# 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.

- 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.

- 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.