SDOF Cantilever Beam with Lumped Mass✔


Consider a mass mounted on the end of a cantilever beam. Assume that the end-mass is much greater than the mass of the beam.






where,

E: the modulus of elasticity = 29000 kip/in2

I:  the area moment of inertia = 1728 in4

L: the length = 10000 in

g: gravity = 386.0886 in/sec2

m: mass = 0.0005 kip-sec2/in


Equation of motion for free vibration of a SDOF system:

md2u/dt+ ku=0

d2u + Wn2u=0

Then, the natural frequency of vibration, Wn= √k/m

The stiffness at the end of the beam, k= 3EI/L3 → k= 1.50336e-4 kip/in→ Wn= 0.548 rad/sec

The natural period of vibration, Tn= 2π/Wn → Tn= 11.459 sec


App

Object Link: https://openbrim.org/objidc42impq7jbac3a2wbcwhzk.project

Library

Object Link: https://openbrim.org/objid6j9ohpyqgmcih6zpnn2zko.libobj


Result Comparison


Independent OpenBrIMPercent Difference (OpenBrIM vs Independent)
T1 (sec)11.458611.45740.010%