Page 356 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 10 Problems 343

Figure PlO-28.

10-29 For the system of Fig. PlO-28, show that the symmetric mode for the free vibration
reduces to a 3 x 3 equation. Determine the mass and stiffness matrices for this
problem and calculate the natural frequencies and mode shapes.
10-30 Using the program CFiOLJAC, solve for the eigenvalues and eigenvectors for the
4 x 4 beam in Example 10.5-1.
10-31 The uniform beam of Fig. PlO-31 is supported on an elastic foundation that exerts a
restraining force per unit length of -ky{x) over the right half of the beam. Using two
elements, develop the equations of motion. With kl^/SEI = 10, determine the
natural frequencies and compare with those without the elastic foundation. Plot the
mode shapes for the first two modes.

Figure P10-3L

10-32 Repeat Problem 10-31 assuming the left end is pinned instead of fixed.
10-33 Figure PlO-33 shows one of the “ell” beams of a centrifuge that whirls around the
vertical axis 0 - 0 with angular speed il rad/s. Using the stations indicated,
determine the equation of motion and its natural frequencies. Compare with the case
n = 0.

Mass/unit length = m

E l = 1.0

Figure PlO-33.