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COBEM 2019
25th International Congress of Mechanical Engineering
GENERALIZED PROPORTIONAL DAMPING APPLIED TO A GUITAR MODEL
Submission Author:
Alexandre Löw , RS
Co-Authors:
Alexandre Löw, Herbert Gomes, Gabriel Prado
Presenter: Alexandre Löw
doi://10.26678/ABCM.COBEM2019.COB2019-1809
Abstract
This work proposes an identification of damping considering the generalized-proportional (Rayleigh) damping approximation to a guitar finite element model. Estimates of the damping ratios (as well as natural frequencies) are experimentally obtained via random excitation in a free-free like condition and Subspace Stochastic Identification Covariance (SSI-Cov) analysis. First, the justification for the use of proportional damping approximation is verified by assuring that imaginary parts of selected modes are negligible when compared with their respective real parts. Then, a continuous function in the frequency domain is adjusted in such a way that it fits the identified damping ratios at their respective resonances. The curve fitting is obtained by non-linear least squares and particle swarm optimization. Due to the size of the model, it would be impractical to manipulate full system matrices. Then, System Equivalent Reduction Expansion Process (SEREP) will be applied to reduce the full model to the same number of measured degrees-of-freedom (DOF), still granting the same mode shapes as the full model. Thereafter, with the reduced system matrices, the same function fitted to the damping ratios is applied to the product of the inverse mass matrix by the stiffness matrix in order to achieve the final goal that is to calculate the damping matrix. The practical appeal of the procedure can be evaluated when it is important to run a time-domain simulation of the structure and its transient response is to be compared with measured acceleration or displacement time histories.
Keywords
generelized-proportional damping, experimental modal analysis, guitar vibroacoustics, SSI-Cov
