Question

View History Bookmarks People Tab Window Help The W12 X C Prob-11 x Probl ficrosoft x C Get Hom X C Prob-ITI x C The W12 x | smeetsingh/Downloads/302-QUIZ-283%20F2019.pdf Mail - Jasmeet S.. News chego Your document ch. Prob-2 Derive the equation of the resonance frequency of the uniform cantilever been shown below by using method of conservation of energy Solution must be the principle of consevation of energy. [Solution tips: Um, maximum strain energy is equal to max. kinetic energy of vibrating body.) Solution:

Answer 1

The frequency of vibration is found by considering the conservation of energy in the system; the natural frequency is determined by dividing the expression for potential energy in the system by the expression for kinetic energy.

Rayleigh’s method is based on the principle of conservation of energy. The energy in a dynamic system consists of the kinetic energy and the potential energy.T+U=CONSTANT.,Tmax = Umax

Canhlever beam

m - mass length y = amplitude of deflection Curve * 1 w? fyz dan, the natural where w in Id the beam trequency Te sbain energy of the beam in the wool done on beam which is stored as elastic energy. If the bending moment in m a the slope 4 elastic curve l o. V = 2 fm do

Usually the deflection of beam in small so l the following relationship can be asumed to had o-dg - R do- dat dn dy da Thus de 2 dr da2 room beam theooy m/ IER where R in radius of clovatuse a EI is flexural rigidity. Thus Beam IN

Since Tmax - Umay na Ei dag Cdn2 W2 This enpreson to equency g gives lowest natural toonsuers Gibaaton g toonsue g bean