dynamics 6
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JETRO G. SARAJENASTE 224- STRUCTURAL DYNAMICS
2- 2- 2- -11--12- - -1-1 -1
1- 0 + 2- -12- -1
1--1 - -1-11- 0 + -1 2-
2- -11--1
- -1 -1 -11- 0 + 1 1 0
2- -11--1 - -1
-1 -11- 0 =0
2-. 2- 1- -1 + 1 2-.
0
-1 1- + 2- -1 2- 1- -1 + 1 2- 0 + -1 2- 2- 1- -1
+ -1 1 -1 1- + 1 0 2- 1- -1 + 1 1 0 =0
5simplifying the equation we got a polynomial into 5th degree.
-9 4+283-352+15-1=0Using Synthetic Division, Solve for :
= 0.0811 = 0.6902 = 1.7153 = 2.8314 = 3.6825
mh = 12EI
= 0.081, =15.60 rad/s1 = 0.690, =45.55 rad/s2 = 1.715, =71.81 rad/s3 = 2.831, =92.25 rad/s4 = 3.682, =105.22 rad/s5
Solve for the First Mode:[k-m] =01
2-2-
2-2-
1-
-1-1 -1
-1 -1-1 -1
-1
00 00 0
00 00 0 0
0 =0
12345
using = 0.081, we have
2-2-
2-2-
1-
-1-1 -1
-1 -1-1 -1
-1
00 00 0
00 00 0 0
0 =
1112131415
1.919 -1 -1 1.919
-11.919
0.919
-11.919 -1
-1-1-1
0 0 0 0 0
0 0 0 0 0 0 0
=
1112131415
00000
00000
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