The response of a structure to a virtual dynamometric hammer has been numerically simulated to represent an experimental test. The time histories of the impulsive force 𝐹 at location 𝑥1 and the displacements 𝑥𝑖 at 4 locations on the structure are collected in a matrix (“Data.mat”) organized as follows: [𝑡, 𝐹, 𝑥1,𝑥2, 𝑥3,𝑥4].
Starting from the evaluation of the FRFs between displacements and force, it is requested to:
1) Plot the “experimental” FRF diagrams
2) Estimate and comment the natural frequencies, damping ratios and mode shapes of the resonating modes in the range 0 − 5 𝐻𝑧 employing simplified methods (e.g. half power point method).
OPTIONAL
i. Set up a modal parameter identification program for estimating natural frequencies, damping ratios and modes in the range 0 − 5 𝐻𝑧. Compare the identified FRF with the “experimental” ones. Comment the results obtained.
ii. Compare and comment the modal parameters identified with the methods mentioned above. iii. Employing a modal approach, reconstruct the FRFs and compare with the original ones.
EXTRA
iv. Evaluate the co-located FRF at the location corresponding to displacement 𝑥2.
v. Evaluate the 𝑀, 𝐶, 𝐾 matrices of the numerical model of the 4 d.o.f. (𝑥1,𝑥2,𝑥3, 𝑥4) system.
