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Chap 5. Multi DOF

m. m. 2m. 2m. Chap 5. Multi DOF. Normal Mode Analysis Ex 5.1-1 Undamped 2DOF. To have non-trivial Soln. 1. 1. 0.731. -2.73. In - phase. Out – of - phase. Initial Conditions. In general , undamped 2DOF are coupled.

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Chap 5. Multi DOF

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  1. m m 2m 2m Chap 5. Multi DOF Normal Mode Analysis Ex 5.1-1 Undamped 2DOF

  2. To have non-trivial Soln

  3. 1 1 0.731 -2.73 In - phase Out – of - phase

  4. Initial Conditions In general , undamped 2DOF are coupled Using principal coords (normal coords) , two eqns are decoupled

  5. m2 m1 5.4 Forced Harmonic Vibration

  6. 5.6 Vibration Absorber

  7. Chap 7. Lagrange’s Equation Hamilton’s Principle W.R.Hamilton (1805-1865) : Irish Mathematician

  8. Explicit : Central Difference , Runge-Kunta Implicit : Houbolt , Newmark β , wilson θ , Hughes α • Direct Integration MDM MAM LDRV , Lanczos , Krylov • Superposition Chap 11. Mode-Summation Procedures for Continuous Systems • Superposition & Direct Integration

  9. Mode Superposition Method Mode Displacement Method (MDM)

  10. Krylov Sequence Krylov Sequence

  11. Load Dependent Ritz Vectors (LDRV) Load Dependent Ritz Vectors (LDRV)

  12. References Lanczos Algorithm Nour-Omid, B. and Clough, K.W.,”Dynamic Analysis of Structure using Lanczos Co-ordinates”, Earthquake Eng. And structure Dyn.Vol. 12, pp 565-577 ,1984 Load Dependent Ritz Vectors (LDRV) Kline, K.A., ”Dynamic Analysis Using a Reduced Basis of Exact Modes and Ritz Vectors”, AIAA J, Vol. 24, pp2022-2029, 1986 Wang, S. and Choi, K.K. ,”Continuum Design Sensitivity of Transient Response Using Ritz and Mode Acceleration Methods”, AIAA J ,Vol. 30, pp1099-1109, 1992. Iterative Solution

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