Adatok (alapmértékegységek : mm, N, s)

L1=200;L2=600;L3=300;d1=20;d2=30;d3=20;d4=300;s1=10;s2=1000;s3=2500;m=0.5 (10^(-3));Ex=200000;ρ=7850 (10^(-12));

I1=(((d1^4)π)/64);I2=(((d2^4)π)/64);I3=(((d3^4)π)/64);A1=(((d1^2)π)/4);A2=(((d2^2)π)/4);A3=(((d3^2)π)/4);Θz=(1/4)m ((((d4/2)))^2);

Elemi merevségi és tömegmátrixok

KE=((Iz*RUG)/(L^3))(({{12, 6*L, -12, 6*L}, {6*L, 4*(L^2), -6*L, 2*(L^2)}, {-12, -6*L, 12, -6*L}, {6*L, 2*(L^2), -6*L, 4*(L^2)}}));
ME=((rho*Ae*L)/420)(({{156, 22L, 54, -13L}, {22L, 4(L^2), 13L, -3(L^2)}, {54, 13L, 156, -22L}, {-13L, -3(L^2), -22L, 4(L^2)}}));

Globális merevségi és tömegmátrix létrehozása

K1=KE/.{Iz->I1,RUG->Ex,L->L1};
K2=KE/.{Iz->I2,RUG->Ex,L->L2};
K3=KE/.{Iz->I3,RUG->Ex,L->L3};
M1=ME/.{rho->ρ,Ae->A1,L->L1};
M2=ME/.{rho->ρ,Ae->A2,L->L2};
M3=ME/.{rho->ρ,Ae->A3,L->L3};

Kglob=ConstantArray[0,{8,8}];
Kglob[[{1,2,3,4},{1,2,3,4}]]=Kglob[[{1,2,3,4},{1,2,3,4}]]+K1;
Kglob[[{3,4,5,6},{3,4,5,6}]]=Kglob[[{3,4,5,6},{3,4,5,6}]]+K2;
Kglob[[{5,6,7,8},{5,6,7,8}]]=Kglob[[{5,6,7,8},{5,6,7,8}]]+K3;
Kglob[[1,1]]=Kglob[[1,1]]+s1;
Kglob[[3,3]]=Kglob[[3,3]]+s2;
Kglob[[5,5]]=Kglob[[5,5]]+s3;

Mglob=ConstantArray[0,{8,8}];
Mglob[[{1,2,3,4},{1,2,3,4}]]=Mglob[[{1,2,3,4},{1,2,3,4}]]+M1;
Mglob[[{3,4,5,6},{3,4,5,6}]]=Mglob[[{3,4,5,6},{3,4,5,6}]]+M2;
Mglob[[{5,6,7,8},{5,6,7,8}]]=Mglob[[{5,6,7,8},{5,6,7,8}]]+M3;
Mglob[[7,7]]=Mglob[[7,7]]+m;
Mglob[[8,8]]=Mglob[[8,8]]+Θz;

Kglob//MatrixForm

Mglob//MatrixForm

Megoldás

sol=Eigensystem[Kglob.Inverse[Mglob]];

Eredmények kiértékelése

ord=Ordering[sol[[1]]];

α=(Sqrt[Permute[sol[[1]],ord]])

A=Permute[sol[[2]],ord];

shape[v_]:=Module[{},
N1234={0.25(((1-ξ))^2)(2+ξ),0.125L(((1-ξ))^2)(1+ξ),0.25(((1+ξ))^2)(2-ξ),-0.125L(((1+ξ))^2)(1-ξ)};
v1=N1234.v[[{1,2,3,4}]]/.{L->L1,ξ->(((2x)/L1)-1)};
v2=N1234.v[[{3,4,5,6}]]/.{L->L2,ξ->(((2(x-L1))/L2)-1)};
v3=N1234.v[[{5,6,7,8}]]/.{L->L3,ξ->(((2(x-L1-L2))/L3)-1)};
Piecewise[{{v1,0<x&&x<L1},{v2,L1<x&&x<L1+L2},{v3,L1+L2<x&&x<L1+L2+L3}}]
]

Manipulate[{"α=",α[[n]],Plot[shape[A[[n]].Inverse[Mglob]],{x,0,1100},AxesLabel->{"x [mm]",None},AxesOrigin->{0,0},Ticks->{Automatic,None},ImageSize->300]}//TableForm,{n,1,8,1}]