Arbitrary Response

Arbitrary Response - CE 573 Structural Dynamics Response to...

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CE 573: Structural Dynamics Response to Arbitrary Dynamic Excitation 0 1 ( ) ( ) ( ) sin ( ) t mu ku F t u t F t d m τ ω τ ω + = = ±± τ (In all the examples, assume that the system starts at rest.) Example #1: Step Force – [ ] [ ] 0 0 0 0 2 2 1 ( ) sin ( ) sin ( ) Change of variables: z ( ), 1 ( ) sin cos ( ) 1 cos . For 0: ( ) 1 cos sin 1 t t o o z o o z t t o t o d d F u t F t d t d m m t dz d F F u t z dz z m m F u t t k F u t e t t k ω ω ξω ω τ τ ω τ τ ω ω ω τ ω τ ω ω ω ω ξ ξ ω ξ = = = = = = − = = = = + Answer ω Dynamic Load Factor: Example #2: Rectangular Pulse – for 0 ( ) for 0 d o d t t F F t t t = > During the pulse, the forcing looks like that of a step force.
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