Page 172 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)
P. 172
Chap. 5 Problems 159
The curve for optimum damping then must pass through P with a zero slope, so
that if we substitute (aj/co^y = 2/(2 + ¡jl) into the derivative of Eq. (5.8-5)
equated to zero, the expression for is found. It is evident that these conclusions
apply also to the linear spring-mass system of Fig. 5.8-5, which is a special case of
the damped vibration absorber with the damper spring equal to zero.
Fig. 5.8-6 shows a laboratory model of a 2-DOF building excited by the
ground motion.
PRO B LE M S
5-1 Write the equations of motion for the system shown in Fig. P5-1, and determine its
natural frequencies and mode shapes.
^2 Figure P5-1.
5-2 Determine the normal modes and frequencies of the system shown in Fig. P5-2 when
n = 1.
nk
m — AAAA^— m
Figure PS-2.
5-3 For the system of Prob. 5-2, determine the natural frequencies as a function of n.
5-4 Determine the natural frequencies and mode shapes of the system shown in Fig. P5-4.
5k
3/7?
Figure P5-4.
