# 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.

In dynamic analysis, two related topics need to be considered:
Resonance
Occurs when the input load excitation frequency matches one of the natural frequencies of the structure. In this case, the load amplifies the mode and large displacements can result.
Participation Factor
A measure of how strongly a given mode contributes to the response of the structure when subjected to force/displacement excitation in a specific direction.

So, it is possible that the excitation could match a natural frequency (i.e. a resonance condition), but if the participation factor of the mode is close to 0, then no energy will get into that mode and no dynamic response will occur.

SIMSOLID calculates modal participation, effective mass and cumulative mass factors for each mode in a specified global or local coordinate reference frame.
Modal participation factors
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.
Effective mass factors
The Effective mass factors associated with each mode represents 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. 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.