structuralDamping

(To be removed) Specify damping parameters for transient or frequency response structural model

structuralDamping will be removed. Use femodel to specify Rayleigh damping parameters and solve to specify modal damping instead. (since R2023a) For more information on updating your code, see Version History.

Syntax

structuralDamping(structuralmodel,"Alpha",a,"Beta",b)

structuralDamping(structuralmodel,"Zeta",z)

damping = structuralDamping(___)

Description

structuralDamping(structuralmodel,"Alpha",a,"Beta",b) specifies proportional (Rayleigh) damping parameters a and b for a structuralmodel object.

For a frequency response model with damping, the results are complex. Use the abs and angle functions to obtain real-valued magnitude and phase, respectively.

example

structuralDamping(structuralmodel,"Zeta",z) specifies the modal damping ratio. Use this parameter when you solve a transient or frequency response model using the results of modal analysis.

damping = structuralDamping(___) returns the damping parameters object, using any of the previous input syntaxes.

Examples

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Rayleigh Damping Parameters

Open Live Script

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)

Figure contains an axes object. The axes object contains 6 objects of type quiver, text, patch, line.

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 with properties:

      RegionType: 'Cell'
        RegionID: 1
    DampingModel: "proportional"
           Alpha: 10
            Beta: 2
            Zeta: []

Input Arguments

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`structuralmodel` — Transient or frequency response structural model
`StructuralModel` object

Transient or frequency response structural model, specified as a StructuralModel 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, see Modal Damping Depending on Frequency.

Data Types: double | function_handle

Output Arguments

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`damping` — Handle to damping parameters
`StructuralDampingAssignment` object

Handle to damping parameters, returned as a StructuralDampingAssignment object. See StructuralDampingAssignment Properties.

More About

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Modal Damping Depending on Frequency

To use the individual value of modal damping for each mode, specify z 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, and zeta is a vector of corresponding damping ratio values.

Version History

Introduced in R2018a

expand all

R2025a: To be removed

structuralDamping will be removed. Use femodel to specify Rayleigh damping parameters and solve to specify modal damping instead.

For example, you can specify the Rayleigh damping parameters for the beam as follows.

model = femodel(AnalysisType="structuralTransient", ...
                 Geometry="SquareBeam.stl");
model.DampingAlpha = 10;
model.DampingBeta = 2;

To specify modal damping, use the DampingZeta argument of the solve function.

RfrModalAll = solve(model,flist, ...
                    ModalResults=Rm, ...
                    DampingZeta=0.02);

The unified finite element model workflow defines the type of a problem and all of its parameters as the properties of an femodel object. This object enables you to specify physical parameters for structural, thermal, and electromagnetic types of analyses. The solver in the unified workflow uses only the parameters (properties) appropriate for the current analysis type while ignoring all other properties. If you switch the analysis type by setting the AnalysisType property of the model, the solver uses the appropriate set of properties corresponding to the new analysis type.

For more help migrating your existing code that uses StructuralModel to the unified finite element workflow, see Migration from Domain-Specific to Unified Workflow.

R2020a: Modal damping

For modal transient and modal frequency response models, specify damping as a percentage of critical damping for a selected vibration frequency.

structuralDamping

Syntax

Description

Examples

Rayleigh Damping Parameters

Input Arguments

`structuralmodel` — Transient or frequency response structural model
`StructuralModel` object

`a` — Mass proportional damping
nonnegative number

`b` — Stiffness proportional damping
nonnegative number

`z` — Modal damping ratio
nonnegative number | function handle

Output Arguments

`damping` — Handle to damping parameters
`StructuralDampingAssignment` object

More About

Modal Damping Depending on Frequency

Version History

R2025a: To be removed

R2020a: Modal damping

See Also

Topics

structuralDamping

Syntax

Description

Examples

Rayleigh Damping Parameters

Input Arguments

structuralmodel — Transient or frequency response structural model StructuralModel object

a — Mass proportional damping nonnegative number

b — Stiffness proportional damping nonnegative number

z — Modal damping ratio nonnegative number | function handle

Output Arguments

damping — Handle to damping parameters StructuralDampingAssignment object

More About

Modal Damping Depending on Frequency

Version History

R2025a: To be removed

R2020a: Modal damping

See Also

Topics

`structuralmodel` — Transient or frequency response structural model
`StructuralModel` object

`a` — Mass proportional damping
nonnegative number

`b` — Stiffness proportional damping
nonnegative number

`z` — Modal damping ratio
nonnegative number | function handle

`damping` — Handle to damping parameters
`StructuralDampingAssignment` object