ON THE EIGENFREQUENCIES OF LONGITUDINALLY VIBRATING RODS CARRYING A TIP MASS AND SPRING-MASS IN-SPAN

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.