hw2_spring_09

# hw2_spring_09 - below), plot the real and imaginary parts...

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EML 6267 Assignment #2 Spring 2009 Please remember to put your name on your assignment. Due: 1/28/09 1. (20 pts.) Consider a 2DOF lumped parameter, chain-type model undergoing forced vibration. k 1 = 2 x10 5 N/m k 2 = 5.5 x10 4 c 1 = 60 N-s/m c 2 = 16.5 m 1 = 2.5 kg m 2 = 1.2 a. (5 pts.) Show that proportional damping exists. b. (5 pts.) Determine the natural frequencies and eigenvectors if a force F 1 = F 0 e i ω t is acting on coordinate x 1 of the system. c. (10 pts.) Determine the FRFs Q 1 /R 1 , Q 2 /R 2 , X 2 /F 1 and X 1 /F 1 . Express them mathematically and plot the Real and Imaginary parts of these FRFs (please include your computer code, use a frequency range of 0 to 100 Hz, and use units of m/N for your vertical axes). 2. (20 pts.) Determine the [m], [c], and [k] matrices in local coordinates for the model shown below. Hint: your matrices should be symmetric. m 2 k 1 x 1 x 2 c 1 m 1 c 2 m 3 x 3 k 2 k 3 k 4 k 5 c 3

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3. (20 pts.) Using complex matrix inversion and your results from Problem 2 (see values
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Unformatted text preview: below), plot the real and imaginary parts of: a. (5 pts.) the direct FRF X 2 /F 2 b. (5 pts.) the cross FRF X 1 /F 3 c. (5 pts.) the cross FRF X 3 /F 1 d. (5 pts.) verify that reciprocity holds by comparing your solutions from parts b. and c. k 1 = 4 x10 6 N/m k 2 = 6 x10 6 k 3 = 4 x10 6 k 4 = 2 x10 6 k 5 = 1 x10 6 c 1 = 100 N-s/m c 2 = 200 c 3 = 175 m 1 = 0.7 kg m 2 = 0.9 m 3 = 1.1 Please include your computer code. For your plots, use a frequency range of 0 to 1000 Hz and units of m/N for the vertical axes. 4. (20 pts.) Determine the mass, stiffness and damping coefficients for a SDOF system from the following experimental direct FRF. 5. (20 pts.) Complete problem 4 from chapter 2 of the text. 200 210 220 230 240 250 260 270 280 290 300-2-1 1 2 x 10-6 Real (m/N) 200 210 220 230 240 250 260 270 280 290 300-4-3-2-1 x 10-6 Frequency (Hz) Imag (m/N)...
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## This note was uploaded on 04/23/2009 for the course EML 6267 taught by Professor Schmitz during the Spring '08 term at University of Florida.

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hw2_spring_09 - below), plot the real and imaginary parts...

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