University : | University of Portsmouth UniLearnO is not sponsored or endorsed by this college or university. |
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Subject Code : | P25752 | Country : | Australia |
P25752 – Engineering Mathematics and Numerical Analysis
Question 1 – Beam Analysis
Design Matlab functions to:
1. enter the length of a statically determined beam and positions of the pinned support and the roller support. The process must be user-friendly, with step-by-step instructions and appropriate control of the entered data.
2. enter the magnitude and the position of the loading factors lateral to the beam axis, including point loads, moments and uniformly distributed loads. The number of loading factors of each kind must be defined by a user interactively. The input data control must be implemented.
3. calculate reaction forces
4. construct the Bending Moment and Shearing Force Diagrams for the beam directly underneath the Free Body Diagram.
5. enter the type and the dimensions of the cross-section of the beam and calculate the position of the centroid (Neutral Axis normal to the load) and the Second Moment of Area (Moment of Inertia) with respect to the Neutral Axis.
6. calculate internal stresses for maximum and minimum bending moments and plot their distribution on the cross-section.
Question 2:
A certain company makes televisions, stereo units, and speakers. Its parts inventory includes chassis, picture tubes, speaker cones, power supplies, and electronics. The inventory, required components, and profit for each product appear in the following table. Determine how many of each product to make in order to maximize the profit.
Question 3:
Quenching is the process of immersing a hot metal object in a bath for a specified time to obtain certain properties such as hardness. A copper sphere 25 mm in diameter, initially at 300°C, is immersed in a bath at 0°C. The following table gives measurements of the sphere’s temperature versus time. Find a functional description of these data using commands, not GUI. Plot the function and the data on the same plot.
Question 4
1. Develop the mathematical model for the two-mass suspension model shown in Figure Q4.
2. Develop a Simulink model of this system to obtain the plots of x1 and x2. The input y(t) is a unit step function, and the initial conditions are zero.
Test your model using the following values: m1 = 250 kg, m2 = 40 kg, k1 = 1.5 × 104 N/m, k2 = 1.5 × 105 N/m, and c1 = 1917 N-sec/m.
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