YES the vibro-acoustic response remains totally LINEAR when converting the time-domain signals into FRF
Linear means the perfect proportionality between the excitation and the response: that remains the only way to assess it in practice
Linearity implies that the excitation frequency content is not altered in the response: auto spectra must remain the same in any point
Friction and viscosity induce non-linearities, visco-elasticity and acoustic radiation are the only damping laws that do not alter linearity
Linearity relate to low amplitude oscillations, where elasticity modulus of all implied materials is constant: if stress level are exceeding the elasticity limit and induce plastic deformations somewhere in the system then it cannot be linear anymore
The concept of Transfer Function is only defined for linear time invariant systems. Nonlinear system models rather stick to time domain descriptions as nonlinear differential equations rather than frequency domain descriptions
Jeongwon Kim, The FRF of a linear system is always linear. This is because the FRF is a measure of the system's response to a harmonic input, and the output of a linear system to a harmonic input is always harmonic. If the FRF of a system is not linear, then the system is not linear. This could be due to a number of factors, such as non-linearities in the system's equations of motion, saturation in the system's components, or friction.
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