Linear Response Functions and the Phenomenological Equations of Internal Friction

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Abstract
Linear response function analysis has been applied to the internal friction problem. With the use of the Kramers‐Kronig relations, the analysis takes on a very convenient form which is of particular usefulness for experimental analysis. The Fourier transform of the response function is related very simply to the phase lag and the modulus defect. The general formulation is applied to simple cases of relaxation and resonance. It is also applied to the space‐dependent vibrating dislocation model of Granato and Lücke, and the effects of higher modes are treated. It is shown that on the high‐frequency side of the damping peak, for low damping, the higher modes contribute an increase in the damping which has the same frequency dependence as the fundamental. For high damping, the situation is indeterminate on the far high‐frequency side, but for frequencies near the peak, the fundamental mode analysis of Granato and Lücke is unchanged.