Abstract
A simple method for determining viscoelasticity over a wide frequency range using the frequency response function (FRF) mobility obtained by the center impedance method is presented. As user data comprise the FRF between the velocity of the excitation rod and excitation force, it is challenging to separate the signal and noise. Our proposed method is based on the FRF obtained from the analytical solution of the equation of motion of the viscoelastic beam and relationship between the complex wavenumber (real wavenumber and attenuation constant) of flexural wave and viscoelasticity. Furthermore, a large loss factor can be handled over a wide frequency range without using the half-power bandwidth. In this study, actual FRF mobility data containing noise were processed using preprocessing, inverse calculation, and postprocessing. Preprocessing removed low-coherence data, compensates for the effects of instrument gain, and transformed the FRF into its dimensionless equivalent. Then, inverse calculations were used to solve the mobility equation and determine the complex wavenumber. In postprocessing, the complex wavenumber obtained by the inverse calculation was curve fitted using functions with mechanical significance. Consequently, the storage modulus based on the curve-fitted complex wavenumber was a monotonically increasing frequency function. The loss factor had a smooth frequency dependence such that it has the maximum value at a single frequency. The proposed method can be applied to composite materials, where the application of time-temperature superposition is challenging. We utilized the measured FRF mobility data obtained over a duration of several seconds, and this method can also be applied to materials with large loss factors of 1 or more.
Highlights
Acoustic radiations from the surface of plates at the floor of a car decrease with its bending vibrations, which is effective for reducing noise from interiors of automobiles, railway trains, and aircrafts
To develop a denoising method as discussed, inverse calculation was applied to these data, which resulted in unrealistic viscoelasticities with large fluctuations of frequency
We presented a method for estimating the frequency dispersion of viscoelasticity from the measured frequency response function (FRF) mobility data using the center impedance method for a beam specimen
Summary
Acoustic radiations from the surface of plates at the floor of a car decrease with its bending vibrations, which is effective for reducing noise from interiors of automobiles, railway trains, and aircrafts. Polymeric composites have been widely used for this purpose, and vibration damping properties of various plate materials must be evaluated To this end, tests are performed at the point of beam vibrations, and the storage modulus and loss factor of the specimen are estimated from the responses. For thin viscoelastic rods and beams (plates), a simple relationship between the viscoelasticity and complex wavenumber exists [8, 9] Upon combining these with an analytical solution for the FRF (mobility (V/F)) between the velocity and excitation force, the viscoelasticity of the material can be determined over a wide frequency range from FRF data using complex wavenumbers [9]. E complex wavenumber and viscoelasticity (storage modulus and loss factor) were determined for arbitrary frequencies by inverse calculations using dimensionless mobility data obtained from preprocessing. The FRF mobility was calculated using the curve-fitted complex wavenumber as compared with the measured results. e application of the inverse complex wavenumber formula on the curvefitted complex wavenumber transformed the viscoelasticity (storage modulus and loss factor) to a smooth frequency function
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