Page 57 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

44 Free Vibration Chap. 2

2-26 The engine-valve system of Fig. P2-26 consists of a rocker arm of moment of inertia 7,
a valve of mass m ,, and a spring spring of mass m^. Determine its effective mass at A.

ms

Figure P2-26. Engine valve system.
2-27 A uniform cantilever beam of total mass ml has a concentrated mass M at its free
end. Determine the effective mass of the beam to be added to M assuming the
deflection to be that of a massless beam with a concentrated force at the end, and
write the equation for its fundamental frequency.
2-28 Repeat Prob. 2-27 using the static deflection

y(x) == 4- 3
24 El
for the uniformly loaded beam, and compare with previous result.
2-29 Determine the effective rotational stiffness of the shaft in Fig. P2-29 and calculate its
natural period.

Figure P2-29.
2-30 For purposes of analysis, it is desired to reduce the system of Fig. P2-30 to a simple
linear spring-mass system of effective mass and effective stiffness Determine
and in terms of the given quantities.