PSI - Issue 24

Filippo Cianetti et al. / Procedia Structural Integrity 24 (2019) 526–540 Author name / Structural Integrity Procedia 00 (2019) 000–000

532

7

From the FRF obtained between the 8 nodes, by means of the Quadrature Picking technique Døssing (1988b) the experimental modal shape of displacement have been reconstructed, in fact:

ϕ i , m · ϕ o , m 2 σ

¨ z ( ω m ) ≈ i

(13)

ω m

where ¨ z ( ω m ) is the acceleration in the acquisition direction, and the subscript m , i , and o stand for the conditions evaluated at the m − th mode, the input nodes and the output nodes respectively. The numerical experimental com parison was based on the dynamic amplification operated by the real or virtual component at each frequency in terms of the amplitude of the FRF Morettini et al. (2019) and evaluating the correspondence of the modal forms of dis placement between the prototype component and its numerical representation Allemang (2003); Døssing (1988b). In Fig. 6 the experimental data (blue) is paired with the model (red); the trends of the FRF, albeit in a non-quantitave way, indicate a good consistency especially in the first modes. In general, the more rigid and less damped numerical models tend to shift resonances towards higher frequencies and to overestimate the response of the system. As regards modal identification, the experimental modal shapes starting from the imaginary part of the FRF has been reconstructed, these are showed and compared graphically (Fig. 7) in a stylized form of the frame consisting of lines that connect only the nodes (red line in Fig. 5).

undeformed experimental numerical

undeformed experimental numerical

undeformed experimental numerical

(a) mode 1

(b) mode 2

(c) mode 3

undeformed experimental numerical

undeformed experimental numerical

undeformed experimental numerical

(d) mode 4

(e) mode 5

(f) mode 6

Fig. 7: Numerical vs Experimental Mode Shapes.