( ) ( ) 2 1 1 k j X T Y k j m η η ω + = = + − (7) which can be expressed in terms of modal quantities as 2 2 0 0 2 2 2 0 0 j T R jI j ω ωη ω ω ωη + = = + − + (8) On the other hand, the relative transmissibility is ( ) 2 2 1 1 r Z X Y m T T Y Y k j m ω η ω − = = = − = + − (9) or 2 2 2 2 0 0 rT j ω ω ω ηω = − + (10) The relative transmissibility is important because (i) it is related to the actual deformation of the mount and (ii) the direct numerical integration of the equation of motion using the RungeKutta 4th order expansion it is implemented to yield the relative displacement z from which the mass displacement x can be calculated and finally the absolute transmissibility computed. However, of greatest value is the absolute transmissibility because this is directly measurable (as the ratio between output and input). Also, the nonlinear identification algorithm needs to be applied to the (measured) absolute transmissibility. In Eqn.(8) or Eqn.(10) the two unknowns are the natural frequency, 0ω, and the loss factor, η, which can be both amplitudedependent, while the frequency of excitation, ω, the real (R) and the imaginary (I) parts of the response are all measurable quantities. It is noticeable that the expressions of the FRF and of the absolute transmissibility, Eqns. (2) and (8) are very similar as their denominator is equal and their numerator is independent of the excitation frequency. This is not the case for the relative transmissibility, Eqn.(10), whose numerator contains the excitation frequency ω. It is possible to use Eqn.(8) in the same way as the FRF has been used to extract the modal parameters as function of the amplitude of the displacement response and computing the modal quantities Eqns.(3,4). Repeating the calculations for different response levels enable one to obtain the required natural frequency and damping as functions of the displacement amplitude of the mass (or absolute response). It is crucial that the CONCERTO identification method is applied to the absolute transmissibility data, and attention is paid in relating the amplitude dependency to the actual deformation of the mount which is the relative displacement. NUMERICAL SIMULATIONS OF FRF AND TRANSMISSIBITLIY DATA FOR NL SYSTEMS A comprehensive analysis of the method implemented in CONCERTO based on Frequency Response Functions data is given in reference [7]. In the present paper, in order to verify the extension of the method to transmissibility data, a comparison is performed between the 482
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