Fundamentals of Engineering Thermodynamics
8th Edition
ISBN: 9781118832301
Author: SHAPIRO
Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT
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Chapter 11.9, Problem 13E
To determine
What do the variables
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An aluminum rod of length L
=
1m has mass density p = 2700 kg and
Young's modulus E = 70 GPa. The rod is fixed at both ends. The exact
natural eigenfrequencies of the rod are wexact
E
=
√
ρ
for n=1,2,3,. . . .
1. What is the minimum number of linear elements necessary to
determine the fundamental frequency w₁ of the system? Discretize
the rod in that many elements of equal length, assemble the global
system of equations KU = w² MU, and find the fundamental
frequency w₁. Compute the relative error e₁ = (w1 - wexact) /w exact
Sketch the fundamental mode of vibration.
2. Use COMSOL to solve the same problem. Show the steps necessary
to find the fundamental frequency and mode of the rod. What is the
relative error using linear elements and a normal mesh?
Chapter 11 Solutions
Fundamentals of Engineering Thermodynamics
Ch. 11.9 - Prob. 1ECh. 11.9 - Prob. 2ECh. 11.9 - 3. What is an advantage of using the Redlich–Kwong...Ch. 11.9 - To determine the specific volume of superheated...Ch. 11.9 - Prob. 5ECh. 11.9 - Prob. 6ECh. 11.9 - Prob. 7ECh. 11.9 - Prob. 8ECh. 11.9 - Prob. 9ECh. 11.9 - Prob. 10E
Ch. 11.9 - Prob. 11ECh. 11.9 - Prob. 12ECh. 11.9 - Prob. 13ECh. 11.9 - Prob. 14ECh. 11.9 - Prob. 15ECh. 11.9 - Prob. 1CUCh. 11.9 - Prob. 2CUCh. 11.9 - Prob. 3CUCh. 11.9 - 4. Evaluate the compressibility factor Z of water...Ch. 11.9 - Prob. 5CUCh. 11.9 - Prob. 6CUCh. 11.9 - Prob. 7CUCh. 11.9 - Prob. 8CUCh. 11.9 - 9. For an ideal gas obtain expressions for the (a)...Ch. 11.9 - Prob. 10CUCh. 11.9 - Prob. 11CUCh. 11.9 - Prob. 12CUCh. 11.9 - Prob. 14CUCh. 11.9 - Prob. 15CUCh. 11.9 - Prob. 16CUCh. 11.9 - Prob. 17CUCh. 11.9 - Prob. 18CUCh. 11.9 - Prob. 19CUCh. 11.9 - Repeat parts (a)–(d) of Example 11.1 if the carbon...Ch. 11.9 - Prob. 21CUCh. 11.9 - Prob. 22CUCh. 11.9 - Prob. 23CUCh. 11.9 - Prob. 24CUCh. 11.9 - Prob. 25CUCh. 11.9 - Prob. 26CUCh. 11.9 - Prob. 27CUCh. 11.9 - Prob. 28CUCh. 11.9 - Prob. 29CUCh. 11.9 - Prob. 30CUCh. 11.9 - Prob. 31CUCh. 11.9 - Prob. 32CUCh. 11.9 - Prob. 33CUCh. 11.9 - Prob. 34CUCh. 11.9 - Prob. 35CUCh. 11.9 - Prob. 36CUCh. 11.9 - Prob. 37CUCh. 11.9 - Prob. 38CUCh. 11.9 - Prob. 39CUCh. 11.9 - Prob. 40CUCh. 11.9 - Indicate whether the following statements are true...Ch. 11.9 - Prob. 42CUCh. 11.9 - Prob. 43CUCh. 11.9 - Prob. 44CUCh. 11.9 - Prob. 45CUCh. 11.9 - Prob. 46CUCh. 11.9 - Prob. 47CUCh. 11.9 - Prob. 48CUCh. 11.9 - Prob. 49CUCh. 11.9 - Prob. 50CUCh. 11.9 - Owing to safety requirements, the pressure within...Ch. 11.9 - Ten pounds mass of propane have a volume of 2 ft3...Ch. 11.9 - The pressure within a 23.3-m3 tank should not...Ch. 11.9 - Estimate the pressure of water vapor at a...Ch. 11.9 - Prob. 7PCh. 11.9 - A rigid lank contains 1 kg of oxygen (O2) at p1 =...Ch. 11.9 - Prob. 11PCh. 11.9 - Prob. 13PCh. 11.9 - Prob. 14PCh. 11.9 - Prob. 15PCh. 11.9 - Prob. 16PCh. 11.9 - Prob. 17PCh. 11.9 - Prob. 18PCh. 11.9 - Prob. 20PCh. 11.9 - Prob. 21PCh. 11.9 - Prob. 22PCh. 11.9 - Prob. 23PCh. 11.9 - Using Eq. 11.35. check the consistency of
the...Ch. 11.9 - Prob. 25PCh. 11.9 - Prob. 26PCh. 11.9 - A gas enters a compressor operating at steady...Ch. 11.9 - Prob. 28PCh. 11.9 - Prob. 29PCh. 11.9 - The Mollier diagram provides a graphical...Ch. 11.9 - Derive the relation cp = −T(∂2g/∂T2)p.
Evaluating...Ch. 11.9 - Prob. 32PCh. 11.9 - Prob. 33PCh. 11.9 - Prob. 34PCh. 11.9 - Prob. 35PCh. 11.9 - Prob. 36PCh. 11.9 - At 0°C, the specific volumes of saturated solid...Ch. 11.9 - Prob. 38PCh. 11.9 - Prob. 39PCh. 11.9 - Prob. 42PCh. 11.9 - Prob. 43PCh. 11.9 - Prob. 44PCh. 11.9 - Prob. 46PCh. 11.9 - Prob. 47PCh. 11.9 - Prob. 48PCh. 11.9 - Prob. 49PCh. 11.9 - Prob. 50PCh. 11.9 - Prob. 51PCh. 11.9 - Prob. 52PCh. 11.9 - Prob. 53PCh. 11.9 - Prob. 54PCh. 11.9 - Develop expressions for the volume expansivity β...Ch. 11.9 - Prob. 56PCh. 11.9 - Prob. 57PCh. 11.9 - Prob. 58PCh. 11.9 - Prob. 59PCh. 11.9 - Prob. 60PCh. 11.9 - Prob. 61PCh. 11.9 - Prob. 62PCh. 11.9 - If the value of the specific heat cυ of air is...Ch. 11.9 - Prob. 65PCh. 11.9 - Prob. 66PCh. 11.9 - Prob. 67PCh. 11.9 - Prob. 68PCh. 11.9 - Prob. 69PCh. 11.9 - Determine the maximum Joule-Thomson inversion...Ch. 11.9 - Prob. 71PCh. 11.9 - Show that Eq. 11.77 can be written as
Using this...Ch. 11.9 - If the specific heat cv of a gas obeying the van...Ch. 11.9 - Prob. 75PCh. 11.9 - Prob. 76PCh. 11.9 - Prob. 77PCh. 11.9 - Prob. 78PCh. 11.9 - Prob. 79PCh. 11.9 - Prob. 80PCh. 11.9 - Prob. 81PCh. 11.9 - Prob. 82PCh. 11.9 - Prob. 83PCh. 11.9 - Prob. 84PCh. 11.9 - Prob. 85PCh. 11.9 - Prob. 86PCh. 11.9 - Prob. 87PCh. 11.9 - Prob. 88PCh. 11.9 - Oxygen (O2) undergoes a throttling process from...Ch. 11.9 - Prob. 90PCh. 11.9 - Prob. 91PCh. 11.9 - Prob. 92PCh. 11.9 - Prob. 93PCh. 11.9 - Prob. 94PCh. 11.9 - Prob. 95PCh. 11.9 - Prob. 96PCh. 11.9 - Prob. 97PCh. 11.9 - Prob. 99PCh. 11.9 - Prob. 100PCh. 11.9 - Prob. 101PCh. 11.9 - Prob. 102PCh. 11.9 - A rigid vessel initially contains carbon dioxide...Ch. 11.9 - Prob. 104PCh. 11.9 - Prob. 105PCh. 11.9 - Prob. 106PCh. 11.9 - Prob. 107PCh. 11.9 - Prob. 108PCh. 11.9 - Determine the fugacity, in atm, for
butane at 555...Ch. 11.9 - Using the equation of state of Problem 11.14(c),...Ch. 11.9 - Prob. 111PCh. 11.9 - Prob. 113PCh. 11.9 - Prob. 114PCh. 11.9 - Prob. 115PCh. 11.9 - Prob. 116PCh. 11.9 - Prob. 117PCh. 11.9 - Prob. 118PCh. 11.9 - Prob. 119PCh. 11.9 - Prob. 120PCh. 11.9 - Prob. 121PCh. 11.9 - Prob. 122PCh. 11.9 - Prob. 123PCh. 11.9 - A tank contains a mixture of 75% argon and 25%...Ch. 11.9 - Prob. 125PCh. 11.9 - Prob. 126PCh. 11.9 - Prob. 127PCh. 11.9 - Prob. 128P
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