The prediction of dynamic stress and strain in randomly vibrating structures using vibrational velocity measurements

[Truncated] Three different methods for the prediction of dynamic stress and strain in randomly vibrating structures from measurements of vibrational velocity are investigated.
The first method is based on correlations between the spatial maxima of dynamic strain and velocity. This method, referred to as strain-velocity correlation, is defined using (i) derived farfield relationships between the propagating wave components of dynamic strain and velocity, and (ii) factors for the effects of evanescent waves in nearfield regions. Strain-velocity correlation provides predictions of maximum mean-square dynamic strain in both narrowband and broad-band excited beams, plates and cylindrical shells.
The second method considered uses finite differencing of simultaneous velocity measurements at three or four equally spaced positions to obtain autospectral, spatial and time history predictions of dynamic strain in both nearfield and farfield regions. The number of simultaneous measurements is reduced from three or four to only two if the response is stationary and frequency response function formulations are used. This method is applicable to beams and plates.