natural frequencies of the system

sorry.. this is a very silly question. I saw somewhere how to look at the natural frequencies of a system defined as

modelpde = createpde("structural","static-planestress");

where I pass

structuralProperties(modelpde, ...

'YoungsModulus',E, ...

'PoissonsRatio',nu, ...

'MassDensity',mass);

edge=[1 2 3 4];

structuralBC(modelpde, ...

'Edge',edge, ...

'Displacement',[0 0]); as I want the perimeter to be fixed.

I need to see the natural frequencies of this system, and I thought they were extracted directly by

results=solve(modelpde);

I think I read it had to be done differently but cannot seem to find the documentation about it.

Could please send me the link?

Thanks

Answer 1

[Garmit Pant]

Hello Jorge Garcia Garcia

It is my understanding that you are trying to solve a PDE and further extract the natural frequencies of the system from the solution.

Given that you are defining your model as follows:

modelpde = createpde("structural","static-planestress");

This will create an object of the ‘StructuralModel’ class with the ‘AnalysisType’ property set as “static-planestress”.

On passing this object to the “solve” function, the output returned is a ‘StaticStructuralResults’ object. Static structural analysis does not compute natural frequencies and only computes the following properties:

modalresults =

StaticStructuralResults with properties:

Displacement: [1×1 FEStruct]

Strain: [1×1 FEStruct]

Stress: [1×1 FEStruct]

VonMisesStress: [6511×1 double]

Mesh: [1×1 FEMesh]

Natural frequencies of the system can be computed and accessed by passing an object of the ‘StructuralModel’ class with the ‘AnalysisType’ property set as “modal-<insert required type>” to the function ‘solve’ that will then return a ‘ModalStructuralResults’ object and accessing its ‘NaturalFrequencies’ property.

You can refer to the following code snippet to extract the natural frequencies of a system:

length = 5; 
height = 0.1; 
E = 3e7; 
nu = 0.3; 
massDensity = 0.3/386; 
%Create a modal static-stress model, assign a geometry, and generate a mesh. 
modelpde = createpde("structural","modal-planestress") 

modelpde = 
  StructuralModel with properties:

              AnalysisType: "modal-planestress"
                  Geometry: []
        MaterialProperties: []
        BoundaryConditions: []
    SuperelementInterfaces: []
                      Mesh: []
             SolverOptions: [1×1 pde.PDESolverOptions]

gdm = [3;4;0;length;length;0;0;0;height;height]; 
g = decsg(gdm,'S1',('S1')'); 
geometryFromEdges(modelpde,g);% 
% Define a maximum element size (five elements through the beam thickness). 
hmax = height/5; 
msh=generateMesh(modelpde,Hmax=hmax); 
%Specify the structural properties and boundary constraints. 
structuralProperties(modelpde,'YoungsModulus',E, ... 
    'MassDensity',massDensity, ...  
    'PoissonsRatio',nu); 
structuralBC(modelpde,Edge=4,Constraint="fixed"); 
%Compute the analytical fundamental frequency (Hz) using the beam theory. 
I = height^3/12; 
analyticalOmega1 = 3.516*sqrt(E*I/(length^4*(massDensity*height)))/(2*pi) 

analyticalOmega1 = 126.9498

%Specify a frequency range that includes an analytically computed frequency and solve the model. 
modalresults = solve(modelpde,FrequencyRange=[0,1e6]) 

modalresults = 
  ModalStructuralResults with properties:

    NaturalFrequencies: [32×1 double]
            ModeShapes: [1×1 FEStruct]
                  Mesh: [1×1 FEMesh]

%The solver finds natural frequencies and modal displacement values at nodal locations. To access these values, use modalresults.NaturalFrequencies and modalresults.ModeShapes. 
modalresults.NaturalFrequencies 

ans = 32×1

1.0e+05 * 0.0080 0.0499 0.1393 0.2718 0.4468 0.6174 0.6630 0.9188 1.2125 1.5423

For more information on this, you can refer the following MathWorks Documentation:

1. Refer to the “Input Arguments” section. https://in.mathworks.com/help/pde/ug/createpde.html
2. Refer to the “Output Arguments” section. https://in.mathworks.com/help/pde/ug/pde.femodel.solve.html#bvizufn-3
3. Refer to the “Properties” section. https://in.mathworks.com/help/pde/ug/pde.modalstructuralresults.html

I hope this helps!