SolSec 4.10 - Problems and Solutions Section 4.10 (4.83...

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Problems and Solutions Section 4.10 (4.83 through 4.90) 4.83* Solve the system of Example 1.7.3 for the vertical suspension system of a car with m = 1361 kg, k = 2.668 x 10 5 N/m, and c = 3.81 x 10 4 kg/s subject to the initial conditions of x (0) = 0 and v (0) = 0.01 m/s 2 . Solution: Use a Runge Kutta routine such as the one given in Mathcad here or use the toolbox:
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4.84* Solve for the time response of Example 4.4.3 (i.e., the four-story building of Figure 4.9). Compare the solutions obtained with using a modal analysis approach to a solution obtained by numerical integration. Solution: The following code provides the numerical solution. which compares very well with the plots given in Figure 4.11 obtained by plotting the modal equations. One could also plot the modal response and numerical response on the same graph to see a more rigorous comparison.
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4.85* Reproduce the plots of Figure 4.13 for the two-degree of freedom system of Example 4.5.1 using a code. Solution: Use any of the codes. The trick here is to construct the damping matrix from the given modal information by first creating it in modal form and then transforming it back to physical coordinates as indicated in the following Mathcad session:
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4.86*. Consider example 4.8.3 and a) using the damping ratios given, compute a damping matrix in physical coordinates, b) use numerical integration to compute
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SolSec 4.10 - Problems and Solutions Section 4.10 (4.83...

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