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Structural Analysis
Dynamics of Structures with MATLAB Applications
124 SOLVED PROBLEMS
Question: 2.1
Consider a SDOF system shown in Figure 2.1. It undergoes undamped free vibrations. The mass = 40 kNs²/m, stiffness k = 3500 kN/m. Determine the natural frequency and natural period of vibration. The initial conditions are given as: x(0) = 0.01 m, x(0) = 0.1 m/s. Hence, plot a graph of ...
Verified Answer:
The complete solution is given by Equations (2.6) ...
Question: A2.7
Determine the solution of the following linear simultaneous equations using MATLAB. A = [5 2 3 4 5 4 7 0 9] , B = {10 13 16} ...
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Question: A2.6
(a) Determine the inverse and determinant of the following matrix using MATLAB. A = [50 20 0 20 75 -10 0 10 100] (b) Find the eigenvalues of A. ...
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Question: A2.5
[A]= [24 15 10 35 20 0 56 20 45] [B] = [34 -20 0 25 45 -9 67 9 22] Using MATLAB, Find (i) A + B = C (ii) A – B = C (iii) A B = C (iv) AB + B = C ...
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Question: 2.8
A SDOF system with a friction damper vibrates with an initial displacement of 50 mm. It completes 4 cycles in 0.8 second when its amplitude reduces to 5 mm. Estimate the coefficient of friction and when does the system come to rest. ...
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Period of vibration T = 0.8/4 = 0.2 sec Frequency ...
Question: 2.7
A displacement–time plot for a free vibration analysis of a SDOF system gives a displacement of 7.5 mm at time t1 and 1 mm after 7 cycles. Determine logarithmic decrement and damping ratio. ...
Verified Answer:
Logarithmic decrement is given by
\pmb{\del...
Question: 2.6
A SDOF frame has a mass = 5000 kg, lateral stiffness k = 4 × 10^6 N/m and a damping ratio of 4%. Determine its undamped and damped natural frequency. If the frame is displaced by 25 mm and released suddenly, determine the peak displacements of first five cycles of vibrations. ...
Verified Answer:
Undamped natural frequency
\omega =\sqrt{\f...
Question: 2.5
Consider a SDOF system shown in Figure 2.2. It undergoes underdamped free vibrations. The mass = 40 kNs²/m, stiffness k = 3750 kN/m and c = 50 kNs/m. The initial conditions are given as: x(0) = 0.01 m, x(0) = 0.1 m/s. Plot the inertia, damping and spring forces. ...
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Mass m = 40 kN s²/m Stiffness k = 3750 kN/m Dampin...
Question: 2.4
Consider a SDOF system shown in Figure 2.2. It undergoes underdamped free vibrations. The mass = 40 kNs²/m and stiffness k = 3750 kN/m. The initial conditions are given as: x(0) = 0.01 m, x(0) = 0.1 m/s. Plot the influence of 0, 5% and 10% damping on the displacement–time history. ...
Verified Answer:
The response of a SDOF system can be determined us...
Question: 14.8
Re-do Example 14.5 and locate the performance point using the EC8-Part 1 method. ...
Verified Answer:
For T = 0.3 sec, stiffness = 43820 N/m This is a s...
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