Estimation of Fundamental Natural Frequency,

natalia-silvester
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Estimation of Fundamental Natural Frequency, Damping Ratio and Equivalent Mass 421L521L (Lab 8) Single DOF Modeling E, I, L, ρ E, I, L, ρ M k c x mxcxkx f(t) x(t) Aexp(-ξωnt)COS(ωnsqrt(1-ξ2)t- ψ)Bsin(ωt) Time response Transient

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01
Estimation of Fundamental Natural Frequency, Damping Ratio and Equivalent Mass 421L/521L (Lab 8)<br>
02
Single DOF Modeling E, I, L, ρ E, I, L, ρ M k c x mx”+cx’+kx = f(t)

x(t) = Aexp(-ξωnt)COS(ωnsqrt(1-ξ2)t- ψ)+Bsin(ωt)
Time response = Transient response + Forced response(sinusoidal)

Where,
ωn=sqrt(k/m), undamped natural frequency, rad/s
ξ =c/sqrt(2mk), damping ratio
ωd=ωnsqrt(1-ξ2), damped natural frequency, rad/s k, stiffness, N/m
m, mass, kg
c, damping coefficient, N/(m/s) E: Young’s modulus
I: Moment of inertia
L: length
ρ: mass per unit length Cantilever Fixed-Fixed accelerometer<br>
03
Visualization of responses Exponential part Sinusoidal part Transient
response Forced response
(Sinusoidal input) Transient response
+ Forced response<br>