A cantilever beam at low frequency behaves like an underdamped 1 DOF mass/spring/damper system.(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Cantilever Beam problem

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