Page 406 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Sec. 12.6 Mykiestad’s Method for Beams 393

Figure 12.5-4.

The mode shapes ean be found by printing out for each of the preceding
frequencies.

12.6 MYKLESTAD’S METHOD FOR BEAMS
When a beam is replaced by lumped masses connected by massless beam sections,
a method developed by N. O. Myklestad^ can be used to progressively compute the
deflection, slope, moment, and shear from one section to the next, in a manner
similar to the Holzer method.

Uncoupled flexural vibration. Figure 12.6-1 shows a typical section of an
idealized beam with lumped masses. By taking the free-body section in the manner
indicated, it will be possible to write equations for the shear and moment at / + 1
entirely in terms of quantities at /. These can then be substituted into the
geometric equations for 6 and y.
From equilibrium considerations, we have

K+i = m ^ y , ( 12.6-1)
M „ , = M , - 1^.,,/, ( 12.6-2)

From geometric considerations, using influence coefficients of uniform beam

^N. O. Myklestad, “A New Method of Calculating Natural Modes of Uncoupled Bending
Vibration of Airplane Wings and Other Types of Beams,” J. Aero. Sci. (April 1944), pp. 153-162.
N. O. Myklestad, “Vibration Analysis,” McGraw-Hill, N.Y. (1944).