1. 結構動力分析 Structural Dynamic Analysis
Chapter 15
結構動力分析
Structural Dynamic Analysis

2. Contents 15.1 何謂動力分析？ What Are Dynamic Analyses? 15.2 解題方法
15.1 何謂動力分析？
What Are Dynamic Analyses?
15.2 解題方法
Solution Methods
15.3 質量與阻尼
Mass and Damping
15.4 實例：圓柱形子彈的撞擊模擬
Example: Copper Cylinder Impacting on a Rigid Wall
15.5 動態負載
Dynamic Loads
15.6 初始條件
Initial Conditions
15.7 積分時間間隔
Integration Time Steps
15.8 練習題：火箭的飛行
Exercise: Rocket Flight

3. 何謂動力分析？ What Are Dynamic Analyses?
第15.1節
何謂動力分析？
What Are Dynamic Analyses?

4. Dynamic Effects Inertia force Damping force Elastic Force
External force
Dynamic Effects

5. 15.1.1 Transient Dynamic Analysis

6. Modal Analysis (1/3)

7. Modal Analysis (2/3)

8. 15.1.2 Modal Analysis (3/3) Avoid resonance Exploit resonance
Assess structural stiffness
Structural modal degrees of freedom
Further dynamic analyses
etc.

9. 15.1.3 Harmonic Response Analysis

10. 第15.2節
解題方法
Solution Methods

11. Solution Methods for Equation of Motion
Direct Integration
Mode Superposition
Implicit
Explicit
Reduce
Full

12. 15.2.1 Direct Integration Implicit method (ANSYS)
Explicit method (LS-DYNA)

13. 15.2.2 Implicit vs. Explicit Methods
Implicit method
Explicit method

14. 15.2.3 Mode Superposition Method

15. Reduced Method
where

16. 15.2.5 Methods for Nonlinear Dynamic Analysis
For nonlinear analysis, the only methods applicable is DIRECT INTEGRATION method.
Reduced method can not be used for nonlinear analysis.
Either implicit or explicit methods can be used.

17. 第15.3節
質量與阻尼
Mass and Damping

18. 15.3.1 Consistent vs. Lumped Mass Matrices
Consistent mass matrix
Lumped mass matrix

19. Damping
Damping effects is the total of all energy dissipation mechanisms
Hysteresis (solid damping)
Viscous damping
Dry-friction (Coulomb damping)

20. 15.3.3 Idealization of Structural Damping
Structural dampings are usually small (2%-7%).
Equivalent viscous damping is assumed in ANSYS, i.e.,

21. 15.3.4 How ANSYS Forms Damping Matrix?
Alpha damping
Beta damping
Material dependent beta damping
Element damping matrices
Frequency-dependent damping matrix

22. 實例: 圓柱型子彈的撞擊模擬 Copper Cylinder Impacting on a Rigid Wall
第15.4節
實例: 圓柱型子彈的撞擊模擬
Copper Cylinder Impacting on a Rigid Wall

23. Problem Description x y L D
Initial Velocity Vo

24. 15.4.2 Modeling Consideration
Material: bilinear plastic model.
VISCO106 (2D viscoplastic solid) is used.
Use axisymmetric model.

25. ANSYS Procedure (1/4) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21
FINISH
/CLEAR
/TITLE, UNITS: SI
/PREP7
  ET, 1, VISCO106,,, 1
  MP,   EX, 1, 117E9
  MP, NUXY, 1,  0.35
  MP, DENS, 1,  8930
  TB, BISO, 1
  TBDATA,, 400E6, 100E6
  TBPLOT, BISO, 1
  RECTNG, 0, , 0,
  LESIZE, 1,,, 4
  LESIZE, 2,,, 20
  MSHAPE, 0, 2D
  MSHKEY, 1
  AMESH, ALL
  FINISH

26. ANSYS Procedure (2/4) 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
/SOLU
  ANTYPE, TRANS
  TRNOPT, FULL
  NLGEOM, ON
  IC, ALL, UY, 0, -227
  NSEL, S, LOC, X, 0
  D, ALL, UX, 0
  NSEL, S, LOC, Y, 0
  D, ALL, UY, 0
  NSEL, ALL
  /PBC, U,, ON
  EPLOT
  TIME, 80E-6
  DELTIM, 0.4E-6
  KBC, 1
  OUTRES, ALL, 4
  SOLVE
  FINISH

27. ANSYS Procedure (3/4) 44 45 46 47 48 49 50 51 52 53 54 55 56 57
/POST26
  TOPNODE = NODE(0,0.0324,0)
  NSOL, 2, TOPNODE, U, Y, DISP
  DERIV, 3, 2, 1,, VELO
  /GRID, 1
  /AXLAB, X, TIME s
  /AXLAB, Y, DISPLACEMENT m
  PLVAR, 2
  /AXLAB, Y, VELOCITY m/s
  PLVAR, 3
  FINISH

28. 15.4.3 ANSYS Procedure (4/4) 59 60 61 62 63 64 65 /POST1 SET, LAST
  PLDISP, 2
  PLNSOL, EPTO, EQV
  ANTIME, 30

29. 第15.5節
動態負載
Dynamic Loads

30. Dynamic Loads: An Example01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18
/SOLU
  ...
  F, ...        ! 22.5 at the nodes
  TIME, 0.5     ! Ending time
  DELTIM, ...   ! Integration step
  KBC, 0        ! Ramped loading
  AUTOTS, ON    ! Option
  OUTRES, ...   ! Option
  SOLVE         ! Load step 1
  F, ...        ! 10 at the nodes
  TIME, 1       ! Ending time
  SOLVE         ! Load step 2
  FDELE, ...    ! Zero the force
  TIME, 1.5     ! Ending time
  KBC, 1        ! Stepped loading
  SOLVE         ! Load step 3
0.5
1.0
1.5
Time (s)
Force (N)
22.5 10

31. 初始條件 Initial Conditions
第15.6節
初始條件
Initial Conditions

32. 15.6.1 Example: An Stationary Plate Subjected to an Impulse Load
This is the default initial condition. No input is needed.

33. 15.6.2 Example: Initial Velocity on a Golf Club Head
This simple initial condition can be specified by using IC command.
  NSEL, ALL
  IC, ALL, UY, 0, V0

34. 15.6.3 Example: Plucking a Cantilever Beam01 02 03 04 05 06 07 08 09 10 11 12 13 14
/SOLU
  ANTYPE, TRANS
  ...
  TIMINT, OFF  ! Transient effects off
  TIME, 0.001  ! Small time interval
  D, ...       ! Apply displacement at desired nodes
  KBC, 1       ! Stepped loads
  NSUBST, 2    ! To avoid non-zero velocity
  SOLVE
  TIMINT, ON   ! Transient effects on
  TIME, ...    ! Actual time at end of load
  DDELE, ...   ! Delete the applied displacement

35. 15.6.4 Example: Dropping an Object from Rest01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17
/SOLU
  TIMINT, OFF     ! Transient effects off
  TIME,     ! Small time interval
  NSEL, ...       ! Select all nodes on the object
  D, ALL, ALL, 0  ! Temporarily fix them
  NSEL, ALL
  ACEL, ...       ! Apply acceleration
  KBC, 1          ! Stepped loads
  NSUBST, 2       ! To avoid non-zero velocity
  SOLVE           ! Load step 1
  TIMINT, ON      ! Transient effects on
  TIME, ...       ! Actual time at end of load
  DDELE, ALL, ALL ! Release them
  SOLVE           ! Load step 2

36. 積分時間間隔 Integration time Steps
第15.7節
積分時間間隔
Integration time Steps

37. Response Frequency
Response
Time
Minimum
response
time

38. 15.7.2 Abrupt Changes in Loading
0.5
1.0
1.5
Time (s)
Force (N)
22.5 10

39. Contact Frequency

40. Wave Propagation

41. 15.8 Exercise: Rocket Flighty
140 in.
Thrust
Time
100 lb
1 sec. 1 2 3