M. Gurgoze, ON THE EIGENFREQUENCIES OF CANTILEVERED BEAMS CARRYING A TIP MASS ANDSPRING-MASS IN-SPAN, International journal of mechanical sciences, 38(12), 1996, pp. 1295-1306
The present study is concerned with the derivation of the eigenfrequen
cies and their sensitivity of a cantilevered Bernoulli-Euler beam carr
ying a tip mass (primary system) to which a spring-mass (secondary sys
tem) is attached in-span. After establishing the exact frequency equat
ion of the combined system, a Dunkerley-based approximate formula is g
iven for the fundamental frequency. Using the normal mode method, a se
cond approximate Frequency equation is established which is then used
for the derivation of a sensitivity formula for the eigenfrequencies.
The Frequency equations of some simpler systems are obtained from the
general equation as special cases. These frequency equations are then
numerically solved for various combinations of physical parameters. Th
e comparison of the numerical results with those from exact Frequency
equations indicate clearly that the eigenfrequencies of the combined s
ystem described above can be accurately determined by the present meth
od. Copyright (C) 1996 Elsevier Science Ltd.