The fundamental frequencies of longitudinally vibrating rods carrying tip mass and transversally vibrating beams carrying tip mass by using several methods

The present paper is concerned with the determination of frequency equation and sensitivity eigenfrequencies a fixed-free longitudinally vibrating rod transversally beam carrying tip mass by using several methods. First, exact equations such systems are established, then approximate formulas given for fundamental methods which contain equivalent system, Rayleigh quotient, Dunkerley’s formula continuous system model. applicability proximity these versus solutions reviewed. results compared in wide range relevant parameters to give clear idea about validity proposed formulas. These new derived can be very useful design engineer who interested eigencharacteristics similar their sensitivity.