結構動力分析 Structural Dynamic Analysis 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 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

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

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

15.1.1 Transient Dynamic Analysis

15.1.2 Modal Analysis (1/3)

15.1.2 Modal Analysis (2/3)

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

15.1.3 Harmonic Response Analysis

第15.2節 解題方法 Solution Methods

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

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

15.2.2 Implicit vs. Explicit Methods Implicit method Explicit method

15.2.3 Mode Superposition Method

15.2.4 Reduced Method where

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.

第15.3節 質量與阻尼 Mass and Damping

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

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

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

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

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

15.4.1 Problem Description x y L D Initial Velocity Vo

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

15.4.3 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, 0.0032, 0, 0.0324   LESIZE, 1,,, 4   LESIZE, 2,,, 20   MSHAPE, 0, 2D   MSHKEY, 1   AMESH, ALL   FINISH

15.4.3 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

15.4.3 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

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

第15.5節 動態負載 Dynamic Loads

Dynamic Loads: An Example 01 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

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

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

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

15.6.3 Example: Plucking a Cantilever Beam 01 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

15.6.4 Example: Dropping an Object from Rest 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 /SOLU   TIMINT, OFF     ! Transient effects off   TIME, 0.001     ! 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

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

15.7.1 Response Frequency Response Time Minimum response time

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

15.7.3 Contact Frequency

15.7.4 Wave Propagation

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