- #1
kev.thomson96
- 13
- 0
A cantilever beam at low frequency behaves like an underdamped 1 DOF mass/spring/damper system.
We are trying to find the roots of the Characteristic equation which are lambda1,2 = -dampingRatio x wnatural /sqrt(1-dampingRatio)
Relevant formulas and given values:
damping ratio = c/2sqrt(m/k)
wnatural = sqrt(k/m)
wdamped = wnatural x sqrt(1-dampingRatio^2)
log decrement = (1/n)ln(x1/xn+1) = 2pi(damping ratio)/sqrt(1-dampingRatio)
beam width = 50 mm
beam depth = 3.8 mm
Modulus of elasticity = 200 GPa
density = m/v = 7800 kg/m^3
deflection x = Fl^3/3EI, l is length and I is second moment of area
kequivalent = kbeam + kshaker, where kshaker = 45 N/m.
I've only found I = bh^3/12 = 15.83 x 10^-12 m and from then on I'm stuck
We are trying to find the roots of the Characteristic equation which are lambda1,2 = -dampingRatio x wnatural /sqrt(1-dampingRatio)
Relevant formulas and given values:
damping ratio = c/2sqrt(m/k)
wnatural = sqrt(k/m)
wdamped = wnatural x sqrt(1-dampingRatio^2)
log decrement = (1/n)ln(x1/xn+1) = 2pi(damping ratio)/sqrt(1-dampingRatio)
beam width = 50 mm
beam depth = 3.8 mm
Modulus of elasticity = 200 GPa
density = m/v = 7800 kg/m^3
deflection x = Fl^3/3EI, l is length and I is second moment of area
kequivalent = kbeam + kshaker, where kshaker = 45 N/m.
I've only found I = bh^3/12 = 15.83 x 10^-12 m and from then on I'm stuck