M. Gurgoze, ON THE EIGENFREQUENCIES OF LONGITUDINALLY VIBRATING RODS CARRYING A TIP MASS AND SPRING-MASS IN-SPAN, Journal of sound and vibration, 216(2), 1998, pp. 295-308
The present paper is concerned with the determination of the frequency
equation and sensitivity of the eigenfrequencies of a fixed-free long
itudinally vibrating rod carrying a tip mass to which a spring-mass sy
stem is attached in-span. First, the exact frequency equation is estab
lished, and then an approximate formula is given for the fundamental f
requency, based on Dunkerley's procedure. Moreover, using the normal m
ode method, a second approximate but very accurate frequency equation
is established with the help of which a sensitivity formula is derived
later. Frequency equations of some simpler systems are also obtained
from the general expressions by using limiting processes. These novel
equations can be very useful for a design engineer who is interested i
n the eigencharacteristics of similar systems, and their sensitivity.
(C) 1998 Academic Press.