A Linearity Check in Modal Testing involves measuring the FRF function with a different force level input to the structure. If the force level doubles, and the FRF still looks the same (FRF from both tests overlay well), then the structure is said to be linear in this force range.
Siemens PLM Software Inc.
Here is a plot of what a linearity check might look like.
Frequency Response Functions (FRFs) are measured at three different force levels (double, then double again is typical). The FRF, which is the ratio of the force input to the acceleration response, should stay the same if the structure is behaving in a linear manner.
If the FRF changes drastically, for example, if the frequencies shift, then the structure is not behaving in a linear manner in the range of forces being applied.
The autopowers of the force inputs (left) should be quite different, while the FRFs should be the same (right).