Vpliv neravne podlage na nihanje avtomobilskega vzmetenja

Podlago opišemo s funkcijo h(t). Privzeli bomo, da je na cesti prepreka višine h=0,05m.

h[t_]=If[Abs[t-2]<0.2,0.05,0];

Plot[h[t],{t,0,10},PlotStyle->Blue,PlotRange->{{-1,10},{-0.01,0.1}},AxesStyle->Arrowheads[{0.04}],AxesLabel->{"t","h"},LabelStyle->{12,Bold}]

f[y_]=Convolve[10/Sqrt[Pi]*Exp[-100t^2],h[t],t,y];

Plot[f[t],{t,0,10},PlotStyle->Blue,PlotRange->{{-1,10},{-0.01,0.1}},AxesStyle->Arrowheads[{0.04}],AxesLabel->{"t","h"},LabelStyle->{12,Bold}]

Poglejmo, kako dana prepreka vpliva na nihanje voznikovega sedeža. Najprej bomo privzeli, da ni dušenja in da ima vzmetenje lastni frekvenci 1Hz in 0,25Hz. Na grafih vidimo, da mehkejše vzmetenje povzroči manjše nihanje in manjši vertikalni pospešek voznikovega sedeža.

k=4*Pi^2;

c=0;

s1=NDSolve[{y''[x]+c*y'[x]+k*y[x]==k*f[x]+c*f'[x],y[0]==0,y'[0]==0},y,{x,0,30},PrecisionGoal->100];

k=1/4Pi^2;

c=0;

s2=NDSolve[{y''[x]+c*y'[x]+k*y[x]==k*f[x]+c*f'[x],y[0]==0,y'[0]==0},y,{x,0,30},PrecisionGoal->100];

Plot[{Evaluate[y[x]/.s1],Evaluate[y[x]/.s2]},{x,0,10},PlotStyle->{Blue,Black},PlotRange->{-0.15,0.15},AxesLabel->{"t","x"},LabelStyle->{12,Bold}]

Plot[{Evaluate[y''[x]/.s1],Evaluate[y''[x]/.s2]},{x,0,10},PlotStyle->{Blue,Black},PlotRange->{-10,10},AxesLabel->{"t","a"},LabelStyle->{12,Bold}]

Sedaj bomo privzeli, da ima vzmetenje lastno frekvenco 1Hz in analizirali vpliv koeficienta dušenja. Na grafih vidimo, da mehkejše vzmetenje povzroči manjše nihanje in manjši vertikalni pospešek voznikovega sedeža.

k=4Pi^2;

c=0.1*4Pi;

s1=NDSolve[{y''[x]+c*y'[x]+k*y[x]==k*f[x]+c*f'[x],y[0]==0,y'[0]==0},y,{x,0,30},PrecisionGoal->100];

k=4Pi^2;

c=4Pi;

s2=NDSolve[{y''[x]+c*y'[x]+k*y[x]==k*f[x]+c*f'[x],y[0]==0,y'[0]==0},y,{x,0,30},PrecisionGoal->100];

Plot[{Evaluate[y[x]/.s1],Evaluate[y[x]/.s2]},{x,0,10},PlotStyle->{Blue,Black},PlotRange->{-0.15,0.15},AxesLabel->{"t","x"},LabelStyle->{12,Bold}]

Plot[{Evaluate[y''[x]/.s1],Evaluate[y''[x]/.s2]},{x,0,10},PlotStyle->{Blue,Black},PlotRange->{-10,10},AxesLabel->{"t","a"},LabelStyle->{12,Bold}]

Sedaj bomo privzeli, da je na cesti stopnica višine h=0,05m.

h[t_]=If[t<1,0,0.05];

Plot[h[t],{t,0,5},PlotStyle->Blue,PlotRange->{{-1,5},{-0.01,0.1}},AxesStyle->Arrowheads[{0.04}],AxesLabel->{"t","h"},LabelStyle->{12,Bold}]

f[y_]=Convolve[10/Sqrt[Pi]*Exp[-100t^2],h[t],t,y];

Plot[f[t],{t,0,5},PlotStyle->Blue,PlotRange->{{-1,5},{-0.01,0.1}},AxesStyle->Arrowheads[{0.04}],AxesLabel->{"t","h"},LabelStyle->{12,Bold}]

Privzeli bomo, da ima vzmetenje lastno frekvenco 1Hz in analizirali vpliv koeficienta dušenja.

k=4Pi^2;

c=0.1*4Pi;

s1=NDSolve[{y''[x]+c*y'[x]+k*y[x]==k*f[x]+c*f'[x],y[0]==0,y'[0]==0},y,{x,0,30},PrecisionGoal->100];

k=4Pi^2;

c=4Pi;

s2=NDSolve[{y''[x]+c*y'[x]+k*y[x]==k*f[x]+c*f'[x],y[0]==0,y'[0]==0},y,{x,0,30},PrecisionGoal->100];

Plot[{Evaluate[y[x]/.s1],Evaluate[y[x]/.s2]},{x,0,5},PlotStyle->{Blue,Black},PlotRange->{-0.15,0.15},AxesLabel->{"t","x"},LabelStyle->{12,Bold}]