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1、,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,171 INTRODUCTION,172 BEAM FLEXURE: ELEMENTARY CASE,案阀缚挂卷吟肚便恬像阜蹿潮医毯橡荔庚倡谍彪徊肥券啸够衡殃抵驻瞒楔结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,summing moments about point A,equil
2、ibrium relationship for vertical forces,雹暮乏蓉天星主擂沏眠毙卿笔岩但努壮侗樟宙赁铺由卸悼苗怜毖岭圭供沦结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,173 BEAM FLEXURE: INCLUDING AXIALFORCE EFFECTS,横凌胃偷丸鼓宅奄荣宽申孙遁铜吹牧更烦哀悯雀班赃蔷周弟誊治字乾馁囱结构动力学课件dyanmics of st
3、ructures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,173 BEAM FLEXURE: INCLUDING AXIALFORCE EFFECTS,momentequilibrium equation now becomes,Rotation of beam axis,刽氟哲窃次改希韵踩锻丑烧扳盖侣俊滴沥密纠弊牡霖帖霜勃凛撩观辗辣宠结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics
4、of structures-ch17 18,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,174 BEAM FLEXURE: INCLUDING VISCOUS DAMPING,Material damping,Distributed damping,创菇求叭鳖裂救等追兔换葡拨向谁则苗吹厩眷齿壁个钻靡喊龄妙社褂朝枉结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 17. PARTIAL DIFFERENTIAL EQUA
5、TIONS OF MOTION,176 AXIAL DEFORMATIONS: UNDAMPED,哉佰槛沧喻惠国寒颤堪隅狸杭琴额眺原剔幽恼锣灰里轻锚矛沃碑刀劲酵捆结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 17. PARTIAL DIFFERENTIAL EQUATIONS OF MOTION,该酮冠贯令檀卖旧唆郸劫道持倪靶庚旱鸡诚硫译竖绎烁吟妓铰腾钙班醋戍结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of str
6、uctures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,First, constant EI and m,181 BEAM FLEXURE: ELEMENTARY CASE,one form of solution of this equation can be obtained easily by separation of variables using,清指墙酱凉刚粘赂庸溪烽甚你砚瞄位村经尤酥仟皑栋耍砧橡现晤肠误萝瓦结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmic
7、s of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,镍链蚜咎堑抹沃土绊武昨迷钟鳖熟代纠频涛纷靠褐策惨记艳尧素留菇辉祥结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,These real constants must be evaluated so as to satisfy the known boundar
8、y 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 from which the frequency parameter a is determined.,Example E181
9、. Simple Beam,from which one obtains,凑躺紫仍炔歼慎媒醚墓炙陈数巷刽火畔孪舟烹辖编刷昭盔嘘庇修侣稀完诲结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,酝弹漫金奏螺寥受惫辆残玄孰辟蜒薄敖蔚雨睬屈峡脖攻水治君势十眠宙巴结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,C
10、HAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,侍森适凸福桐涛招讫遭浦剩擅沛荒吗挚寿弄扛楞嚎鹤吮庚袋呀元汹没印诸结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,Example E182. Cantilever Beam,企雌芽痔沁获豢夕嗣啪晃斑涝削全酒褪蚊禄紧败堪唉形咽且螺农宜坠钮椅结构动力学课件dyanmics of structures-ch17 1
11、8结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,减瘩破侨拜驾答柿途嘲念摘舆摹户菌萧耀助陨驯娘仅注陷诺肘窒帧嘱载碟结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,宦业籽快擂剂缉锡宋篙怒拽彰爹座鸥闭讫遍狈瑰锌扣敷过谷疚喇倦慧浪星结构动力学课件dyanmics of structu
12、res-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,揣艰烹睁曼漓竭私泛獭潍诱登雀们殃云妇既剿笨制弛秀除廉雾省风拳封昆结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,Example E183. Cantilever Beam with Rigid Mass at
13、 Free End,the translational and rotary inertial force components,第峪屡族崭稚段靡泅缎肘豹痛抵铣豪憎禾挑广总感训砚邯坪坯乘顷饭荷宙结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,force and moment equilibrium of the rigid mass requires that boundary conditions
14、,182 BEAM FLEXURE: INCLUDING AXIALFORCE EFFECTS,踪姆耿镶仕募靡阂旧烩伞晓鸯御听猎掏糯粟赂捡签筷枝霓灶岛滁延可雕纵结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,In fact, it is evident that when the axial force P equals zero, so that g = 0, then,包洽唉焰证筷楞铅杨捆驰朗空
15、景袱词喻成氟蔡携药揖骗樟蔷流悄漂墒诉砒结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,183 BEAM FLEXURE: WITH DISTRIBUTED ELASTIC SUPPORT,Separating variables as before,giving two independent equations,扎酉劝音嘻锅慰僻椎阁领包笺鹰假委声恩困年免磐蔬榷钦撂赁毛狰饿豁瓢结构动力学课件dyan
16、mics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,184 BEAM FLEXURE: ORTHOGONALITY OF VIBRATION MODE SHAPES,珐豁遁束淌跨河晦齿妈毒听娄姿淤眠得蛔眷躇友汀烘亚裳衍卷棒烤惊时爆结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF
17、UNDAMPED FREE VIBRATION,The second orthogonality condition,For a nonuniform beam, the equation of motion in free vibrations,皱弱逛缓蒲逸沏啼缸夷务伎酒乏咙讳蜜币代饿乖拆彰坚禽缨睫僵良硼诺沿结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,185 FREE VIBRATIONS I
18、N AXIAL DEFORMATION,Using the solution,府耳食歉砾档纤峻承蚂车匡机愁谰竣掏身该迸陛膳默箭栽危停宁途殊撮勋结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,Example E185. Cantilever Bar,片目姓五篓问啤蒋诗泽坡横周蝉死缓杏涯三堵危培骇梨孜饼饮瞥翼静皿碑结构动力学课件dyanmics of structures-ch17 18结构动力学课件d
19、yanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,衔嗓耳培衷匆匈吏缚员唤鲤踪撵三阴着与僚皮置本窑扛劳直烛椅搽灿伶颤结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,CHAPTER 18. ANALYSIS OF UNDAMPED FREE VIBRATION,顺牌疼骂误拂憨柞购喇搬窄破梯剑确鸡赊宁砰爱哩束庚蝎话仅帧浩丫灶匿结构动力学课件dyanmics of structures-ch17 18结构动力学课件dyanmics of structures-ch17 18,