Obtain natural frequencies of a structural model.

I have created a mechanical model:

modelTwoDomain = createpde("structural", "transient-planestress");
structuralProperties(modelTwoDomain, 'YoungsModulus', E, 'PoissonsRatio', nu, 'MassDensity', mass);
structuralIC(modelTwoDomain, "Displacement", [0; 0], "Velocity", [0; 0]);

and someboundary conditions.

My question is if I use the command res = solve(modelTwoDomain, ti), where ti is a time vector, the resultant object res, does not contain natural frequencies. How can I obtain or check the natural frequencies of the system?

Thanks very much.

Answer 1

[Sam Chak]

Hi @Jorge Garcia Garcia

Since the natural frequencies are related to the eigenvalues of the structural system, I believe you can use the solvepdeeig() command to solve the PDE for eigenvalues. I followed the example in the link and successfully found the eigenvalue of the system.

model = createpde(3);
importGeometry(model,"BracketTwoHoles.stl");
pdegplot(model,"FaceLabels","on","FaceAlpha",0.4)

applyBoundaryCondition(model,"dirichlet","Face",1,"u",[0;0;0]);

E = 200e9;  % elastic modulus of steel in Pascals
nu = 0.3;   % Poisson's ratio
specifyCoefficients(model,"m",0,...
                          "d",1,...
                          "c",elasticityC3D(E,nu),...
                          "a",0,...
                          "f",[0;0;0]);

evr = [-Inf,1e7];
generateMesh(model);
results = solvepdeeig(model,evr);

% Checking the Eigenvalues
lambda = results.Eigenvalues

lambda = 3×1

1.0e+06 * 1.2460 2.2761 6.2349

V = results.Eigenvectors;

subplot(3,2,1)
pdeplot3D(model,"ColorMapData",V(:,1,1))
title("x Deflection, Mode 1")
subplot(3,2,3)
pdeplot3D(model,"ColorMapData",V(:,2,1))
title("y Deflection, Mode 1")
subplot(3,2,5)
pdeplot3D(model,"ColorMapData",V(:,3,1))
title("z Deflection, Mode 1")

subplot(3,2,2)
pdeplot3D(model,"ColorMapData",V(:,1,3))
title("x Deflection, Mode 3")
subplot(3,2,4)
pdeplot3D(model,"ColorMapData",V(:,2,3))
title("y Deflection, Mode 3")
subplot(3,2,6)
pdeplot3D(model,"ColorMapData",V(:,3,3))
title("z Deflection, Mode 3")

[Jorge Garcia Garcia]

Thanks! will give it a go! thanks very much