CTR11102/11502 Resit CourseworkStructural Dynamics and Earthquake Engineering DesignCTR11102/CTR11502Resit Component 1The total marks of this coursework is 100.Please send the coursework to me by 25th of July 2021.Dr Aamir Khokhar1Q1: The rigid bar of mass (m) shown in Figure 01 is subject to a time varying uniformlydistributed force. Derive the equation of motion and calculate the natural circular frequency.Assume small angles of rotation.[10 marks]kRigid beammcF0(t)Figure 012Q2: A wind turbine is modelled as a concentrated mass (the turbine) atop a weightless towerof height L (Figure 02). To determine the dynamic properties of the system, a large crane isbrought alongside the tower and lateral force F =200 kN is exerted along the turbine axis asshown in Figure 02. This cause a horizontal displacement of 30mm. The cable attaching theturbine to the carne is severed instantaneously, and the resulting free vibration of the turbineis recorded. At the end of the two complete cycles, the time was 1.25 second and thevibration amplitude of 20mm was recorded. From the data above determine the following:a) The undamped natural frequency, 𝜔𝑛b) The effective stiffness of the system, kc) The effective mass of the system, md) The effective damping factor, ζ[10 marks]Figure 02F = 200 kN3Q3 (a): A concentrated weight (W = 3000 N) dropped from a height at the overhanging endof an un-damped cantilever beam of length (L = 10m), shown in Figure 03. The impact ofweight causes a downward displacement of 75 mm and velocity of 100 mm/sec in the samedirection from its static equilibrium position. Assume E = 210 GPa. Determine:i. The natural frequency of the system, ωn and the natural period, Tnii. The maximum displacement and the phase angle φiii. Determine displacement, velocity and acceleration at, 5, 10 and 20 secondsiv. Plot the resulting displacement, velocity and acceleration as a function of time in thefirst five seconds and locate maximum velocity and acceleration produced due toimpact.Q3 (b): If dampers of damping factor (ζ) are required to place underneath of the beam toexamine the behaviour of vibration. What value you will choose for (ζ) that couldsubstantially reduce the amplitude of the maximum displacement, velocity and acceleration.Support your chosen (ζ) values with sufficient evidence mainly by plotting different graphs.[15 marks](Make sure you submit the computer programme print copy with the submission)Figure 034Q4: A water tower shown in Figure 4(a) is subjected to a blast loading illustrated in Figure4(b). Assume W = 500 kN, k = 45000 kN/m, ζ= 0.05, F0 = 600 kN and td = 0.1 sec. Developa computer model and evaluate the dynamic response of the tower by any of two followingnumerical methods:1. Interpolation of the excitation2. Finite difference expression of velocity and acceleration3. Assumed variation in accelerationPlot the displacement 𝑥(𝑡), velocity ẋ(𝑡) and acceleration 𝑥̈(𝑡) responses in the time interval0 ≤ t ≤ 1.0 sec. (Note: acceleration response only required for method 2 and 3)[30 marks]W(a) Water tank (b) Blast loadingFigure 4: Water tower subjected to blast loading5Q5: For three-storey shear frame building shown in Figure Q5, determine the naturalfrequencies and corresponding mode shapes and sketch three mode shapes.[35 marks][Total marks = 100]Figure Q5

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