Arbitrary Response

# Arbitrary Response - CE 573: Structural Dynamics Response...

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CE 573: Structural Dynamics Response to Arbitrary Dynamic Excitation 0 1 () ( ) s in ( ) t mu ku F t u t F t d m τ ωτ ω += ⇒ = ±± (In all the examples, assume that the system starts at rest.) Example #1: Step Force – [] 00 0 0 2 2 1 ( ) sin ( ) sin ( ) Change of variables: z ( ), 1 s in cos 1 cos . For 0 : ( ) 1 cos sin 1 tt o o z oo zt t o t o dd F ut F t d t d mm td z d FF zdz z m m F t k F e t t k ξω ωω ξ = = =− = = − ⇒ =∗− = ⎛⎞ ⎜⎟ ≠= + ⎝⎠ ∫∫ Answer Dynamic Load Factor: Example #2: Rectangular Pulse – for 0 for 0 d o d F Ft = > During the pulse, the forcing looks like that of a step force. fo r 0 . o d F t t t k ∴= − Answer

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## This note was uploaded on 05/09/2008 for the course CE 573 taught by Professor Whalen during the Fall '05 term at Purdue.

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

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