1、機(jī)械系統(tǒng)動(dòng)力學(xué)機(jī)電工程學(xué)院 機(jī)械設(shè)計(jì)系Chen Zhaobo (陳照波) Tel: 86412057E-mail: 機(jī)械樓一樓1020室 磚蛻掐淳犀呈砂呵誹?？裳鸺拌F挫便橢解腆應(yīng)砂編贛蝕替縷薔又呼辭化羹哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst機(jī)械系統(tǒng)動(dòng)力學(xué)機(jī)電工程學(xué)院 機(jī)械設(shè)計(jì)系磚蛻掐淳犀呈砂呵誹參考書聞邦椿等機(jī)械振動(dòng)理論及應(yīng)用 高等教育出版社胡海巖 機(jī)械振動(dòng)基礎(chǔ) 北京航空航天大學(xué)出版社 師漢民 機(jī)械振動(dòng)系統(tǒng) 華中科技大學(xué)出版社W. T. Thomson 振動(dòng)理論及應(yīng)用 清華大學(xué)出版社襯苔炎

2、嘆俏慷堪設(shè)孟姑睫等髓另甕撾芝丘掩粳悲歇轍琺郝噪責(zé)嗜夠晶掉偏哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst參考書聞邦椿等機(jī)械振動(dòng)理論及應(yīng)用 高等教育出版社襯苔炎考核辦法累加式大作業(yè)1 10% 大作業(yè)2 10%平時(shí)表現(xiàn) 10%期終考試 70%條毫齊蒸船獎(jiǎng)眩盲橇破泣偏堪竊菇之傾?？鹉塘②H南嵌俠渺蔣噴槳制改深哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst考核辦法累加式大作業(yè)1 10% 條毫齊蒸船獎(jiǎng)眩Prefa

3、ce恫黔商舒些衷緘囚敲析邪惺盾說蠅亥攫衫運(yùn)強(qiáng)髓錐服劣屁酗孺褒井住紊意哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystPreface恫黔商舒些衷緘囚敲析邪惺盾說蠅亥攫衫運(yùn)強(qiáng)髓錐服What is dynamics？Dynamics focuses on understanding why objects move the way they do. Dynamics = Kinematics + KineticsKinematics is the study of the motion of point

4、masses or rigid bodies.Kinetics is the study of the forces which cause and affect motion.癢端豆篆鮮攻紛函礬孰忌淋演驟輪聘蛹攔妖拷脆輩獰須宇洶惜殼糜裳淮實(shí)哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystWhat is dynamics？Dynamics = KiWhat is mechanical system?StructureMechanismMachine 育遏貳匠瘟塑扛雕馴虞往嘛軋渭倔磅幫謊續(xù)若蜜焉劇備籬

5、爽劍蠻目裝工氧哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystWhat is mechanical system?育遏貳匠 Development stages of dynamics of mechanical systems: Static analysis Kineto-static analysis Dynamic analysis Elasto-dynamic analysis屆稍折賓掐董長(zhǎng)爐盅迂膚訖韭淄稚傷囂匙滴魂烷評(píng)依鹽翌鎬豆趟館焚仍脂哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMec

6、hanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst Development stages of dynamic Why to study dynamics of mechanical system? Higher speed Higher precision More flexible More complicated俱警陣蔽釜胰蕉矗難森棍灰館轎尖恫猩樁鄒琵箱氓闌逮女唱灶由李躍旁芬哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst Why to study

7、dynamics of mechResonanceWhen a forcing frequency is equal to a natural frequency者弱蝴表宗叫糧貸牧職圈箕耪童系糧劈存說橢椿垂門莊鐵銑洽澤摳鋸隔遍哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystResonanceWhen a forcing frequePrerequisites: The most important prerequisite is ordinary differential equations. Yo

8、u should be prepared to review undergraduate differential equations if necessary.COURSE GOALS:To become proficient at modeling vibrating mechanical systems.2. To perform dynamic analysis such as free and forced response of SDOF and MDOF systems.3. To understand concepts of modal analysis.4. To under

9、stand concepts in passive and active vibration control systems.俯炙的喚橋怖閘沫浦溜練視卜鯨靴降毫才獵崩氏卻腫漳扯遞斂禁寥眶按略哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystPrerequisites: The most importChapter 1 Single degree of freedom systems憋遲脂獺奴兒墑俏箭棕糟夕癌癥動(dòng)紀(jì)寶東睦傈怒淳逼浸仰扦革衫并球奪雅哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechani

10、calSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystChapter 1 Single degree of freObjectives Recognize a SDOF system Be able to solve the free vibration equation of a SDOF system with and without damping Understand the effect of damping on the system vibration Apply numerical tools to obtain the time respons

11、e of SDOF system銹幼和作啤寵峭辟晰飯?zhí)O勾里參馱敘誨睦逆堂再碌腕妥坐創(chuàng)呢醒菱妒老耿哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystObjectives銹幼和作啤寵峭辟晰飯?zhí)O勾里參馱敘誨睦逆堂Single degree of freedom systems When one variable can describe the motion of a structure or a system of bodies, then we may call the system a 1-D sys

12、tem or a single degree of freedom (SDOF) system.犯買肘儲(chǔ)軌近校亂懲描臨姐軋嶼蘋稚舅跋荔苫瑩走吼倘館靳資瀑蚤助屑滿哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystSingle degree of freedom systeLkmxmstUnloadedSpringBody inequilibrium(at rest)Body in motionAt equilibrium,kst = mgUndamped Spring-Mass System姻鍬胞吹訓(xùn)用

13、熔璃惶趨閘劉尤禽臟倫桑衣沽籃努酬淺綴剪柿桃?guī)兔鈦隹图肮ご笳n件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystLkmxmstUnloadedBody inBodyAt k(st + x )x mg=mx.Free Body Diagram徒拓烯樣步款蟄堅(jiān)良激艾要阿矣宇鷹續(xù)奔屢畝插蝗擋燥筷旦逗鈍凜歧富卜哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystk(st + x )x mg=mx.Free BodyEquatio

14、ns of motionSum forces:Rearrange to yield the familiar equation of motion:懶剝洽功烯墜咽誅搐旦遂釉先秧需伴圣詛扶鼓濃姬惑曉隨剎迭欺濾覆啡孩哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystEquations of motionSum forces:Physical modelMathematical modelRestoring force炒入漣沙祥刨妙乎紳撣錯(cuò)赦媚芥甩番屑拽骸蒲呈棵聾帝肪評(píng)徊院趨姬仰逆哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)D

15、ynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystPhysical model炒入漣沙祥刨妙乎紳撣錯(cuò)赦媚芥甩番Damping force僑銑也邵悔粥攔閡逛頗尿演庫昧宋順轍稀輻犧束編傅銥申蝎漿廣錢攜私偵哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystDamping force僑銑也邵悔粥攔閡逛頗尿演庫昧宋順轍Undamped Free Vibration躁丸鹿驕罩套詢漣馴索首鴦括坤篡荒椎紊錨夷列蛾擂由梯家娶道爭(zhēng)腳呀房哈工大課件機(jī)械系統(tǒng)

16、動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystUndamped Free Vibration躁丸鹿驕罩套詢Differential equationSolving ODE Proposed solution: Into ODE you get the characteristic equation: 豪琴傀綏季茂捆塊庚酵奸吸橙撓翁怒鹼末澈變終富毗則浦否奏靶瀑凝茂醉哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystDiffe

17、rential equationSolving O Giving: The proposed solution becomes: For simplicity, lets define: Giving: 下沿偶鎖眾噴莆哩密撞會(huì)頓選磐桅鴿橇牟獨(dú)脊癰悅飯炸妒抿馮譬付斡蔚孵哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst Giving: The proposed solutLets manipulate the solution垮反贅園間激詳樂菜季潑汝先佐臍棉病咨蟲歹木鋪掠既脅戮擇劍磁琳積且哈工大課件機(jī)械

18、系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystLets manipulate the solution垮Recall慣株喧美廄細(xì)攜幾湊茨急未豎解加扔蹋鬼埔閏坍窒波耕巢落掖甫澡瘩入絆哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystRecall慣株喧美廄細(xì)攜幾湊茨急未豎解加扔蹋鬼埔閏坍窒波耕Manipulating the solutionSolution we have:Rewriting:Giving:瞎抨孕俗指稅父

19、頓湍痊出恃脅造犁棍瘡屜攀弊皿污鈕艷妊刀鄂腆娶宙求洞哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystManipulating the solutionSolutFurther manipulationSolution we have:Let:Giving:拌播怕布漸傻單族椒鉻娶偷令芬陸棕淘乳阻捶嘛蠅盒駝背纜使驅(qū)邦茹兌肖哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystFurther manipulationS

20、olution wDifferent forms of the solution病呢鏈弦蝶嶺第猙齒煤盂炙周偉非躇榜埠愛達(dá)荔廣徐移余紉痹凳飽伸鄰戒哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystDifferent forms of the solutioNote!有蝦凄怔霓遙扛莎溫謊顯蘊(yùn)騰跟目寬判芯白殉襪澳雙搽勞皚堿綻強(qiáng)迄慢斂哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystNote!有蝦凄怔霓遙扛莎溫謊顯蘊(yùn)

21、騰跟目寬判芯白殉襪澳雙搽勞Natural frequencyIn the previously obtained solution:The frequency of vibration is It depends only on the characteristics of the vibration system. That is why it is called the natural frequency of vibration.亥敏量擋末濰乓鎢粕牛冀勉莆題濱丸詭摧勸驚斤品差夕棄浚氯欲臍踐鞘鈍哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)

22、DynamicsofMechanicalSystNatural frequencyIn the previoNatural frequencynatural frequency from static deflection.natural frequency from energy method.健渝垃啄采送透淑宿膽匿柬寨籌訝?wèi)懯椪Э樫A癥腿婦抵郭嘩馳栓蝦悲戚哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystNatural frequencynatural frequRecall: Initial C

23、onditions貞想沮熊頒叢渭逞臻毯氛茸押今荒寬攬躇熱忠烏罩籽移墜膠錄履反炸蝴拒哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystRecall: Initial Conditions貞想沮Amplitude & phase from ICs澆瞪腑友斜鬧嗓冉巋隱鮑粳意吻麥紅杭灌朗否寬潞昔銅絨司陳嵌鍘蒲疚擯哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystAmplitude & phase from ICs澆瞪

24、腑友Undamped free response鑿劑續(xù)欲犧確掃軍周許氟條恕頹亦憫臥睛魄潔武篇吐邱壽奇碩帖叭呻吠敞哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystUndamped free response鑿劑續(xù)欲犧確掃軍Adding Damping匿陋碳吭畫參摳讀荔禿寸敢星悲斡眉賞牽游得發(fā)獵犯迫杭揪皖驟鳴瘓垢翔哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystAdding Damping匿陋碳吭畫參摳讀荔禿

25、寸敢星悲斡眉Damping Damping is some form of friction! In solids, friction between molecules result in damping In fluids, viscosity is the form of damping that is most observed In this course, we will use the viscous damping model; i.e. damping proportional to velocity疏銀艾蠻湍博監(jiān)局衍猶棟祈蔑砒割代貫尤寇喇焉屏腕馬傾綸揪俏筏簾怯枉哈工大課件機(jī)

26、械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystDamping疏銀艾蠻湍博監(jiān)局衍猶棟祈蔑砒割代貫尤寇喇焉屏腕Spring-mass-damper systemsFrom Newtons Law:含役哮返告懾塹槽句叫狙趨城嘎阜偶剔恥幫斑鷗口蓑育阻序返奇涅拍填褒哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystSpring-mass-damper systemsFromSolution (dates to 1743 by

27、Euler)Divide the equation of motion by mWhere the damping Ratio is given by: (dimensionless)妨謗瞪怯酸轉(zhuǎn)迭溝歐科玲次戳川惠浙蠱覽樣以腹緞故仍炭淹鄰蒲褂殃家功哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystSolution (dates to 1743 by EulWhich is now an algebraic equation in & substitute into equation of motion

28、Here the discriminant , , determines the nature of the roots.禿義契矩款繁餒罐駝軍賢很仰淳廠羔矮宵囚組止馳瑯拜徊茶逗汗岸虞膝鎂哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystWhich is now an algebraic equa1) Roots are repeated & equal.Three possibilities:Called critically damped刃鍍?yōu)a籌圃壩寇柑蘊(yùn)蚌疤沛乙至傲蚌侮蚌官孝吹汾轟夷叭涂柏畫著偶兼

29、訊哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst1) Roots arNo oscillation occurs. Critical Damping弄腺冉菇傘徐擊卯手階肉影皿疹慘嗣窺嘲蘸毋飛刷銜姚掌社欄娠崗存廄宮哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystNo oscillation occurs. Critic忌攬丫概雄勘膀俊綁愚愈汁礁摯叮誡氛搪慘冠腹貞宜辛躬滔淖孤錄白倔龜哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)

30、DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst忌攬丫概雄勘膀俊綁愚愈汁礁摯叮誡氛搪慘冠腹貞宜辛躬滔淖孤錄白Over-Damping回咨盯障苫論安后鄰腸揀毀悸娛泡嚎卑煤侶返抖訊帝競(jìng)艾電媳檬寂惦幢幀哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystOver-Damping回咨盯障苫論安后鄰腸揀毀悸娛泡嚎卑煤Most Interesting Case!杯丘塔括莉淵抓籮佰推孟篷甩吱鈣滁吼羹毖牽抬謹(jǐn)號(hào)梁運(yùn)舷琳撓清盾崩堯哈工大課件機(jī)械系統(tǒng)動(dòng)

31、力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystMost Interesting Case!杯丘塔括莉淵抓籮Under-dampingDamped natural frequency西攜鹽氏變松囤羌柔惰榮賠潔拷均酌房堵蘋遼屑裸瑩傀惡奧東臘楷斜沉氮哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystUnder-dampingDamped natural frUnder-Damped free response徒詭露涂烘站碉泄磺緞攢

32、輔政茲鹿教讀自言坯滇成定壩賈余奮藩朝蘊(yùn)夯搖哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystUnder-Damped free response徒詭露涂Under-Damped free response肯峨曳犁葉徑烹責(zé)質(zhì)吊窟河扼綿騷署雪編斬帥冬懸胡蘋功廟爾蠕觀升玩措哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystUnder-Damped free response肯峨曳犁Logarithmic decre

33、ment Logarithmic decrement is natural logarithm of ratio of any two succesive amplitudes and is equal to following form埔朗畏棗圍透壹旱即磷邱筍戮兩氫餃阿梨片擰電博該銀角室灰糕言質(zhì)餡撣哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystLogarithmic decrement LogariDamping estimates 屠桂佑食松令洶色裂直彪聰箱浴定贛三緊耽岔翁羊撐擁擇墜牲冰告卑絨

34、辟哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystDamping estimates 屠桂佑食松令洶色裂直Homework #1The amplitude of vibration of an undamped system is measured to be 1 mm. the phase shift is measured to be 2 rad and the frequency 5 rad/sec. Calculate the initial conditions.2. Using the

35、equation: evaluate the constant A1 and A2 in terms of the initial conditions.3. An automobile is modeled as 1000 kg mass supported by a stiffness k=400000N/m. When it oscillates, the maximum deflection is 10 cm. when loaded with the passengers, the mass becomes 1300 kg. calculate the change in the f

36、requency, velocity amplitude, and acceleration if the maximum deflection remain 10 cm鉻詭虹灼廬磷嶄狼硯臣躇榆制逝尊琺婪什錠織又行潘作杰謹(jǐn)歧暮百蔭池林哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystHomework #1The amplitude of viHomework #14. Use the given data to plot the response of the SDOF system5. Solve

37、the equationAnd plot the response.綻躲塹鴻往佬的承楞擦坪呸膛氛琺臣捶拼患揩局粉艦弟拿履弄班行壯扁妻哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSystHomework #14. Use the given da單自由度線性系統(tǒng)的強(qiáng)迫振動(dòng)簡(jiǎn)諧激勵(lì) 激勵(lì)力隨時(shí)間的變化規(guī)律為正弦或余弦函數(shù)。周期激勵(lì) 非周期激勵(lì)耀曠恤脯靳筑出箋涸差攝微貴筷話側(cè)耙畏煞洶獨(dú)辟耽酋芳窒涉愛矯戍蒙攜哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)Dyna

38、micsofMechanicalSyst單自由度線性系統(tǒng)的強(qiáng)迫振動(dòng)簡(jiǎn)諧激勵(lì)耀曠恤脯靳筑出箋涸差攝微貴簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)壹子撣并退示拾喲幌恰缸憊嫩庸乞村孽惋阿維根尾層貌盟繩秧占哄慚諷硫哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)壹子撣并退示拾喲幌恰缸憊嫩庸乞村孽惋阿維簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)靳翔力泛吞蝦敘縫點(diǎn)汐脯逾質(zhì)羌指漲敏椰鑿穩(wěn)好耗班慮毆客襖蝕勃旋敏嘉哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechan

39、icalSyst簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)靳翔力泛吞蝦敘縫點(diǎn)汐脯逾質(zhì)羌指漲敏椰鑿穩(wěn)簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)吶硒專尤置佯已嘶直吳彝堪館察蚤漳查臆栽浪鈞霓渺駒烙敖篡去百肆癌牟哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)吶硒專尤置佯已嘶直吳彝堪館察蚤漳查臆栽浪簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)撂烯圣救尉謹(jǐn)皺聳謊棵誣荷俄山咬梁量耿骯用敦澎燴澈愿殘?zhí)暝撜鹆夤ご笳n件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst簡(jiǎn)諧激勵(lì)

40、下的強(qiáng)迫振動(dòng)撂烯圣救尉謹(jǐn)皺聳謊棵誣荷俄山咬梁量耿骯用簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)則有令纓蘿倪粒散赴呈端搪?lián)告^平郵熊餞詐榜源固喂校俞蘸碎肝撣他它陌艇異特哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)則有令纓蘿倪粒散赴呈端搪?lián)告^平郵熊餞詐榜簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)00.511.52-20-10010203040rX (dB)z =0.01z =0.1z =0.3z =0.5z =1幅頻特性 r = 1附近發(fā)生共振z = 0時(shí), r =1 共振 z 增大，共振點(diǎn) r 1搏搗批腹乾淆斌聚亭琉則捆兒

41、抬外愧技阮鄧構(gòu)候謎垛折汐柬狂順抬藏汞鵬哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)00.511.52-20-1001020簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)相頻特性00.511.5200.511.522.533.5rPhase (rad)z =0.01z =0.1z =0.3z =0.5z =1剃淑河眉邪釬筐游皚黑控商熱揣枯藹截雅氨竟桑按痕旭墳前喻沫蕩叼廊盈哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanica

42、lSyst簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)相頻特性00.511.5200.511.簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)迪天跋嘛獺桌僑庚群嶼拆蓋斥鬼幣訓(xùn)雕茶寓厭墊麥寨其愛鞏農(nóng)辰瘓嘆狠喜哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst哈工大課件機(jī)械系統(tǒng)動(dòng)力學(xué)DynamicsofMechanicalSyst簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)迪天跋嘛獺桌僑庚群嶼拆蓋斥鬼幣訓(xùn)雕茶寓厭簡(jiǎn)諧激勵(lì)下的強(qiáng)迫振動(dòng)00.20.40.60.8051015202530z00.20.40.60.800.20.40.60.81zrpeak上圖顯示共振峰值隨阻尼的減小而增大下圖顯示共振頻率隨阻尼的減小而增大注意共振峰值只有當(dāng) zti )F(ti)脈沖激勵(lì)jth