Measurement of Inelastic Amplitude Decay (bamp)

Because there will be some beam divergence from any real, finite source, the program, bamp, makes a correction for beam divergence before measuring inelastic decay. Currently, the only option is for a spherical divergence correction. Under this model, the amplitude, A, of a spherically divergent wave at distance, r, from the source is given by

$$A=\left(\frac{A_{o}r_{o}}{r}\right)\cdot\exp\left(-\alpha\left(r-r_{o}\right)\right),$$ (13)

where $A_{o}$ is the amplitude at a reference offset $r_{o}$ . Here, amplitude is the particle velocity as measured by a moving coil velocity phone (dynamic stress/impedance). The decay at any frequency may be expressed in terms of $\alpha$ (1/m, also sometimes referred to as nepers/m). Alternatively, decay may be expressed in decibels as

$$dB=20\log_{10}\left(\frac{Ar}{A_{o}r_{o}}\right)=-20\left(\log_{10}e\right)\alpha(r-r_{o}).$$ (14)

Program, bamp, writes the measured inelastic decay, $\alpha$ , at each frequency and writes the results to a file, bamp.his, which is later read by cainv3.m.