ME – 124

*ME124*

I Semester M.E. (Civil) Degree Examination, July 2016 Major : (Structures/PSC) 2K8SE103 : STRUCTURAL DYNAMICS Time : 3 Hours

Max. Marks : 100

Instructions : i) Answer any five full questions. ii) Assume any missing data suitably. 1. Write short notes :

(4×5=20)

i) Under damped system ii) Free and forced vibrations iii) Resonance iv) Combination of springs 2. a) Explain the displacement response of undamped free vibrations.

10

b) Obtain the equation for logarithmic decrement.

10

3. Obtain the energy balance equation from an energy conservation perspective.

20

4. a) Explain transmissibility with respect to a force.

10

b) A machine for manufacturing electronic circuits is to be mounted on a factory floor using vibration isolating suspension. The vibrations of floor during normal usage has a predominant frequency of 10 Hz with max amplitude of 20×10−4 mm. The greatest amplitude that can be tolerated by the machine for reliable operation is 1×10−4 mm.

10

a) Determine the required natural frequency of the machine on its suspension assuming that there will be 2 % of critical damping. b) If the mass of the machine is 1500 kg, what will be its static deflection ? P.T.O.

*ME124*

ME – 124 5. a) Explain eigen values and eigen vectors.

b) The flexibility matrix and load matrix of a vibrating system are given below. Compute the fundamental frequency using Raleigh’s method.

10 10

4 3.2 ⎤ ⎡ 4 ⎢ 4 4.8 4 ⎥ mm / N Flexibility matrix = ⎢ ⎥ ⎢⎣3.2 4 4 ⎥⎦ ⎧ 60 ⎫ Load matrix = ⎪⎨100 ⎪⎬ N ⎪ 80 ⎪ ⎩ ⎭ 6. a) Obtain the general equation for mass matrix. b) Obtain mass matrix for a flexural member.

6 14

7. Explain sensitivity analysis with respect to natural frequencies, mode shapes and response.

20

8. Determine the natural frequencies and mode shapes for the frame structure shown in figure (1). The floor is considered to be absolutely rigid.

20

Figure 1 ———————