structuralDamping
Specify damping parameters for transient or frequency response structural model
Syntax
Description
structuralDamping(
specifies proportional (Rayleigh) damping parametersstructuralmodel
,'Alpha',a
,'Beta',b
)a
andb
for astructuralmodel
object.
For a frequency response model with damping, the results are complex. Use theabs
andangle
functions to obtain real-valued magnitude and phase, respectively.
structuralDamping(
specifies the modal damping ratio. Use this parameter when you solve a transient or frequency response model using the results of modal analysis.structuralmodel
,'Zeta',z
)
returns the damping parameters object, using any of the previous input syntaxes.damping
= structuralDamping(___)
Examples
Rayleigh Damping Parameters
Specify proportional (Rayleigh) damping parameters for a beam.
Create a transient structural model.
structuralModel = createpde('structural','transient-solid');
Import and plot the geometry.
gm = importGeometry(structuralModel,'SquareBeam.stl'); pdegplot(structuralModel,'FaceAlpha',0.5)
Specify Young's modulus, Poisson's ratio, and the mass density.
structuralProperties(structuralModel,'YoungsModulus',210E9,...'PoissonsRatio',0.3,...'MassDensity',7800);
Specify the Rayleigh damping parameters.
structuralDamping(structuralModel,'Alpha',10,'Beta',2)
ans = StructuralDampingAssignment属性:RegionType: 'Cell' RegionID: 1 DampingModel: "proportional" Alpha: 10 Beta: 2 Zeta: []
Solution to Frequency Response Structural Model with Damping
Solve a frequency response problem with damping. The resulting displacement values are complex. To obtain the magnitude and phase of displacement, use theabs
andangle
functions, respectively. To speed up computations, solve the model using the results of modal analysis.
Modal Analysis
Create a modal analysis model for a 3-D problem.
modelM = createpde('structural','modal-solid');
Create the geometry and include it in the model.
gm = multicuboid(10,10,0.025); modelM.Geometry = gm;
Generate a mesh.
msh = generateMesh(modelM);
Specify Young's modulus, Poisson's ratio, and the mass density of the material.
structuralProperties(modelM,'YoungsModulus',2E11,...'PoissonsRatio',0.3,...'MassDensity',8000);
Identify faces for applying boundary constraints and loads by plotting the geometry with the face and edge labels.
pdegplot(gm,'FaceLabels','on','FaceAlpha',0.5)
figure pdegplot(gm,'EdgeLabels','on','FaceAlpha',0.5)
Specify constraints on the sides of the plate (faces 3, 4, 5, and 6) to prevent rigid body motions.
structuralBC(modelM,'Face',[3,4,5,6],'Constraint','fixed');
Solve the problem for the frequency range from-Inf
to12*pi
.
Rm = solve(modelM,'FrequencyRange',[-Inf,12*pi]);
频率响应分析
Create a frequency response analysis model for a 3-D problem.
modelFR = createpde('structural','frequency-solid');
Use the same geometry and mesh as you used for the modal analysis.
modelFR.Geometry = gm; modelFR.Mesh = msh;
Specify the same values for Young's modulus, Poisson's ratio, and the mass density of the material.
structuralProperties(modelFR,'YoungsModulus',2E11,...'PoissonsRatio',0.3,...'MassDensity',8000);
Specify the same constraints on the sides of the plate to prevent rigid body modes.
structuralBC(modelFR,'Face',[3,4,5,6],'Constraint','fixed');
Specify the pressure loading on top of the plate (face 2) to model an ideal impulse excitation. In the frequency domain, this pressure pulse is uniformly distributed across all frequencies.
structuralBoundaryLoad(modelFR,'Face',2,'Pressure',1E2);
First, solve the model without damping.
flist = [0,1,1.5,linspace(2,3,100),3.5,4,5,6]*2*pi; RfrModalU = solve(modelFR,flist,'ModalResults',Rm);
Now, solve the model with damping equal to 2% of critical damping for all modes.
structuralDamping(modelFR,'Zeta',0.02); RfrModalAll = solve(modelFR,flist,'ModalResults',Rm);
Solve the same model with frequency-dependent damping. In this example, use the solution frequencies fromflist
and damping values between 1% and 10% of critical damping.
omega = flist; zeta = linspace(0.01,0.1,length(omega)); zetaW = @(omegaMode) interp1(omega,zeta,omegaMode); structuralDamping(modelFR,'Zeta',zetaW); RfrModalFD = solve(modelFR,flist,'ModalResults',Rm);
Interpolate the displacement at the center of the top surface of the plate for all three cases.
iDispU = interpolateDisplacement(RfrModalU,[0;0;0.025]); iDispAll = interpolateDisplacement(RfrModalAll,[0;0;0.025]); iDispFD = interpolateDisplacement(RfrModalFD,[0;0;0.025]);
Plot the magnitude of the displacement. Zoom in on the frequencies around the first mode.
figure holdonplot(RfrModalU.SolutionFrequencies,abs(iDispU.Magnitude)); plot(RfrModalAll.SolutionFrequencies,abs(iDispAll.Magnitude)); plot(RfrModalFD.SolutionFrequencies,abs(iDispFD.Magnitude)); title('Magnitude') xlim([10 25]) ylim([0 0.5])
Plot the phase of the displacement.
figure holdonplot(RfrModalU.SolutionFrequencies,angle(iDispU.Magnitude)); plot(RfrModalAll.SolutionFrequencies,angle(iDispAll.Magnitude)); plot(RfrModalFD.SolutionFrequencies,angle(iDispFD.Magnitude)); title('Phase')
Input Arguments
structuralmodel
—Transient or frequency response structural model
StructuralModel
object
Transient or frequency response structural model, specified as aStructuralModel
object. The model contains the geometry, mesh, structural properties of the material, body loads, boundary loads, boundary conditions, and initial conditions.
Example:structuralmodel = createpde('structural','transient-solid')
a
—Mass proportional damping
nonnegative number
Mass proportional damping, specified as a nonnegative number.
Data Types:double
b
—Stiffness proportional damping
nonnegative number
Stiffness proportional damping, specified as a nonnegative number.
Data Types:double
z
—Modal damping ratio
nonnegative number|function handle
Modal damping ratio, specified as a nonnegative number or a function handle. Use a function handle when each mode has its own damping ratio. The function must accept a vector of natural frequencies as an input argument and return a vector of corresponding damping ratios. It must cover the full frequency range for all modes used for modal solution. For details, seeModal Damping Depending on Frequency.
Data Types:double
|function_handle
Output Arguments
damping
— Handle to damping parameters
StructuralDampingAssignment
object
Handle to damping parameters, returned as aStructuralDampingAssignment
object. SeeStructuralDampingAssignment Properties.
More About
Modal Damping Depending on Frequency
To use the individual value of modal damping for each mode, specifyz
as a function of frequency.
function z = dampingFcn(omega)
Typically, the damping ratio function is a linear interpolation of frequency versus the modal damping parameter:
structuralDamping(modelD,'Zeta',@(omegaMode) ... interp1(omega,zeta,omegaMode))
Here,omega
is a vector of frequencies, andzeta
is a vector of corresponding damping ratio values.
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