For a cantilever beam shown below, assume the mass is concentrated at two locati

Question

For a cantilever beam shown below, assume the mass is concentrated at two locations (free end, and middle length), m = 1000 kg. This beam has rectangular cross-section with section height = 0.4 m, section width = 0.1 m, half beam length L= 5 m. Beam material’s Modulus of elasticity is E = 20 GPa. Modal damping ratio is assumed to be 2%.

a.) Find the stiffness coefficient k22

b.) Find the natural frequency

c.) First mode shape vector

d.) 2nd mode shape vector

Explanation / Answer

a) Stiffness 22 = load required at 2 for unit vertical deflection at 2=3EI/L3

E=20 GPa=20*109 N/m2 , I=0.1*0.43/12=5.33*10-4 m4

L=5m

K22 = 3*20*109*5.33*10-4/53 = 256000 N/m

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