Page 279 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

266 Computational Methods Chap. 8

8-20 For the system shown in Fig. P8-20, write the equation of motion and convert to the
standard form.

^VWV-K

3m
4/f
Figure P8.20.

8-21 The stiffness matrix for the system shown in Fig. P8-21 is given as
3 -1 -1
K = k - 1 2 -1
- 1 - 1 2
Determine the Choleski decomposition U and U ^

k
-AAA/V-

k k
m -A V W - IT) —VW W m
'^1 "^3 Figure P8.21.
8-22 Given the mass and stiffness matrices
3 0 3 -1
M K = k
0 2 - 1 2
determine the natural frequencies and mode shapes using the standard form and the
Choleski-Jacobi method.
8-23 Repeat Example 8.10-1 by decomposing the stiffness matrix and compare the results
with those given in the example.
8-24 Express the following equation in standard form using Choleski decomposition of the
mass matrix.
‘ 4 1 O' 2 -1 0 ]' iXA /Q
A 1 4 1 + - 1 2 - 1 0
0 1 2 0 - 1 1 J ,0
8-25 Repeat Prob. 8-24 by decomposing the stiffness matrix.
8-26 Verify the equation of motion for the system of Fig. P8-26:
m^ 0 (^1 + ^2 ^3)
m, = k, = m and k

0 W2 1^2/ —ki (^2 + ^4)
Determine the eigenvalues and eigenvectors using CHOLJAC.