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ADVANCED DYNAMICS OF STRUCTURES / QUIZ / November 11, 2009 ADVANCED DYNAMICS OF STRUCTURES / QUIZ / November 11, 2009 1. Write down the equation of motion of the rigid-body assemblage in terms of ) ( t θ the rotation angle of the support by using the principle of the virtual work. Obtain the free vibration period k M T / α = of the assemblage and determine . Find p for the resonance condition in terms of the parameters of the system M , k and a . 3a 3a 2a 2k Total mass 4M q(t)=q sin pt o 5a Q(t)=aq sin pt o θ( t ) Hinge k =ka 2 1 Total mass M 3k 2. Obtain the displacement function ) ( t v of the undamped SDOF system subjected to the external load o t t o e p t p / ) ( = assuming that the system starts from the rest, i.e., 0 ) 0 ( ) 0 ( = = = = t v t v . m and k denote the mass and the stiffness of the system, respectively. p t p(t) o -t/t p(t)=p e o o p(t) m v( ı ) k/2 k/2 0 3. The frame shown can be assumed as a single-degree-of-freedom system and it is subjected to a ground motion of impulse character
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