Optimization Based Identification of the Dynamic Properties of Linearly Viscoelastic Materials Using Vibrating Beam Technique

Sandwich structures with viscoelastic core and metal face sheets are increasingly used in automotive industry to significantly reduce the amplitude of vibration and noise radiation. Several experimental methods such as dynamic mechanical analysis (DMA) and vibrating beam technique (VBT) are used to characterize the dynamic properties of viscoelastic materials as a function of frequency and temperature. This paper investigates the use of a free-free beam setup, as an alternative solution to the classical clamped-free VBT, for a better control of the effect of boundary conditions on the laminated steel specimen. The new setup is developed in combination with a frequency response function based optimization method, to automatically derive the dynamic properties of viscoelastic core materials and generate their master curves. A solver based on the normal mode superposition method, considering the added mass effect of the impedance head, is used in the cost function of the optimization approach. The sandwich model is based on the Ross–Kerwin–Ungar equation, and the four-parameter fractional derivative model is used in conjunction with the Williams–Landel–Ferry equation to describe the frequency and temperature dependent behavior of the viscoelastic material. The master curves are a direct result of the optimization process. Several applications are described to assess the performance of the present method. In particular, a systematic comparison with both the classical VBT and DMA (when available) is presented.