Višja dinamika

Udarna motnja

Dr. Janko Slavič, April 2014

Udarna motnja

Remove["Global`*"]

Popis udarne motnje

Vzbujevalna sila (pospešek) v normirani obliki

f[t_,t0_]:=
Piecewise[{
{f0(Sin[π(t/t0)]),0≤t<t0}
}]

Plot[f[t,t0]/.{t0->1,f0->1},{t,-1,2},Frame->True,Axes->False]

Udarna motnja

Odziv na enotski impulz

g[t_]:=(1/(ω0d))(E^(-δ ω0 t))Sin[ω0d t]
ω0d:=ω0 (Sqrt[1-(δ^2)])

Konvolucijski integral

x[t_]=Integrate[f[τ,t0]g[t-τ],{τ,0,t},Assumptions->t∈Reals]

x1[t_]=PiecewiseExpand[x[t],{0≤t<t0,t>0}]

x2[t_]=PiecewiseExpand[x[t],{t0<t,t>0,t0>0}]

Brez dušenja:

x1[t]/.δ->0
FullSimplify[x2[t]/.δ->0]

Udarna motnja

Primer

m:=5000
t0:=0.5
k:=(10^7)
F0:=300 (10^3)
ω0:=(Sqrt[(k/m)])
f0:=(F0/m)
δ:=0.1

x[t]

xSol[t_]:=Piecewise[{
{x1[t],0<t<t0},
{x2[t],t≥t0∧t>0}
}]

Plot[{xSol[t]},{t,-t0,2t0},Frame->True,Axes->False,PlotRange->All]