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MOS16-CE08 Structural Dynamics July 2016 Assignment 1: Free Vibrations Date: 18/07/2016



1. A building consists of 4 columns of size 350 x 300mm, with bay width as 3m. The slab thickness is 120mm, and floor to floor height is 3m. Considering the grade of concrete as M25, find the natural frequency and time period of building in two orthogonal directions.



2. Generate the stiffness matrix for following frames r1



r5 4



r2



r3 2



r4 53



r6



r7 32



r8 45



3. Write the equation of motion for the system below



4. A simplified model of a rack and pinion steering system is shown in the figure below. A gear of radius r and polar moment of inertia J is attached to a shaft of Torsion stiffness kt. The gear rolls without slip on the rack of mass m. The rack is attached to a spring of stiffness k. Derive the differential equation governing the equation of motion of the system.



5. A 2.5kg slender bar is of length 40cm is pinned at one end. A 3kg particle is to be attached to the bar. How far from the pin support should the particle be placed such that the period of the bar’s oscillation is 1 sec? 6. A 4.53 kg mass attached to the lower end of a spring whose upper end is fixed vibrates with a natural period of 0.45 s. Determine the natural period when a 2.26 kg mass is attached to the midpoint of the same spring with the upper and lower ends fixed.