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PED – 059

*PED059*

I Semester M.E. (Civil) Degree Examination, January 2015 2K8SE103 : STRUCTURAL DYNAMICS (Structures PSC) Time : 3 Hours

Max. Marks : 100

Instructions : i) Answer any five full questions. ii) Assume any missing data suitably. 1. Define the following :

(4×5=20)

i) Resonance ii) Degree of Freedom. iii) Sensitivity analysis. iv) Frequency domain and time domain analysis. 2. a) Explain D’Alembert’s principle. b) Explain the displacement response for undamped free vibration. 3. a) Obtain the equation for logarithmic decrement.

10 10 10

b) A platform of weight = 2000 N is supported by four equal columns. Experimentally it has been determined that a static force of 500 N applied horizontally to the platform, produces a displacement of 2.5 mm. Damping is taken as 5% of critical damping. Determine for this structure the following : 10 i) Undamped natural frequency. ii) Absolute damping co-efficient. iii) Logarithmic decrement. iv) No. of cycles and the time required for the amplitude of motion to be reduced from an initial value of 2.5 mm to 0.25 mm. 4. Explain the following with neat sketches :

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i) Undamped free vibration. ii) Under damping. iii) Over damping. iv) Critical damping. P.T.O.

*PED059*

PED – 059 5. a) Obtain the transmissibility equation with respect to force.

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b) A machine for manufacturing electronic circuits is to be mounted on a factory floor using a vibration isolating suspension . The vibration of floor during normal usage has a predominant frequency of 10 Hertz 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 ? 6. a) Obtain the orthogonality property between the natural modes.

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b) The flexibility matrix and the load matrix of a vibrating system are given below. Compute the fundamental frequency using Rayleigh’s method. ⎡ 4 ⎢ Flexibility matrix = ⎢ 4 ⎢ ⎢⎣3.2

4 48 4

3 .2 ⎤ ⎥ 4 ⎥ mmN , load matrix = ⎥ 4 ⎥⎦

⎧ 60 ⎪ ⎨100 ⎪ 80 ⎩

⎫ ⎪ ⎬N. ⎪ ⎭

7. a) Differentiate between lumped mass matrix and consistent mass matrix. b) Explain sensitivity analysis of response with an example.

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8. Determine the damped response with Penzien-Wilson damping using the normal mode method. 20 __________________