ModalStructuralResults

Structural modal analysis solution

Description

A ModalStructuralResults object contains the natural frequencies and modal displacement in a form convenient for plotting and postprocessing.

Modal displacement is reported for the nodes of the triangular or tetrahedral mesh generated by generateMesh. The modal displacement values at the nodes appear as an FEStruct object in the ModeShapes property. The properties of this object contain the components of the displacement at the nodal locations.

You can use a ModalStructuralResults object to approximate solutions for transient dynamics problems. For details, see solve.

Creation

Solve a modal analysis problem by using the solve function. This function returns a modal structural solution as a ModalStructuralResults object.

Properties

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Properties of an FEStruct object are read-only.

Natural frequencies of the structure, returned as a column vector.

Data Types: double

Modal displacement values at the nodes, returned as an FEStruct object. The properties of this object contain components of modal displacement at nodal locations.

Finite element mesh, returned as a FEMesh object. For details, see FEMesh Properties.

Examples

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Find the fundamental (lowest) mode of a 2-D cantilevered beam, assuming prevalence of the plane-stress condition.

Specify the following geometric and structural properties of the beam, along with a unit plane-stress thickness.

length = 5;
height = 0.1;
E = 3E7;
nu = 0.3;
rho = 0.3/386;

Create a model plane-stress model, assign a geometry, and generate a mesh.

structuralmodel = createpde('structural','modal-planestress');
gdm = [3;4;0;length;length;0;0;0;height;height];
g = decsg(gdm,'S1',('S1')');
geometryFromEdges(structuralmodel,g);

Define a maximum element size (five elements through the beam thickness).

hmax = height/5;
msh=generateMesh(structuralmodel,'Hmax',hmax);

Specify the structural properties and boundary constraints.

structuralProperties(structuralmodel,'YoungsModulus',E, ...
'MassDensity',rho, ...
'PoissonsRatio',nu);
structuralBC(structuralmodel,'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*(rho*height)))/(2*pi)
analyticalOmega1 = 126.9498

Specify a frequency range that includes an analytically computed frequency and solve the model.

modalresults = solve(structuralmodel,'FrequencyRange',[0,1e6])
modalresults =
ModalStructuralResults with properties:

NaturalFrequencies: [32x1 double]
ModeShapes: [1x1 FEStruct]
Mesh: [1x1 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/(2*pi)
ans = 32×1
105 ×

0.0013
0.0079
0.0222
0.0433
0.0711
0.0983
0.1055
0.1462
0.1930
0.2455
⋮

modalresults.ModeShapes
ans =
FEStruct with properties:

ux: [6511x32 double]
uy: [6511x32 double]
Magnitude: [6511x32 double]

Plot the y-component of the solution for the fundamental frequency.

pdeplot(structuralmodel,'XYData',modalresults.ModeShapes.uy(:,1))
title(['First Mode with Frequency ', ...
num2str(modalresults.NaturalFrequencies(1)/(2*pi)),' Hz'])
axis equal  