The measured receptance data around two resonant picks of a structure are tabulated in the followings. Find the natural frequencies, damping ratios, and mode shapes of the structure. (30 points) (@)×10 m/N α₁₂ (@)×10 m/N w/2z (Hz) 99 0.1176 0.17531 0.1114 -0.1751i 101 -0.0302 0.2456i -0.0365 -0.2453i 103 -0.1216 0.1327i -0.1279-0.1324i 220 0.0353 0.0260i -0.0419+0.0259i 224 0.0210 0.0757i |-0.0273 +0.0756i 228 -0.0443 0.0474i 0.0382 +0.0474i

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
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The measured receptance data around two resonant picks of a structure are tabulated in
the followings. Find the natural frequencies, damping ratios, and mode shapes of the
structure. (30 points)
(@)×10 m/N
α₁₂ (@)×10 m/N
w/2z
(Hz)
99
0.1176 0.17531
0.1114 -0.1751i
101
-0.0302 0.2456i
-0.0365 -0.2453i
103
-0.1216 0.1327i
-0.1279-0.1324i
220
0.0353 0.0260i
-0.0419+0.0259i
224
0.0210 0.0757i |-0.0273 +0.0756i
228 -0.0443 0.0474i 0.0382 +0.0474i
Transcribed Image Text:The measured receptance data around two resonant picks of a structure are tabulated in the followings. Find the natural frequencies, damping ratios, and mode shapes of the structure. (30 points) (@)×10 m/N α₁₂ (@)×10 m/N w/2z (Hz) 99 0.1176 0.17531 0.1114 -0.1751i 101 -0.0302 0.2456i -0.0365 -0.2453i 103 -0.1216 0.1327i -0.1279-0.1324i 220 0.0353 0.0260i -0.0419+0.0259i 224 0.0210 0.0757i |-0.0273 +0.0756i 228 -0.0443 0.0474i 0.0382 +0.0474i
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