Mode set theory and damping

A mode set:

• Is a reduced form of the structural dynamic characteristics of a structure.

• Contains modal stiffness (K), modal mass (M), and modal damping (B) data.

• Has fewer degrees of freedom than the original model, because the mode set uses modal coordinates.

• Solves more quickly and efficiently than the original model.

Mode set theory

Modal stiffness (also known as generalized stiffness) =

Modal mass (also known as generalized mass) =

where:

• eigenvectors

• transpose of the eigenvectors

• Stiffness = .

• Mass = .

Because ,

where

• is the displacement

• is the unitless modal participation factor

• has units of length.

The units of modal stiffness are:.

The units of modal mass are: .

The mode set contains both the stiffness and mass information, but has no damping data.

You must compute the equivalent modal damping so that you can specify this information in the mode set.

Modal, viscous, and structural damping

For Simcenter Nastran SOL 103 Eigenvalue solutions that you solve in release 2020.2 and later, the software computes values for modal damping, equivalent viscous damping, and structural damping and writes them to the OP2 file.

• Modal viscous damping =

• Structural damping =

• Viscous damping matrix =

• Structural damping matrix = .

Mode shapes are not orthogonal with respect to the damping matrices, and therefore modally projected damping matrices result in non-diagonal matrices. By retaining only the diagonal values, the software converts the damping values to an equivalent modal and equivalent structural damping and writes those values to the damping matrices.

• Viscous damping:

• Structural damping:

The equation of motion of a single degree of freedom (DOF) damped linear oscillator using Newton's 2nd law of motion is written as:

where:

• = mass

• = damping

• = stiffness

• = mass displacement

• = exciting displacement

		m = mass
	k = stiffness
	b = damping
	u = displacement or excitation

Damping is expressed as the percentage of critical damping:

where:

= the critical viscous damping ratio which is

Mass =

Natural frequency =

The equivalent modal structural damping is expressed as a percentage, and is the modal structural damping ratio which is a unitless quantity. It is equal to the ratio of modal damping over modal stiffness.

Note:

If you use a mode set in a transient response solution, you must convert into the equivalent viscous damping ratio. This conversion is valid only at modal frequencies and not at all excitation frequencies.

Equivalent critical viscous damping ratio =

Using parameters to control damping

For Simcenter Nastran, you can use parameters to control the damping that the software computes during a SOL 103 Eigenvalue solution.

• To have the software output modal viscous and structural damping diagonal matrices, set PARAM, MDLDAMP=YES in the input file. In the Simcenter Nastran environment, in Pre/Post, on the Bulk Data page in the Solution dialog box, select the Output Diagonalized Modal Damping Matrices (MDLDAMP) check box.

• To have the software combine modal structural damping and viscous damping and write out the critical viscous damping ratio only, set PARAM, KDAMP=1 in the input file. In the Simcenter Nastran environment, in Pre/Post, use the Solution Parameters modeling object dialog box to set PARAM, KDAMP=1 for a solution.To have the software compute modal structural damping only, set PARAM, KDAMP=-1 in the input file. In the Simcenter Nastran, in Pre/Post, use the Solution Parameters modeling object dialog box to set PARAM, KDAMP=-1 for a solution.

How do I

Displaying alternate FEM representations

Replace a FEM file with a mode set or FRF set

Editing modes or functions in mode sets and FRF sets

Edit a mode set or FRF set

Learn more

Mode sets

Controlling mesh creation for mode sets

Generating modal model results for a mode set

Replace a component FEM file in an assembly FEM with a mode set

Plot mode, ATV, or VATV set contours

Viscous and structural damping values in mode sets (Simcenter Nastran)

Using Modal Expansion to expand measurements to a FEM

Mapping measured or computed modes to a mesh

Expanding mode shapes to a mesh workflow

Quick links

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Related Topics

Assembly FEM

Mode set theory and damping, Simcenter 3D 2021.1 Series

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