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- Structural Dynamics - SD
- 2017
- PYQ
**Jntuk/GDMM ENNGG.COLLEGE - GDMM**- Civil Engineering
- B.Tech
**61 Views**- 2 Offline Downloads
- Uploaded 5 months ago

Code No:CE1903 R14 M. Tech I Semester Regular Examinations, April 2015 STRUCTURAL DYNAMICS (Structural Engineering) Time: 3 Hours Max. Marks : 60 Note: Answer any Five Questions. All questions carry equal marks. 1. a) Explain various dampers and their functions. (4M) b) Deduce an expression for the response of a single degree freedom free vibration system with viscous damping? (8M) 2. A single degree of freedom structure for which the weight W= 667.5 kN set into vibration by releasing it from an initial displacement of 50 mm. Given that its maximum displacement after one complete oscillation is 30 mm and that it occurs in 0.85 s, evaluate the following quantities on the assumption that damping is of the viscous type. (12M) a) The logarithmic decrement of the system, , and the associated damping factor, . b) The damped natural period of vibration Td. c) The undamped natural period, T d) The stiffness, K and e) The coefficient of viscous damping, c 3. a) Derive the equation of motion for critically damped system for a single degree freedom system. (6M) b) A machine of weight W = 2000N and making 150 rpm, is supported by four helical springs made of steel wire of diameter d = 12mm. the diameter corresponding to centre line of helix is D=10cm and the number of coils is 10. Determine the maximum vertical disturbing force transmitted to the foundation if the centrifugal force of unbalance for the angular speed equal to 1 radians per second is P=5N. Take damping ratio ζ= 0.05 and modulus of shear = 0.8 x107 N/cm2. (6M) 4. a) Determine the natural frequency of un-damped MDF system and mode shapes for the structure shown in figure 1, where m= 1000kg and k=7000kN/m. (8M) Page 1 of 2

Figure 1 b) Write short notes on lumped mass system and consistent mass matrix. (4M) 5. Define “pulsating excitation” with examples. Explain the methods to find the responses of these excitations. Explain in detail the classical method of evaluating the response of SDF system to rectangular pulse force. (12M) 6. A force Po sin ωt acts on an undamped SDOF system of mass m and spring constant of k, which was at rest at t=0. a) Determine the expression for steady state response. b) Determine an expression for the total response. c) Sketch the transient, steady state and total response for the following numerical vales: m = 5 kg, k = 10 kN/m, Po = 100 N, and ω =40 rad/s. d) For an excitation frequency ratio of ω/ωn = 1.5, what is the ratio of the maximum total response to the maximum steady-state response. (12M) 7. a) Prove the Orthogonality of natural modes for MDF un-damped system. (6M) b) Explain mode superposition method for determination of the response of a MDOF system. (6M) 8. Evaluate the first three natural frequencies of vibration and corresponding mode shapes for a simply supported beam of span L with mass per unit length m and constant flexural rigidity EI. Use the continuous distributed mass method (12M) ### Page 2 of 2

Subject Code: G8703/R13 M. Tech – I Semester Regular/Supplementary Examinations, April, 2015 STRUCTURAL DYNAMICS (Common to SE and SD) Time: 3 Hours Max Marks: 60 Answer any FIVE questions All questions carry EQUAL marks **** 1. a) List out and explain different prescribed dynamic loadings with applications b) Discuss force-displacement relation for linearly elastic and inelastic systems c) Explain How equation of motion are formulated for earthquake motion leading to lateral displacement and rotation using simplification methods 2. a) Derive expression for response of a SDOF system subjected to free vibration. b) A block of mass 0.10kg is suspended from a spring having a stiffness of 25N/m. the block is displaced downwards from the equilibrium position through a distance of 2cm and released with an upward velocity of 3cm/sec. Determine (i) Natural Frequency (ii) Period of Oscillation (iii) Maximum Velocity (iv) Maximum Acceleration (v) Phase angle 3. a) Derive expression for response of a SDOF system subjected to damped free vibration. Draw the plot showing response of the structure to damped free vibration explaining salient features involved. b) The successive amplitudes from a free vibration test for a structure are 0.9, 0.46, 0.3 and 0.12 units respectively. Determine the damping ratio (assuming it to be very small) of the system considering (i) each cycle separately and (ii) considering them all together. 4. a) Draw the plot showing response of the structure to damped Harmonic Excitation PoSinωt explaining salient features involved. b) Explain the significance of Displacement Response factor Rd. Discuss the variation of Rd with damping as the excitation frequency is varying from gradually varying to rapidly varying stage while the structure is undergoing vibration. 5. a) Derive equation of motion of multi degree freedom systems by (i) Newton’s equation of motion (ii) Mass spring damper system (iii) Dynamic equilibrium b) Explain effect of Lateral vibration due to ground motion on MDOF Systems www.manaresults.co.in 1 of 2 ||'''||||''|'|'''|||

Subject Code: G8703/R13 6 . a) Explain Free vibration of a cantilever beam with first five modes of vibration. b) Determine the natural frequencies and mode shapes of vibration for the beam shown in figure 2 adopting the stiffness matrix. Normalized modes have unit vertical deflection at the free end. Show that the modes show orthogonality relation. U2 U1 EI L/2 2m L/2 m 7. a) Derive partial differential equation governing the motion of the beam with distributed mass and elasticity subjected to external dynamic forces. b) Considering distributed mass and elasticity from fundamentals derive expressions for first three natural frequencies and draw mode shapes for a Simply Supported beam. 8. a) Resonance b) Dynamic magnification Factor c) Duhamel’s Integral ***** www.manaresults.co.in 2 of 2 ||'''||||''|'|'''|||

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