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Linear static analysis
The applied force is:
and the stress:
This induces a strain:
The elongation is:
F = mg = 1000 N
σ = F S = × = ×
−8 10
/ 1000 / 2.5 10 4 10 Pa
ε = σ = × × =
10 11
/ E 4 10 / 2 10 0.2
∆ L= Lε = 0.2 m
Linear dynamic analysis
The cable mass is:
−8
m= ρV = ρLS = 8000ii 1 2.5×
10 M
and is therefore negligible with respect to the concentrated mass M .
By schematizing this system as a single-d.o.f. oscillator, the pulsation of the
oscillation would be:
ω = 2 π f = K / M
where f indicates the frequency and K the stiffness. The latter is given by:
F σS EεS E∆L ES
K = = = = S =
∆L ∆L ∆L L∆L
L
1