Kerala University 2009 M.Tech Structural Engineering Cmc1001: dynamics of structures - Question Paper

First Semester M.Tech. Degree Examination,june 2009

Stream: Structural Engineering and Construction Management

CMC 1001 : DYNAMICS OF STRUCTURES

Time:3 hrs Max Marks: 100

Instructions: Answer any five full questions.

1. A rigid uniform bar of length(l) and having mass per unit length(P) is hinged at one end and is restrained by a viscous damper of constant(C) at the free end,and by a spring of stiffness(K) at a distance 'a' from the hinged end.If the bar is undergoing free vibration, derive the equation of motion.Determine the natural frequency and the critical damping coefficient.

2. A portable harmonic loading machine provides an efficient means by evaluating the dynamic properties of the structures in the field. By operating the machine at two different frequencies and noting the structural response amplitude and phase angle in each case,it is possible to determine the dynamic properties of SDOF system. In a test of this type on a single storeyed frame,the shaking machine was operated at frquencies 16rad/sec and 25rad/sec, with a force amplitude of 2.5 kN.the response amplitude and phase angles were measured as 0.180mm and 15 and 0.370mm and 55 respectively. Find all the dynamic properties of the frame.

3. Find out the maximum elastic force developed in the structure having mass 1000 tonnes and effective stiffness 10MN/m,when subjected to an impulsive force as shown in fig.

4. a) what is a shear building. Explain the assumptions used in idealizing a multistored building as a shear building

b) For the 2-DOF system having lumped masses m1= 23.83 tonnes and m2=11.68 tonnes and spring stiffness k1=5452 kN/m and k2=7858kN/m,determine the natural frequencies and mass orthonormalised modal matrix.

5. Determine the maximum response of the frame shown in fig.(2),when it is subjected to a suddenly applied constant acceleration y=0.28g at base.Natural frequency w1=11.9 rad/sec and w2=33.1 rad/sec.The normalised modal matrix is

0.00486 0.00428

Z= 0.00614 -0.00697

6. a) Derive the equation of motion for beams subjected to axial force, and undergoing flexural vibration.

b) Find the first three natural frequencies and modeshapes of a simply supported beam with uniform flexural rigidity and mass m per unit length. Sketch the mode shapes.

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