Clear["Global`*"]

Time step of excitation:

dT=0.02;

Load the excitation. This is El Centro. Use ReadList[ ] function to read a list from a file. el-centro.inp is an example of such a file.

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Now we need a function that returns the ground acceleration for each time instant. first entry in mList is for T=0.
GetIndex returns the lower index in the span:

GetIndex[t_]:=IntegerPart[(t/dT)]+1;

For example, for t=0.06, dT=0.02 we expect the fourth entry:

mList[[GetIndex[0.06]]]

Now define the function:

GetGroundAcceleration[t_]:=mList[[GetIndex[t]]]+(mList[[GetIndex[t]+1]]-mList[[GetIndex[t]]])FractionalPart[(t/dT)];

For example, for t=0.03, the ground acceleration in units of G is:

GetGroundAcceleration[0.03]

The rest is easy:

Manipulate[
ParametricPlot[
Evaluate[{x1[t],a ((YP[[2]])/(YP[[1]])) x1[t]+(1-a) YP[[2]] x3[t]}/.
Quiet@NDSolve[
{x1'[t]==x2[t],
x2'[t]==((-1)/Mass)(c x2[t]+a ((YP[[2]])/(YP[[1]])) x1[t]+(1-a) YP[[2]] x3[t] -Mass*9.81*GetGroundAcceleration[t]),
x3'[t]==((x2[t])/(YP[[1]]))(1-((Abs[x3[t]])^n) (γ Sign[x2[t] x3[t]]+(1-γ))),
x1[0]==0,
x2[0]==0,
x3[0]==0},
{x1[t],x2[t],x3[t]},
{t,0,tTotal},AccuracyGoal->5,Method->{"DiscontinuityProcessing"->False}]],
{t,0,tTotal},
ImageSize->{500,500},PlotRange->{{-.3,.3},{-4,4}},AspectRatio->1/1,AxesLabel->{"u","F"}],
{{tTotal,30,"Total time"},dT,30,Appearance->"Labeled"},
{{Mass,28.6,"m"},0.1,30,0.01,Appearance->"Labeled"},
{{n,2.0,"n"},0.1,10,0.01,Appearance->"Labeled"},
{{c,0.0,"c"},0.0,10,0.01,Appearance->"Labeled"},
{{a,0.05,"a"},0.0,1,0.01,Appearance->"Labeled"},
{{γ,0.9,"γ"},0.01,1,0.01,Appearance->"Labeled"},
{{YP,{0.111,2.86}},{0.01,0.01},{10,10},Locator}]