动分析随机振动分析流程第10页/共35页利用分析向导可以简单地建立分析流程.可以看到运行随机振动分析之前需要进行模态分析.随机振动分析随机振动分析随机振动分析流程第11页/共35页点击
4、OK可以看到如图所示信息当提示“Specify Number of Modes”，输入12随机振动分析随机振动分析随机振动分析流程第12页/共35页下一步是插入约束，插入fixed support.随机振动分析随机振动分析随机振动分析流程第13页/共35页模态分析结束.可以查看模态结果，如右图所示.可以查看动画.随机振动分析随机振动分析随机振动分析流程第14页/共35页可以看到在谱分析中的初始条件已经自动设置成模态分析的结果.设置阻尼（恒定阻尼比）随机振动分析随机振动分析随机振动分析流程第15页/共35页插入一个PSD Base Excitation.在弹出的PSD Base Excitati
5、on详情串口，选择新的PSD载荷.选择带G的加速度PSD，单位G2/Hz.设置PSD曲线随机振动分析随机振动分析随机振动分析流程第16页/共35页选择激励方向为Y.选择Solve.求解结束后可以查看结果，可以选择1sigma到3sigma结果.随机振动分析随机振动分析随机振动分析流程第17页/共35页如果列出了结果更改阻尼比为，查看结果.随机振动分析随机振动分析随机振动分析流程第18页/共35页按阻尼比重新计算.随机振动分析随机振动分析随机振动分析流程第19页/共35页练习练习查看如图所示桁架桁架结构在加速度PSD激励下的响应第20页/共35页Workshop Workshop 目标目标目标是
6、研究桁架结构的振动特性.这个练习将检查钢结构桁架由于加速度谱产生的位移和应力.PSD谱可分为加速度、速度和位移.The spectrum will typically be measured during physical tests or documented in a written specification relating to the system or component.The data points can be entered for each Freq&Amplitude,or a function can be entered.AccelerationFrequency
7、F1F2F3F4A2A3A4A1第21页/共35页Workshop Workshop 假定假定The Girder has fixed constraints along all lower edges.The boundary conditions will be applied to edges.第22页/共35页Workshop Workshop 起始页起始页From the WorkBench Project Launcher start Simulation.if already in Simulation use FileNew For training purposes,choo
8、se “No:do not save any items”Once in Simulation click on GeometryFrom File to browse for and open 第23页/共35页Workshop Workshop 设置设置When the Geometry has loaded,choose“Random Vibration”from the Map of Analysis TypesNote,the map will automatically highlight“Modal”too since modal is a precursor to Random
9、 Vibration simulation.Click OK,thus accepting the default number of modesChoose the U.S.inch pound unit system.“Units U.S.Customary(in,lbm,lbf,)”123第24页/共35页Workshop Workshop 前处理前处理-壳体厚度壳体厚度The Girder geometry consists of surface bodies(for shell meshing)The first preprocessing task is to specify th
10、e thickness of all the surfaces.Click to fully expand the Girder“Geometry”branch.In the Details pane,notice that the“Thickness”field are displayed in yellow to indicate they are undefined.Select all the bodies to assign a uniform thickness LMB to select the top Body in the Part list.Hold and LMB on
11、the last Surface Body.Note:By highlighting“all”,we can set the thickness on the first one,and the same thickness gets assigned to all of them.Of course one or more individual bodies can be redefined to different thicknesses later if necessary.Left click in the thickness field and set the thickness=0
12、.5”54第25页/共35页Workshop Workshop 前处理前处理-接触接触The assembly to be shell meshed consists of multiple surface bodies separated by small offsets that account for the physical spacing between the neutral(axis)planes of each piece of steel.We need to use“Bonded”Contact in order to simulate the effect of weld
13、ed and/or bolted assembly connectivity.Click on ConnectionsCreate Automatic Contact6.The Default definition is“Bonded”6第26页/共35页Workshop Workshop 前处理前处理-网格尺寸网格尺寸The assembly consists of multiple slender bodies plus a large flat Roof plate.We want to specify a relatively fine mesh size on the slender
14、 members but a larger element up top.By assigning larger elements on the large roof,we preserve CPU time and are able to use finer (usually more accurate)elements elsewhere.Change to Body Select.On the Outline Tree,RMB on the Mesh objectInsertSizing (for slender bodies)In Details,Replace“Default”siz
15、e with 2(inches)RMB in Graphics Window,Select AllBut then hold and LMB single select on the“roof body”to unselect that part from this Size object.ApplyInsertSizing (for the large“roof”body)Enter“4”for size in Details(for the large top plate).Use Single Select and LMB on the large Body.ApplyPreview t
16、he mesh,MeshGenerate Mesh 7.If desired,repeat the steps above to increase or decrease element sizes as desired to enhance the model or reduce CPU time.Larger Elementson roof 78,910第27页/共35页Workshop Workshop 环境环境For the lower edges of the truss,highlight the“Modal”branch in the Outline and Insert Fix
17、ed Supports.Switch to edge selection mode as necessary Reorient model as necessary throughout.an end view might be most convenient.Switch to Box SelectDrag the LMB to select the edges at the bottom of the lower girders.Click “Apply”in the Details window111213第28页/共35页Workshop Workshop 环境环境For the PS
18、D Base Excitation loads,at the Random Vibration Branch,InsertPSD Base Excitation In the Details of the PSD Load,change“Direction”to“Y Axis”for this particular XYZ orientation.For Load Data chose New PSD Load141516AccelerationFrequencyF1F2F3F4A2A3A4A1第29页/共35页Workshop PSD Workshop PSD 载荷载荷PDS data in
19、 this case is“Acceleration”Table data points,so insure that“PSD Acceleration”and“Table”is selected.Click on OKThen enter the table data for FREQ vs.Acceleration.The graph automatically updates with each data point.Eventually,click on the Simulation tab (at the very top)to exit “Engineering Data”and
20、return Simulation mode.1718第30页/共35页Workshop Workshop 求解求解Insure that the Details“Initial Condition”for the Random Vibration object is“Modal”With the branches for Modal(as well as Random Vibration)prepared,we are ready to solve this simulation.As a final check verify the status symbols next to the b
21、ranches.All branches should have either:Lightening bolt(ready)Green check mark(complete)Solve.ToolBar Button SolveNote:solving from the Toolbar“thunderbolt”causes all unsolved branches to be solved.19.Had we wished to solve only one branch(such as“Modal”in this case)we could have highlighted only th
22、e branch or object to be solved and use RMB Solve.19第31页/共35页Workshop Workshop 模态分析结果模态分析结果After the solution is completed you can review the(precursor)modal shapes for each frequency.In the Outline Tree pertaining to Modal,click on Solution(within the Modal branch)Click on the Modal Solution Branch
23、 in the Tree.Then LMB on the top of the Frequency Column in the“Tabular Data”region,and RMBCreate Mode Shape ResultsThis will insert“Total Deformation”objects in the Tree for all modes solved.Click on Click on“Solve”toolbar button so the new“result”objects can be evaluated20第32页/共35页Workshop Worksho
24、p 随机振动分析结果随机振动分析结果Now review Random Vibration results.Due to the applied spectrum,you can Insert DeformationsStrainsStresses InsertDeformationDirectionalSpecify the Z “Orientation”direction in the Details PaneInsertStrainNormalFor instance,specify Y “Orientation”in the Details PaneInsertStressEquiva
25、lent(von Mises)Click on Solve or RMBEvaluate All Results to evaluate any new objects you have added to the outline tree.Note:Only the new objects get evaluated21.This saves CPU and wall clock time.RMB21222324第33页/共35页Workshop Workshop 评价评价查看和评估结果.要点:模态分析的节点位移是相对值而非真实值。The PSD simulation generates st
26、atistically“Probable”resultant magnitudes that depend on the energy input magnitude and spectrum applied to the system.The Damping data also plays a roll in the magnitude of the response.Review available results,and change the settings under the“Edges”toolbar button.You may choose to show(or not show)elements(edges)and un-deformed model.Element edges WireFrame can become“distracting”during Post-Processing.Turn wireframe off.25looks better without wireframe edges第34页/共35页感谢您的观看！第35页/共35页