Measurements and estimation of frequency-dependent multi-scale viscoelastic damping properties of materials

The state-of-art viscoelastic property measurement and estimation methods at different frequencies/length scales inherently couple structural effects or sometimes lose accuracy for relevant parameters at smaller length scales in the material. We report a unified approach to measuring and estimating the frequency-dependent viscoelastic damping properties across different frequency scales independently of the specimen size effect and boundary conditions. The Dynamic Mechanical Analysis (DMA) method with three-point bending configuration is extended to higher-fidelity modeling in terms of time-frequency scales and material micro-mechanical scales together. The methodology demonstrates ways to identify the possible sources of undesired dynamics in the measurement process and eliminate those effects. It includes exciter tip contact dynamics in three-point bending configuration, anharmonic energy transfer to different frequencies (fractal bifurcation), and unmodelled artifacts or noise. Critically reviewing the standard DMA procedure with normal mode synthesis, this paper proposes a time-frequency Fourier spectral method that resolves a broader frequency range that extends to even acoustic/ultrasonic wave regimes of viscoelastic damping. An algorithm proposed in this paper with the advanced viscoelastic model with multi-parameters (standard linear solid model) estimates the fundamental material parameters at small length scales, which is more insightful to obtain a frequency-dependent correlation of material response to general dynamic loading. Stiffness and damping properties are estimated from measured data and validated for self-consistencies via different controls regarding static preload, specimen resonance, filtered noise, and model fidelity across the frequency range, and certain consistency and convergence properties of a series solution. The unified approach with a single test will be helpful in the design and evaluation of a wide variety of materials and their applications in vibration and acoustic problems. The proposed technique further demonstrates a novel way to extend low-frequency measurement to high-frequency response modeling.