A Robust Technique for Polymer Damping Identification Using Experimental Transmissibility Data

Abstract

This paper presents a robust method to estimate polymers’ damping, based on modal identification methods on frequency functions. The proposed method presents great advantages compared to other traditional methods such as the HPB method for polymeric materials where high damping or noise levels can limit their use. Specifically, this new method is applied on an experimental transmissibility function measured in a composite cantilever beam and the complex modulus is determined as a function of frequency. From this, a regenerated function is obtained based on the Euler–Bernoulli beam theory, and it is compared with experimental data. It can be concluded that the best way to apply the curve-fitting method for further testing of polymeric materials is when it is used with the whole frequency range by means of the MDOF method considering the residuals. In addition, this has the added advantage that the number of experimental tests to be carried out is much lower compared to using the SDOF method.

Soft polymers dynamic characterisation using sandwich theory

“…A laser vibrometer Polytec PDV 100 was used to measure the velocity u˙(t). The data were acquired in real time with the Polytec VIB-E-220 data acquisition system, and they were processed in frequency domain with VibSoft software to obtain the transmissibility function T*(f) which relates the displacements of the measuring point and of the base asin which U*(f) is the Fourier transform of the displacement at the measuring point of the sandwich specimen u(t) and S*(f) is the Fourier transform of the displacement at the base s(t) (for further details see 38 ). As result, the experimental transmissibility curve for the sandwich beam with soft polymer core shown in Figure 4.

Figure 4.Experimental transmissibility curve of the viscoelastic sandwich beam: (a) modulus, (b) phase.

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“…Nevertheless, Brun et al . 38 have recently proposed an alternative robust method to obtain fs and ηs from transmissibility functions instead of frequency response functions 39 by means of the identification of modal properties by curve fitting, as explained in more detail in the Experimental procedure section.…”

“…Nevertheless, Brun et al . 38 have recently proposed an alternative robust method to obtain fs and ηs by means of the identification of modal properties by curve fitting. The analytical equation to fit is based on the modal superposition of transmissibility functions, and is given bywhere As* is a parameter of the s th resonance, mi is the first identified resonance, mj is the j th identified resonance, K* is the complex normalised stiffness residue and M* is the complex normalised mass residue.…”

“…The modal parameters are obtained from the minimisation of the objective function g(boldx) defined aswhere x is the unknowns vector, Texp,k* is the experimental data at each excitation frequency and T*(fk) is the analytic transmissibility function given by equation (15) at each excitation frequency fk. The minimisation of equation (16) is performed with the Nelder-Mead algorithm 42 implemented in the fminsearch function of MATLAB from where the resonance frequencies fs and modal loss factors ηs are obtained (for further details see 38 ). The results given by this method applied on the transmissibility data of Figure 4 are shown in Table 2, in which the resonance frequency fs and loss factor ηs are shown for the first six modes, the ones under 2.5 kHz.…”

“…The standard proposes that the resonance frequency f s corresponds to the frequency of the maximum of the resonance peak, and the modal loss factor η s can be calculated by the well-known half power bandwidth (HPB) method. Nevertheless, Brun et al 38 have recently proposed an alternative robust method to obtain f s and η s from transmissibility functions instead of frequency response functions 39 by means of the identification of modal properties by curve fitting, as explained in more detail in the Experimental procedure section.…”