The Relationship of Traditional Damping Measures for Materials with High Damping Capacity: A Review

In the field of material damping a number of measures are used to express the level of damping which a material possesses. Such measures are required when evaluating material and system responses to dynamic loading conditions. The most widely used measures of damping capacity include the tangent of the phase lag, tan Φ, ratio of loss modulus to storage modulus, E/E', loss factor, η, specific damping capacity, ψ, inverse quality factor, Q - 1 , log decrement, 8, and damping ratio, ζ. Each damping constant is defined in relation to the method used to measure it. Thus it is sometimes difficult to compare the damping capacity of one material to another. By their inherent definitions, the measures of damping capacity listed above can be simply interrelated when damping levels are within the range 0 < tan Φ < 0.14 (that is, tan Φ = E/E' = η = ψ/2π = Q - 1 = δ/π = 2ζ). However, these widely used interrelationships are actually approximations based on two simple anelastic models and an assumption of low damping. This assumption simplifies otherwise complicated nonlinear conversions. When higher levels of damping are of interest (0.14 < tan Φ), the simple linear relationships given here can produce up to 40% error when converting from one damping measure to another. In this paper, the basic measures of damping will be reviewed and the exact formulas that relate the various damping measures will be presented. Both the exact formulas and the approximations will be given in the discussion and in a table contained in the summary section. The nonlinear relationships will be useful in cases involving high damping, especially when damping levels are near tan 4 = 1.