Question

A 120 kg machine is mounted at the mid-span of a 15 m long simply connected beam of E =200 x 106 N/m2 and I = 1.53 x 10-4 m4. An experiment is run on the system during which the machine is subject to a harmonic excitation of magnitude 2000 N at a variety of excitation frequencies. The largest steady state amplitude recorded is 2.5 mm. Estimate the damping ratio of the system.

Answer 1

Given Data: m= 120 kg. I= 15m = 200 x 106 N/m² I = 1.53 x 10-4 m4 F. = 2000 N x = 2.5 mm - Sol :- Stiffness of simply suported beam is given by' (K); K = 48 EI 48 EI 48 x 200 x 106 x 1:53 X10 (15) 4 K = 435.2 N/m

Steady state amplitude (x) is given by; F. /k (1- R2)2 + (2&R)? X But largest amplitude will Occure at R=1 where; R = frequancy Ratio Wn for largest amplitude (Folk) 2 § Xmax -3 R., 2.5 X 10 2000 2x & X 435.2 & = 919.117