where R1 and R2 (I1 and I2) are the real (imaginary) part of the receptance at the amplitude X which have been measured at the frequencies 1ω and 2ω (before and after the resonance peak). The theory presented above is implemented in the COde for Nonlinear identifiCation from mEasured Response To vibratiOn (CONCERTO) which is used for the analysis of both numerical and experimental data [7]. NONLINEAR IDENTIFICATION METHOD USING TRANSMISSIBILITY DATA Consider the Single-Degree-Of-Freedom (SDOF) system depicted in Fig.1. A mass m, suspended on a spring with amplitude dependent complex stiffness ( ) ( ) 1 ( ) k Z j Zη + , where η is the system’s loss factor. It is important to notice that in case of base excitation the characteristics of the support, or mount, are dependent on its effective displacement (or deformation) which is the relative displacement between the mass the base, z = x- y. (a) (b) Fig.1: Schematic representations of a SDOF system of a mass suspended on a nonlinear mount with complex stiffness: (a) force excitation, (b) base excitation The steady-state response under harmonic excitation of the system depicted in Fig.1(b) is ( ) ( ) 2 1 1 m k j X k j Y ω η η − + + = + (5) or ( ) 2 2 1 m k j Z m Y ω η ω − + + = (6) where z = x-y is the relative displacement (and Z its amplitude) between the mass and the base, that is the deformation of the mount and ωthe excitation frequency. Note that the dependency of the stiffness and damping from the amplitude Z has been omitted for clarity. The transmissibility is defined as the nondimensional quantity that at each frequency quantify how much disturbance has passed from the source to the receiver through the transmission path. Two types of transmissibility can be defined. The absolute transmissibility is ( ) ( ) 1 ( ) k X j X η + sin( ) x X tω ϕ = − sin( ) y Y tω = sin( ) f F tω = sin( ) x X tω ϕ = − ( ) ( ) 1 ( ) k Z j Z η + 481
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