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Chapter 15

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

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Chapter 15

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  1. 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 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. 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. 15.1.2 Modal Analysis (1/3)

  7. 15.1.2 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 Full Reduce Full Reduce Solution Methods

  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. 15.2.4 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. 15.3.2 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. 第15.4節 實例: 圓柱型子彈的撞擊模擬 Copper Cylinder Impacting on a Rigid Wall

  23. Initial Velocity Vo y L D x 15.4.1 Problem Description

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

  25. 15.4.3 ANSYS Procedure (1/4)

  26. 15.4.3 ANSYS Procedure (2/4)

  27. 15.4.3 ANSYS Procedure (3/4)

  28. 15.4.3 ANSYS Procedure (4/4)

  29. 第15.5節 動態負載 Dynamic Loads

  30. Force (N) 22.5 10 Time (s) 0 0.5 1.0 1.5 Dynamic Loads: An Example

  31. 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.

  34. 15.6.3 Example: Plucking a Cantilever Beam

  35. 15.6.4 Example: Dropping an Object from Rest

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

  37. Response Minimum response time Time 15.7.1 Response Frequency

  38. Force (N) 22.5 10 Time (s) 0 0.5 1.0 1.5 15.7.2 Abrupt Changes in Loading

  39. 15.7.3 Contact Frequency

  40. 15.7.4 Wave Propagation

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

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