Vibrating Beam

The first 200 words of this essay...

M3 Vibrating Beam

Eoin Kearney

07383002

Objective

The aim of this experiment was to determine the response of a spring-mass-dashpot system to a disturbance and investigate the phenomena associated with the vibration of a beam.

Theory

Moments about pivot neglecting mass of beam

Mx1L1 + Cx3L3 + Kx3L3 =0

Including mass of the beam

(I/ (L1) ^2 + M) x1L1 + Cx3L3 +Kx3L3 =0

To find I the inertia of the beam

I = (m (L^2))/3

Where for the above

M=mass of weight

X1=amplitude of oscillation

X3= amplitude of oscillation

L1= length from the mass

L2= length from the mass

L3= length from the mass

m= mass of beam

C=Dashpot resistance

I=moment of the beam about its pivot

K=spring constant

Taking x1/L1 = x2/L2 = x3/L3

Gives the equations

X1+X2 [CL3^2/(ML1^2+I)] + X1[kL3^2/(ML1^2+I)] = 0

And

X1+ 2PwnX1 + wn^2 X1 = 0

Where

Wn= natural frequency

P= the damping ratio

Equipment

A displacement of the beam is monitored from a point L2 from the