δ(t) F(t) Maximum value
t
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3).The strain is different
FP
FP (t)
M
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m (a) P (d) P(t)
u3 (b) u 1
u2
u6
u5 u4 (e) u 1
u2
u4 u3
u2 (c)
u3 u1 (f) u1
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2). Concern about the process, not only the position
Bridge(USA)
Bridge(Russian)
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2) . Buildings
Multistory masonry buildings Reinforced concrete workshop
The Tangshan Earthquake occurred July 28, 1976. It is the largest earthquake of the 20th century by death toll (around 240,000 to 255,000). Its magnitude is 7.8.
识别值
Ansys 4 6 8
节点号
节点号
4). Damage detection
Amount New-build Reinforce Rebuild
Time
1980-2010 2010-2030 2030-
4). Damage detection model-drived method
Measured value Parameters：E、 A、I and K Object function
Systems with many degree of freedom • Modelling and equation of motion • Modal analysis and Forced oscillations • response spectrum method and time-history analysis Continuous systems • Modelling and equation of motion • Free vibrations
M
4). Dynamic loading will cause fatigue damage
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5) . Material performance will change under dynamic The rate of loading influences the stiffness and resistance characteristic of materials.
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5 Reference
《结构动力学》(美)R.克拉夫,J.彭津,王光远等译，高等教 育出版社 《 结 构 动 力 学 - 理 论 及 其 在 地 震 工 程 中 的 应 用 》( 美 ) Chopra,A.K，谢礼立、吕大刚译，清华大学出版社 Dynamics of structures,(加拿大) Jagmohan L. Humar


除上款的建筑结构，宜采用振型分解反应谱法；
特别不规则建筑、甲类建筑和表5.1.2-1所列高度范围的 高层建筑，应采用时程分析法进行多遇地震作用下的补 充计算；
2). Vibration Control：
2). Vibration Control：
Base isolation Without base isolation
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The Wenchuan earthquake
2). Buildings
The 911 terrorist attacks
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2. Application of Dynamics of Structures
1). Aseismic calculation 《建筑抗震设计规范》GB50011-2010 第5.1.2条 各类结构的抗震计算，应采用下列方法： 高度不超过40m，以剪切变形为主且质量和刚度沿高度 分布比较均匀的结构，以及近似于单质点体系的结构， 可用底部剪力法等简化方法；
3). Drill platform
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4). pipe
The hydrodynamic pressure introduced by opening and closing valves will cause the pipe vibration.
For example, the compressive strength of concrete can increase by
close to 30% for strain rates of 0.05/s, which is typical of the rates
induced in a structure by earthquake loading.
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1. Why we need Dynamics of Structures
1). Bridges
Collapse of Tacoma Narrows
Over-vibration of Volgograd
第1阶振型
1 0.8
第2阶振型
1 0
识别值
Ansys
识别值
Ansys
振型值
振型值
0
0.6 0.4 0.2 0 2 4 6
-1 -2 -3
0
2
4
6
8
节点号
节点号
第6阶振型
1.5 1
第7阶振型
识别值
Ansys
1 0.5
振型值
振型值
0.5 0 -0.5 -1 0 2 4 6 8
0 -0.5 -1 -1.5 0 2
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2). Buildings
the Great Hanshin Awaji Earthquake collapsed 5 storey in1995
Chi Chi earthquake in Taiwan Temple Chile earthquake
• Dynamic loading: any load of which its magnitude, direction, and/or position varies with time.
•
Vibration： mechanical oscillations about an equilibrium point.
Chapter 1 Introduction
§1-1. Objective of the course （课程目的）
To study methods for analyzing the stresses and defections developed in any given type of structure under an arbitrary dynamic loading.
RD
0.5
0
-0.5
g eddin Emb
0 0.5 1 1.5 2 2.5
Statistical analysis
-1
3. Difference between dynamic and static
1). The way to compute the DOF number is different
40
20
...
0Байду номын сангаас5
1
1.5
2
2.5
20
40
60
80
0
0. 2
0. 4
0. 6
0. 8
1. 6
1. 8 x 10
2
4
Structural response
RD
0.5
Baseline condition
RD
Segment 1 Segment 2
0
0
-0.5 1.5 -1 1
ed Emb
0 0.5 1 1.5 2
ding
2.5
0.5
Emb ed
0
ding
80
...
1 1. 2 1. 4
-0.5
Segment k
-1 1.5 0 1
60
40
20
...
0.5
1
1.5
2
2.5
20
40
60
80