ADS_HW01_2009 - v ≤ ≤ by using the initial conditions...

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ADVANCED DYNAMICS OF STRUCTURES / HOMEWORK / October 28, 2009 ADVANCED DYNAMICS OF STRUCTURES / HOMEWORK / October 28, 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 without considering the damping and determine . Find the resonance condition in terms of the parameters of the system, when the damping is neglected. 3a 3a 2a 2a k =2ka 1 2k Total mass M q(t)=q sin pt o 5a Q(t)= aq sin pt o 2 θ( t ) hinge c c =ca 2 1 k =k a 2 1 Total mass 2M Total mass 4M Total mass M k 3a 2. A single degree of system of the mass m , the stiffness k is subjected to the external load ) ( t p . The variation of the external load is given as shown. Assuming the system starts from the rest position, i.e., 0 ) 0 ( = = t v and 0 ) 0 ( = = t v .Find the displacement function ) 5 . 0 0 ( o T t
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Unformatted text preview: v ≤ ≤ by using the initial conditions and ) 5 . ( o T t v ≥ by using the continuity of the displacement and the velocity at o T t 5 . = , where o T . is the free vibration period of the system. Draw the displacement variation static v t v / ) ( where k p v o static / = . o p(t) m v( ı ) k/2 k/2 T /2 t p(t) p o 3. The single-degree-of-freedom system shown is subjected to an external load of impulse characters by assuming that the system starts from the rest, i.e., ) ( ) ( = = = = t v t v & ) ( t Q v K v M o o = + & & . Find out the displacement ) ( t v , the velocity ) ( t v & and the acceleration ) ( t v & & . Obtain the maximum shear force and bending moment. kN g M o 100 = , m kN K o / 600 = , kN Q o 40 = ; m h 10 = Q(t) K M Q(t) t Q o o o v(t) T /40 o T /20 o h...
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