Find the undamped natural period of vibration of the SDOF system shown where the

Question

Find the undamped natural period of vibration of the SDOF system shown where the spring may only carry axial force(negelect strain in he beam). If the peak amplitude decays from 1 to 0.8 inches in one cycle, estimate the percentage critical damping and the damped circular frequency.  

Find the undamped natural period of vibration of the SDOF system shown where the spring may only carry axial force(negelect strain in he beam). If the peak amplitude decays from 1 to 0.8 inches in one cycle, estimate the percentage critical damping and the damped circular frequency.

Explanation / Answer

The massless rod can be assumed to be a spring with spring constant 3EI/(L^3)

So we get two springs in parallel.

Therefore the two springs can be replaced by one spring with spring constant = K1 + K2

= (3EI/(L^3) + 10) kip/in

Undamped frequency = (undefined)

Percentage critical damping = damping ratio*100

We know that damping ratio is related to Logarithmic decrement by

Therefore (undefined)

Damping ratio = 0.0355

Percentage critical damping = 3.55%

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