A scheme for expressing instrumental responses parametrically

abstract This study shows that, provided a seismic instrument as a whole behaves linearly over its response range, and provided its phase response is known accurately, the instrumental responses can be parametrically expressed in terms of transfer functions of linear systems. The scheme is based on the observation that knowing accurately the detailed overall amplitude and phase responses of a linear instrument is tantamount to knowing all the pertinent constants for the construction of its overall transfer function. Because of generally poor quality of empirical phase calibrations, empirical phases are substituted by minimum phases, calculated via a Hilbert transform of amplitude response. Application of the scheme to actual SRO (LP) and USGS (SP) instruments resulted in sufficiently close agreements between parametric and actual responses to warrant the utility of the scheme.

Torsional Vibration Amplitudes at Non-Resonant Speeds with Special Reference to the Interpretation of Torsiograph Records

The seismic torsiograph is commonly used for recording torsional vibration because it can be applied to many different types of oscillating system without elaborate preparatory measures. This instrument is available in several types each suitable for a particular measuring range so that there is little difficulty in selecting equipment to record with reasonable accuracy, the vibratory motion at a chosen point in any present-day transmission system. The motion recorded by a seismic instrument may, however, be very complex; and this implies that care must be taken when attempting to interpret the records in terms of shaft stress, particularly at non-resonant speeds. This problem can be very difficult, and is discussed in the present paper with the help of typical examples. It is shown that the interpretation of records obtained at resonant speeds is comparatively straight-forward, provided that the system is reasonably linear and does not contain components having a complex distribution of mass and, or alternatively, elasticity. Methods for computing shaft stresses from measured amplitudes are discussed, and attention is drawn to the use which can be made of tabulation methods when dealing with records obtained at non-resonant speeds and with systems containing complex components or having a marked degree of non-linearity. Cases where shaft stresses at non-resonant as well as at resonant speeds must be taken into account are by no means unknown. It is shown that under certain conditions a seismic type torsiograph will show no appreciable response or will become very unreliable at some non-resonant speeds. Finally, attention is drawn to the use of torsional strain gauges as an alternative to seismic torsiographs. The strain gauge method enables measurements of total shaft stresses to be made even if the system is markedly non-linear or contains complex components. The development of compact and reliable torsional strain gauge equipment for general use appears to be desirable.