A simple method for the determination of the complex modulus of resilient materials using a longitudinally vibrating three-layer specimen

作者：Policarpo H; Neves M M^*; Maia N M M

来源：Journal of Sound and Vibration, 2013, 332(2): 246-263.

DOI：10.1016/j.jsv.2012.08.023

This paper proposes a new hybrid analytical-experimental methodology for the determination of the complex modulus of resilient materials as for e.g., composition cork-like materials. It is based on a three-layer specimen test and on a simple equation from the analytical model of the specimen. The analytical formulation solves the problem based on the elementary theory of longitudinal vibrations and without taking the transversal motions into account. This methodology is developed to avoid geometric constraints and boundary condition difficulties found on other tests as well as to minimize the computational time and complexity of the coding. The experimental setup and the deduction of the simple equation are described. Metallic layers are used at the extremities of the specimen, for which the Young modulus and mass density are known, while its loss factor may be neglected. For the intermediate resilient layer, which is assumed to present a linear viscoelastic behavior, the mass density is known. Thus, the only unknowns are the storage modulus and loss factor of that intermediate layer. The modal loss factor and the first resonant frequency of the specimen are identified from the experimental receptance frequency response FRF) curve using the rational fraction polynomial method (RFP). By using the first resonance frequency obtained experimentally, the analytical response becomes only a function of the storage modulus, resulting in a simple scalar nonlinear equation. Then, a numerical routine is used to determine, the storage modulus by calculating the first zero of the nonlinear equation. To validate the proposed methodology, the frequency response assurance criterion (FRAC) and the frequency amplitude assurance criterion (FAAC) are used. For the five composition cork materials tested, the complex modulus shown low frequency dependence in the 40 Hz to 1600 Hz range. Correlation values between the analytical and the experimental curves are greater than 95%, thus validating the obtained results and the proposed methodology.

• 出版日期2013-1-21