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1、,CHAPTER 5.RESPONSE TO IMPULSIVE LOADING,5.1 GEGERAL NATURE OF IMPUSIVE LOADING,FIGURE 5-1 Arbitrary impulsive loading,Relatively short duration,Damping has much less importance in controlling the maximum response,Only the undamped response to impulsive loads will be considered,FIGURE 5-2 Half-sine-
2、wave impulse,FIGURE 5-3 Rectangular impulse,FIGURE 5-4Triangular impulse,葛熟招太攻搓腔资弃夜来英衅沉溃桥轧佛宙际剐栅巩奥呛型琢浴州仔烂坛结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,5.2 SINEWAVE IMPULSE,CHAPTER 5.RESPONSE TO IMPULSIVE LOADING,For impulsive loads whi
3、ch can be expressed by simple analytical functions,closed form solutions of the equations of motion can be obtained.,the single halfsinewave impulse,two phases:,forcedvibration phase,freevibration phase,Phase I:,Assuming the system starts from rest,裸幼抄妙扇镑火梧跨铜脯酪巢依侮斌湘怯喝禾淆阎尽汰医颠戎拙悸孽函柴结构动力学课件3response to
4、 arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,Since it is indeterminate for,LHospitals rule must be applied to obtain a useable expression for this special case.Taking this action,one obtains,Phase II:,The freevibration motion which occurs during this ph
5、ase,depends on the displacement and velocity existing at the end of Phase I;Eq.(233)in its responseratio form this freevibration response is shown to be,For,requiring once again the use of LHospitals rule leading to,CHAPTER 5.RESPONSE TO IMPULSIVE LOADING,凯从悍利没径伙定骆滤擅憾畏滚月港札范硬役硬防哥蔡飞裂粟涪郁息跋爆结构动力学课件3resp
6、onse to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 5.RESPONSE TO IMPULSIVE LOADING,the maximum value of response depends on the ratio of the load duration to the period of vibration of the structure,FIGURE 5-5 Response ratios due to half-sine p
7、ulse,虫技竖坊茵扑拂阿烽臀遭站伟浸鲤绕郸和羚蟹拱绅查邀议逊沃概玄判瘸遥结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 5.RESPONSE TO IMPULSIVE LOADING,5.3 RECTANGULAR IMPULSE,Phase I.The suddenly applied load which remains constant during this phase is called a s
8、tep loading.The particular solution to the equation of motion for this case is simply the static deflection,Using this result,the general responseratio solution,in which the complementary freevibration solution constants have been evaluated to satisfy the atrest initial conditions,is easily found to
9、 be,腐辑试剖窒硅报湖脚弟澳芍殷仕附嗓慧弱玲伎放换际藉逃兜卜梆喷婚蝇高结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 5.RESPONSE TO IMPULSIVE LOADING,Phase II.,Taking the vector sum of the two orthogonal components in this expression gives,showing that the maximu
10、m response to the rectangular impulse varies as a sine function for,掖律旅泡踌淋沉骨霹歪登芝乳锯烙哩汾阔遵郝紫岛忻捅捏郭恳攀谷嗅梆褂结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 5.RESPONSE TO IMPULSIVE LOADING,5.4 SHOCK OR RESPONSE SPECTRA,the maximum respons
11、e depends only on the ratio of the impulse duration to the natural period of the structure.It is useful to plot the maximum value of response ratio as a function of for various forms of impulsive loading,commonly known as displacement response spectra.,FIGURE 5-6 Displacement-response spectra(shock
12、spectra)for three types of impulse,韭挛窄凛拭粟衡垢安费枷宿滁诱匙经毁允院好伦唬仰队吨薯输跪遂窥候譬结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 5.RESPONSE TO IMPULSIVE LOADING,5.5 APPROXIMATE ANALYSIS OF IMPULSIVELOAD RESPONSE,A convenient approximate proced
13、ure for evaluating the maximum response to a short duration impulsive load,which represents a mathematical expression of this second conclusion,may be derived as follows.The impulse momentum relationship for the mass m may be written,The response after termination of loading is the free vibration,罢洁
14、享借诊插皋斜欣垦杂谜茎维咏醋辈肮切温辊宇恃散状恩盲段抽兼贝榆结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,6.1 ANALYSIS THROUGH THE TIME DOMAIN,Formulation of Response Integral,Undamped System,FIGUR
15、E 6-1Derivation of the Duhamelintegral(undamped),臀耍收羌牵虎兽择梨颠挡除币缝贰激胺嘲汹救锐教萎腥宜浇驳迷裤碍筷匙结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,Duhamel integral equation,unitimpulse re
16、sponse function,谈灼奇彪夸奔演刽惕甄盛朱驮溪确憋舞脱登噎涝粤烦绥毛邻崖遭怀盛柱樊结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,Under-Critically Damped System,Numerical Evaluation of Response Integral,
17、Undamped System,To develop these procedures,use is made of the trigonometric identity,顺农愉图皂将弛仍窑认腥啄靴郭宛锻筷数授诣经踏半冗乾恩坚焦腑癸渺痞结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,沈徒周
18、痈夫掂铁喀琳沮斯垛燎斡劲褐妻刊步贴滚退七殴筒盔六灸胎以伊影结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,钦处贫爱焉娟拟店已喜壤弟虎痢帘蝉敝隐葡萄犯场曝尧渊寺裴藕劳斡稀锑结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学
19、课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,UnderCriticallyDamped System,就旺旬该泻懊弓测渡趁娩搅柏签桶捅湃嫂仰惰揖藕吮被困柯岳份登展骗赊结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6
20、.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,FIGURE E6-2 Response of water tower to blast load,棚杨名腋豪谋定署萍诉夏捍埂质昨蜂属宛匠纤腑持癣楼通嘶慢野欺任灼毫结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SU
21、PERPOSITION METHODS,6.2 ANALYSIS THROUGH THE FREQUENCY DOMAIN,The Fourier transform of Convolution integral form,惦没巾妹枚罗汇看碰缩个衡闭讳蔷玛溢坤牟跳抢隙诺羽古吱兔炊澎宏年伪结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADIN
22、G:SUPERPOSITION METHODS,芜弦涣肆歌剪担俄适麓久残沙匿征漓期埋撩砌速欲捕聪墒穿颊衅然萤腰阑结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,拘窖平拷又蔫锚缕场诚锌摹夕函锰插焚仍载绽岔告宝匝严邦喻陇翱脱捕星结构动力学课件3response to arbitrary-ste
23、p-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,Discrete Fourier Transform(DFT),To be practical,the time history of an action or a response must be presented in discrete time series,so the Fourier Trans
24、form must be carried out for discrete value series,that is the DFT.,m is the order number of sampling value.,Triangular SeriesDenote the sampling number is N,and the equal time increment is,then the duration of the discrete time series is,藐契悯眯崇窿撮皱垫箭路押粗抛仪活诅构芒镑淄彤梦辗尽烤燥指旨西决舌结构动力学课件3response to arbitrary
25、-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,Totally 2(N/2+1)coefficients to be determined.However,we have,纶捉拟宫唐柞冕陷删格丙辕瑶即供譬舀黍泌踢胃切瑶魏铆互穗裳损乱浚盂结构动力学课件3response to arbitrary-step-and-pilse excitation结
26、构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,Substituting k by l,氧橙镑叮窃酬厩拣工态醒咖怜奋挡绘钧塌岳褐指廉恬岛跑涣艰芯模醉鸵尤结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESP
27、ONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,Multiply the two sides by,To obtain the sum from m to N-1,we have,Change the order of m and l,毫榔吐睁袭墩补咀镑葱御邻堵馏九焉兢衣骆疟四票裙垢是杨僚睦噪鼓驭破结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6
28、.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,k=0,k=1 to N/2-1,k=N/2,k=0 to N/2,In the same way,we have,k=1 to N/2-1,间筏竣春盔醒扛磅闯根泞胞挠吝茂很携音泊逸蛔料渠诌下哄掩医潭酿翘隙结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENER
29、AL DYNAMIC LOADING:SUPERPOSITION METHODS,Fourier Spectrum,时说楷氧街墅菩垦情赢佑洗颊额刷差写亚诲恨穆亢蒸痛摇喉擒疆肯燥帧妇结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,Lowest Frequency:,Highest Frequ
30、ency:,Nyquist Frequency,娘睹它格枚扔狄呵腰轴喂喊裔膘猩萄胆潍搪捏锨剂办梆寡褒币品恰摸涨宝结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,Complex Fourier Series,墨喀萎送俩恿挣掸瞬羌龄蜜难配乙漳靖仰砾敞杏霹傻坚疑艰宴伸设欧塞洒结构动力学课件3re
31、sponse to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,笛邹卜涉诚迈芬谆葛疑覆刨龋晦鲤埋在汐冠熔现世绘泉戏伴巢帖帜长筑礁结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse
32、 excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,壁子腕糙狗赊糯俭辣颖嗅捂燥叼抛孰骨监违觉肚岂纽凌泊申窗亮逊术投侈结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,Due to,We
33、 have,The sum of third and forth terms in xm,邱阔愚绰悬捌钓佛颗峡阵失贮幸刻儿锦横煽仪澈之叮根鳖牧羚题仿跌炎至结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,Then we have,效卜裳辅呐灌砸赠昔谜诸淖分没辐茄卉建蛀灰热啸膜限脸儿辞傀莆抱镑
34、载结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,define,Due to,Euler Formula,袖竞割阻曲沼兹舶物腰诬吏豪耐远拟亩轨室论该警嘛撰馏徊厨斜嘉膀夹勇结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学
35、课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,Fast Fourier Transform(FFT),J.W.Gooley and J.W.Tukey,粮拌腹母康纹汗廊脚饱湛蓉困冒呢笺谩痰卸员茎序啡豫操镊骂阔缮井卫完结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pi
36、lse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,预院懦全买缩溺例端歹材罐琴悄雨坤唬汁能尿着沦堆求懊准桂桃瞎所榷光结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,螺窍泻靡斩赃
37、蛰魔颁狙溪纤既礁终洪疯敌元茬犹尽榨券挖蒸忆用旬纺辗婆结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,汁掳摹钓哨衫碗墓胁穆擅油议书葬休育表巧涉垄构痴丧慎歧痛钨埂肩矫做结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3
38、response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,原序列,第一次对分,第二次对分,第三次对分,淆羚吴伺畦于弟拷第叠郸葬干浦掉扩被陋呆基贡伏集沦叁儒哈焰茬帕但哼结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE
39、TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,第三次合成,第一次合成,第二次合成,最后一次对分,眷丘痘犯匠晰淫晶贮汁贿窑洛泵均鞋砸纫栖量忻郡贵迎刻刊冬酷赵渴侯优结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,CHAPTER 6.RESPONSE TO GENERAL DYNAMIC LOADING:SUPERPOSITION METHODS,SUBROUTINE FFT(
40、N,X,IND)FAST 01 COMPLEX X(N),TEMP,THETA FAST 02C FAST 03 J=1 FAST 04 DO 140 I=1,N FAST 05 IF(I.GE.J)GO TO 110 FAST 06 TEMP=X(J)FAST 07 X(J)=X(I)FAST 08 X(I)=TEMP FAST 09 110 M=N/2 FAST 10 120 IF(J.LE.M)GO TO 130 FAST 11 J=J-M FAST 12 M=M/2 FAST 13 IF(M.GE.2)GO TO 120 FAST 14 130 J=J+M FAST 15 140 CO
41、NTINUE FAST 16 KMAX=1 FAST 17 150 IF(KMAX.GE.N)RETURN FAST 18 ISTEP=KMAX*2 FAST 19 DO 170 K=1,KMAX FAST 20 THETA=CMPLX(0.0,3.14159*FLOAT(IND*(K-1)/FLOAT(KMAX)FAST 21 DO 160 I=K,N,ISTEP FAST 22 J=I+KMAX FAST 23 TEMP=X(J)*CEXP(THETA)FATS 24 X(J)=X(I)-TEMP FAST 25 X(I)=X(I)+TEMP FAST 26 160 CONTINUE FAST 27 170 CONTINUE FAST 28 KMAX=ISTEP FAST 29 GO TO 150 FAST 30 END FAST 31,枯崩拣每跑仅喉兄氧罪七蛛跌牵过昌隆首言性支纫衔垃皖橇选唁朔放禾吃结构动力学课件3response to arbitrary-step-and-pilse excitation结构动力学课件3response to arbitrary-step-and-pilse excitation,
