Lee D., Kim S.

Viscoelastic damping materials are widely used in structures to reduce noises and/or vibrations. To design quiet structures using damping materials, the material properties of viscoelastic materials such as elastic modulus and loss factor are essential information. The properties of the materials are highly nonlinear with respect to both frequency and temperature. In recent years, it is recognized that the nonlinear dynamic characteristics of viscoelastic damping materials can be well described by the fractional derivative model with far fewer parameters than conventional spring-dashpot models. However, to acquire the fractional-derivative-model parameters of a real material, many tests and following tedious curve fitting process are necessary. In this paper, an efficient identification method of material parameters is proposed using an optimization technique. In the proposed method, Oberst-type beam test is assumed. In addition, frequency response functions at the points on the beam are measured from the cantilever Oberst beam. To identify the fractional-derivative-model parameters, the Oberst test beam coated on one side by a viscoelastic material is modeled by finite beam elements. The elastic modulus and loss factors of the equivalent beam elements can be obtained from Ross, Ungar and Kerwin¡¯s equation and the complex modulus expression of the fractional derivative model of the viscoelastic material. Then the frequency response functions on the same points with the measured one can be calculated by modal superposition method with assumed fractional-derivative-model parameters. The differences between the measured and the calculated FRFs are minimized by using a gradient-based optimization algorithm to identify the real values of the parameters. For efficient search iteration, the gradient information is derived analytically. Numerical tests show that the proposed method accurately identifies the fractional-derivative-model parameters of viscoelastic materials. Finally, the identification process is employed to real materials to prove the applicability of the proposed method.