Problem 4: (30) The mass m is supported by an assembly of springs and dampers in addition to a vertical cantilever. Assuming the connections are rigid and weightless, for small oscillations, derive the following:
(i) Equivalent spring constant ke.
(ii) Equivalent damping constant ce.
(iii) Equivalent mass me.
(iv) By using force balance method, derive the equation of motion.
(v) Determine the relationship between ce, ke, and me so that this system will be critically damped.
k3 are parallel
k2 are parallel
(i) (ii) (iii) (iv) (v)
Equivalent spring constant ke
Equivalent damping constant ce. Equivalent mass me. By using force balance method, derive the equation of motion. Determine the relationship between ce, ke, and me so that this system will be critically damped.
Rigid, weightless connection
ara K3 are parallel K2 are parallel
k
C1
C2
m
EI
K
123EI
wow k, k2
Ke