Page 424 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 12 Problems 411

12-12 Using Dunkerley’s equation, determine the fundamental frequency of the three-mass
cantilever beam shown in Fig. P12-12.

o — ^— o —
m m fv
Figure P12-12.
12-13 Using Dunkerley’s equation, determine the fundamental frequency of the beam
shown in Fig. P12-13.
= W, W2 = 4PF, = 2W

LJ

1__ 4 -
4 r 4 4 ^ 4 Figure P12-13.

12-14 A load of 100 lb at the wing tip of a fighter plane produced a corresponding
deflection of 0.78 in. If the fundamental bending frequency of the same wing is 622
cpm, approximate the new bending frequency when a 320-lb fuel tank (including fuel)
is attached to the wing tip.
12-15 A given beam was vibrated by an eccentric mass shaker of mass 5.44 kg at the
midspan, and resonance was found at 435 cps. With an additional mass of 4.52 kg,
the resonant frequency was lowered to 398 cps. Determine the natural frequency of
the beam.
12-16 Using the Rayleigh-Ritz method and assuming modes x/l and sin(7TJc//), determine
the two natural frequencies and modes of a uniform beam pinned at the right end
and attached to a spring of stiffness k at the left end (Fig. PI2-16).

Figure P12-16.

12-17 For the wedge-shaped plate of Example 12.3-1, determine the first two natural
frequencies and mode shapes for bending vibration by using the Ritz deflection
function y = + C2X^.