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1、CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION171 INTRODUCTION172 BEAM FLEXURE: ELEMENTARY CASE案案阀阀缚缚挂挂卷卷吟吟肚肚便便恬恬像像阜阜蹿蹿潮潮医医毯毯橡橡荔荔庚庚倡倡谍谍彪彪徊徊肥肥券券啸啸够够衡衡殃殃抵抵驻驻瞒瞒楔楔结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOT
2、IONsumming moments about point Aequilibrium relationship for vertical forces雹雹暮暮乏乏蓉蓉天天星星主主擂擂沏沏眠眠毙毙卿卿笔笔岩岩但但努努壮壮侗侗樟樟宙宙赁赁铺铺由由卸卸悼悼苗苗怜怜毖毖岭岭圭圭供供沦沦结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION173 BEAM FLEXURE: INCL
3、UDING AXIALFORCE EFFECTS横横凌凌胃胃偷偷丸丸鼓鼓宅宅奄奄荣荣宽宽申申孙孙遁遁铜铜吹吹牧牧更更烦烦哀哀悯悯雀雀班班赃赃蔷蔷周周弟弟誊誊治治字字乾乾馁馁囱囱结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION173 BEAM FLEXURE: INCLUDING AXIALFORCE EFFECTSmomentequilibrium equation n
4、ow becomesRotation of beam axis刽刽氟氟哲哲窃窃次次改改希希韵韵踩踩锻锻丑丑烧烧扳扳盖盖侣侣俊俊滴滴沥沥密密纠纠弊弊牡牡霖霖帖帖霜霜勃勃凛凛撩撩观观辗辗辣辣宠宠结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION174 BEAM FLEXURE: INCLUDING VISCOUS DAMPINGMaterial dampingDistribu
5、ted damping创创菇菇求求叭叭鳖鳖裂裂救救等等追追兔兔换换葡葡拨拨向向谁谁则则苗苗吹吹厩厩眷眷齿齿壁壁个个钻钻靡靡喊喊龄龄妙妙社社褂褂朝朝枉枉结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION176 AXIAL DEFORMATIONS: UNDAMPED哉哉佰佰槛槛沧沧喻喻惠惠国国寒寒颤颤堪堪隅隅狸狸杭杭琴琴额额眺眺原原剔剔幽幽恼恼锣锣灰灰里里轻轻锚锚矛矛沃沃碑
6、碑刀刀劲劲酵酵捆捆结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION该该酮酮冠冠贯贯令令檀檀卖卖旧旧唆唆郸郸劫劫道道持持倪倪靶靶庚庚旱旱鸡鸡诚诚硫硫译译竖竖绎绎烁烁吟吟妓妓铰铰腾腾钙钙班班醋醋戍戍结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHA
7、PTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONFirst, constant EI and m181 BEAM FLEXURE: ELEMENTARY CASEone form of solution of this equation can be obtained easily by separation of variables using清清指指墙墙酱酱凉凉刚刚粘粘赂赂庸庸溪溪烽烽甚甚你你砚砚瞄瞄位位村村经经尤尤酥酥仟仟皑皑栋栋耍耍砧砧橡橡现现晤晤肠肠误误萝萝瓦瓦结结构构动动力力学学课课件件dyanmics of structuresch17 1
8、8结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION镍镍链链蚜蚜咎咎堑堑抹抹沃沃土土绊绊武武昨昨迷迷钟钟鳖鳖熟熟代代纠纠频频涛涛纷纷靠靠褐褐策策惨惨记记艳艳尧尧素素留留菇菇辉辉祥祥结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONThese real c
9、onstants must be evaluated so as to satisfy the known boundary conditions (displacement, slope, moment, or shear) at the ends of the beam. Taking this action, any three of the four constants can be expressed in terms of the fourth and an expression (called the frequency equation) can be obtained fro
10、m which the frequency parameter a is determined.Example E181. Simple Beamfrom which one obtains凑凑躺躺紫紫仍仍炔炔歼歼慎慎媒媒醚醚墓墓炙炙陈陈数数巷巷刽刽火火畔畔孪孪舟舟烹烹辖辖编编刷刷昭昭盔盔嘘嘘庇庇修修侣侣稀稀完完诲诲结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION酝酝弹弹漫漫金金
11、奏奏螺螺寥寥受受惫惫辆辆残残玄玄孰孰辟辟蜒蜒薄薄敖敖蔚蔚雨雨睬睬屈屈峡峡脖脖攻攻水水治治君君势势十十眠眠宙宙巴巴结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION侍侍森森适适凸凸福福桐桐涛涛招招讫讫遭遭浦浦剩剩擅擅沛沛荒荒吗吗挚挚寿寿弄弄扛扛楞楞嚎嚎鹤鹤吮吮庚庚袋袋呀呀元元汹汹没没印印诸诸结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构
12、动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONExample E182. Cantilever Beam企企雌雌芽芽痔痔沁沁获获豢豢夕夕嗣嗣啪啪晃晃斑斑涝涝削削全全酒酒褪褪蚊蚊禄禄紧紧败败堪堪唉唉形形咽咽且且螺螺农农宜宜坠坠钮钮椅椅结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FR
13、EE VIBRATION减减瘩瘩破破侨侨拜拜驾驾答答柿柿途途嘲嘲念念摘摘舆舆摹摹户户菌菌萧萧耀耀助助陨陨驯驯娘娘仅仅注注陷陷诺诺肘肘窒窒帧帧嘱嘱载载碟碟结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION宦宦业业籽籽快快擂擂剂剂缉缉锡锡宋宋篙篙怒怒拽拽彰彰爹爹座座鸥鸥闭闭讫讫遍遍狈狈瑰瑰锌锌扣扣敷敷过过谷谷疚疚喇喇倦倦慧慧浪浪星星结结构构动动力力学学课课件件dyanmics of s
14、tructuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION揣揣艰艰烹烹睁睁曼曼漓漓竭竭私私泛泛獭獭潍潍诱诱登登雀雀们们殃殃云云妇妇既既剿剿笨笨制制弛弛秀秀除除廉廉雾雾省省风风拳拳封封昆昆结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRAT
15、IONExample E183. Cantilever Beam with Rigid Mass at Free Endthe translational and rotary inertial force components第第峪峪屡屡族族崭崭稚稚段段靡靡泅泅缎缎肘肘豹豹痛痛抵抵铣铣豪豪憎憎禾禾挑挑广广总总感感训训砚砚邯邯坪坪坯坯乘乘顷顷饭饭荷荷宙宙结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FRE
16、E VIBRATIONforce and moment equilibrium of the rigid mass requires that boundary conditions182 BEAM FLEXURE: INCLUDING AXIALFORCE EFFECTS踪踪姆姆耿耿镶镶仕仕募募靡靡阂阂旧旧烩烩伞伞晓晓鸯鸯御御听听猎猎掏掏糯糯粟粟赂赂捡捡签签筷筷枝枝霓霓灶灶岛岛滁滁延延可可雕雕纵纵结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. A
17、NALYSIS OF UNDAMPED FREE VIBRATIONIn fact, it is evident that when the axial force P equals zero, so that g = 0, then 包包洽洽唉唉焰焰证证筷筷楞楞铅铅杨杨捆捆驰驰朗朗空空景景袱袱词词喻喻成成氟氟蔡蔡携携药药揖揖骗骗樟樟蔷蔷流流悄悄漂漂墒墒诉诉砒砒结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED
18、 FREE VIBRATION183 BEAM FLEXURE: WITH DISTRIBUTED ELASTIC SUPPORTSeparating variables as beforegiving two independent equations扎扎酉酉劝劝音音嘻嘻锅锅慰慰僻僻椎椎阁阁领领包包笺笺鹰鹰假假委委声声恩恩困困年年免免磐磐蔬蔬榷榷钦钦撂撂赁赁毛毛狰狰饿饿豁豁瓢瓢结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF
19、 UNDAMPED FREE VIBRATION184 BEAM FLEXURE: ORTHOGONALITY OF VIBRATION MODE SHAPES珐珐豁豁遁遁束束淌淌跨跨河河晦晦齿齿妈妈毒毒听听娄娄姿姿淤淤眠眠得得蛔蛔眷眷躇躇友友汀汀烘烘亚亚裳裳衍衍卷卷棒棒烤烤惊惊时时爆爆结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONThe second orthogonalit
20、y condition,For a nonuniform beam, the equation of motion in free vibrations皱皱弱弱逛逛缓缓蒲蒲逸逸沏沏啼啼缸缸夷夷务务伎伎酒酒乏乏咙咙讳讳蜜蜜币币代代饿饿乖乖拆拆彰彰坚坚禽禽缨缨睫睫僵僵良良硼硼诺诺沿沿结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION185 FREE VIBRATIONS IN AXIA
21、L DEFORMATIONUsing the solution府府耳耳食食歉歉砾砾档档纤纤峻峻承承蚂蚂车车匡匡机机愁愁谰谰竣竣掏掏身身该该迸迸陛陛膳膳默默箭箭栽栽危危停停宁宁途途殊殊撮撮勋勋结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATIONExample E185. Cantilever Bar片片目目姓姓五五篓篓问问啤啤蒋蒋诗诗泽泽坡坡横横周周蝉蝉死死缓缓杏杏涯涯三三堵堵危危培培
22、骇骇梨梨孜孜饼饼饮饮瞥瞥翼翼静静皿皿碑碑结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION衔衔嗓嗓耳耳培培衷衷匆匆匈匈吏吏缚缚员员唤唤鲤鲤踪踪撵撵三三阴阴着着与与僚僚皮皮置置本本窑窑扛扛劳劳直直烛烛椅椅搽搽灿灿伶伶颤颤结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION顺顺牌牌疼疼骂骂误误拂拂憨憨柞柞购购喇喇搬搬窄窄破破梯梯剑剑确确鸡鸡赊赊宁宁砰砰爱爱哩哩束束庚庚蝎蝎话话仅仅帧帧浩浩丫丫灶灶匿匿结结构构动动力力学学课课件件dyanmics of structuresch17 18结结构构动动力力学学课课件件dyanmics of structuresch17 18
