Ho6 - 16.20 HANDOUT#6 Fall 2002(Introduction To Structural Dynamics REGIMES(Structural Dynamics Wave Propagation(Quasi Static Static f(natural

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16.20 HANDOUT #6 Fall, 2002 (Introduction To) Structural Dynamics REGIMES (Structural) Wave (Quasi) - Static Dynamics Propagation Static f(natural f(speed of waves frequency of in material) structure) – Structural stiffness speed = – Structural “characteristic length” E ρ = region of transition SPRING-MASS SYSTEMS [Force/length] k d Static equation: F = kq () = dt Dynamic: mq ˙˙ + k q = F t () (No damping) (With damping) + cq ˙ + k q = F t Inertial Load = – (mass) x (acceleration) General form: m = mass matrix ~ ˙˙ mq + kq = F ~ ~ ~ ~ ~ ~ k = stiffness matrix Paul A. Lagace © 2002
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qt or F = force vector mq ˙˙ j + k ij q j = F i ~ ij q = d. o. f. vector ~ d. o. f. = degree of freedom i, j = 1, 2…n n = number of degrees of freedom of system FREE VIBRATION () = C 1 sin ω t + C 2 cos t genera l solution for single spring-mass system natural frequency: = k m FORCED VIBRATION dirac delta function: δ ( t τ ) = 0 @ t ( t ) →∞ @ t = −∞ ( t ) dt = 1 () ( t − τ ) dt = g −∞ gt unit impulse response: 1 = sin ( t ) for t ≥ τ m 0 for t ≤ τ
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This note was uploaded on 02/03/2012 for the course AERO 16.20 taught by Professor Paullagace during the Fall '02 term at MIT.

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Ho6 - 16.20 HANDOUT#6 Fall 2002(Introduction To Structural Dynamics REGIMES(Structural Dynamics Wave Propagation(Quasi Static Static f(natural

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