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Modal Participation Factors

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  - Modal Participation Factors
    - View Modal Participation Factors
      View modal participation, effective mass, and cumulative mass.
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Frequently Asked Questions
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Modal Participation Factors

Mode Shapes

Every structure has the tendency to vibrate at a given set of natural frequencies. Each natural frequency is associated with a shape, called mode shape, that the model tends to assume when vibrating at that frequency.

Modal participation factors

SimSolid calculates modal participation, effective mass, and cumulative mass factors for each mode in a specified global or local coordinate reference frame for only flexible modes. Rigid body modes will be ignored.

Modal participation factors are scalars that measure the interaction between the modes and the directional excitation in a given reference frame. Larger values indicate a stronger contribution to the dynamic response.

Modal participation factor, γ_{i} = \{ϕ_{i}^{T}\} [M] \{V\}

Where,

$\{V\}$: Unit translational direction vector
$\{ϕ\}$: Normalized mode shape
$[M]$: Mass matrix

Modal participation factor ratio

The modal participation factor ratio is the modal participation factor for each translational direction divided by the maximum modal participation factor of all the modes for that direction. So, each of the three directions will have a value of 1.0 for the mode that has the maximum modal participation factor, and the other modes will have a value less than 1.0.

Effective mass factors

The Effective mass factors associated with each mode represent the amount of system mass participating in that mode in a given excitation direction. This value is given as a percentage of the total system mass.

Effective mass = γ_{i}^{2}

Effective mass along direction is the square of modal participation factor of that direction. Therefore, a mode with a large effective mass will be a significant contributor to the system’s response in the given excitation direction.

A common rule of thumb for linear dynamic analysis is that a mode should be included if it contributes more than 1-2% of the total effective mass.

Cumulative mass

The cumulative mass for mode n is the sum of the effective mass factors for modes 1 through n. A common rule of thumb for linear dynamic analysis is to include sufficient modes such that the cumulative mass is at least 80% in the predominant direction of excitation vibration.