Proof of Concept for Determination of Static–Dynamic Material Loss Factor Damping via Simulation and Numerical Methods

The vibration response of a component, particularly the frequency response of the component, can be used in the determination of the loss factor damping, η, due to energy dissipation and the elastic modulus (E). The ASTM E756-04 standard provides the methodology and the guidance for the determination of the loss factor damping and elastic modulus experimentally. This standard specifically calls for the use of a beam with a rectangular cross-section. Also, the theoretical formulation developed there is based on such a beam cross-section. Here, in this paper, the theoretical formulation and numerical simulation for determining the loss factor damping and elastic modulus are a derivation of the methodology used in the ASTM standard and other R&D work, but for a circular plate configuration. The delta change derivation, both theoretically and numerically, is proven to be accurate and validated here. This method is useful in the characterization of materials that have applications in structural vibration, aerospace subcomponents, micro and mini sensory devices, medical devices, and many other areas. Similar to the ASTM standard, the materials could include metals, ceramics, rubbers, plastics, reinforced epoxy matrices, composites, and woods. This paper mainly formulates the technique via numerical and computational methods. It is the intention of the author to also, as a future research agenda, experimentally produce data that can be correlated with this theoretical and numerical methodology.