ON THE EIGENFREQUENCIES OF CANTILEVERED BEAMS CARRYING A TIP MASS ANDSPRING-MASS IN-SPAN

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.