Page 357 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

344 Introduction to the Finite Element Method Chap. 10

10-34 If the pinned-free beam with a torsional spring is rotated about the vertieal axis, as
shown in Fig. PlO-34, determine the new stiffness matrix for the first element of
length 1/2.

Figure PlO-34.

10-35 For the helieopter blade of Fig. PlO-34, determine the stiffness equation for the outer
half of the blade.
10-36 Write the eomplete equation for the two-element blade of Fig. PlO-34, and solve for
the natural frequeneies and mode shapes.
10-37 For the uniform eantilever beam modeled by three elements shown in Fig. PlO-37,
the stiffness matrix is of order 6X 6. Rearrange the stiffness matrix, determine the
3 x 3 redueed stiffness matrix /C* and eompute the eigenvalues and eigenveetors.
Compare the results with those of Prob. 8-15.
I e i
§0 Figure PlO-37.

10-38 Repeat Problem 10-37 with redueed stiffness and eorresponding redueed mass.
' 1 0 O'
Compare with assumed 3 x 3 mass matrix of M = ml 0 1
0 0