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Bulletin of the Seismological Society of America; May 2009; v. 99; no. 2B; p. 1064-1072; DOI: 10.1785/0120080145
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Review Article: Tutorial on Measuring Rotations Using Multipendulum Systems

Vladimir Graizer

U.S. Nuclear Regulatory Commission, Mail Stop T-7E18, Washington, DC, 20555-0001 Vladimir.Graizer{at}nrc.gov graizer{at}comcast.net

This article considers a classical approach of using a combination of pendulums to measure rotations. The idea of using two identical pendulums installed on different sides of the same axis of rotation for separate measurement of rotational and translational motion was apparently first suggested by Golitzin (1912). It was implemented by Kharin and Simonov (1969) in an instrument designed to record strong ground motion (VBPP—a seismograph of large translational motions and rotations). Unfortunately, difficulty in building identical mechanical systems resulted in unreliable measurements of the rotational component. We modified Golitzin’s idea by using the same configuration of pendulums (a two-pendulum system) without the requirement that the pendulums be identical (Graizer et al., 1989). Instead of building two identical pendulums, one needs to calibrate the instrument to obtain the natural parameters of each pendulum and apply postprocessing to separate the rotational and translational motions. The two-pendulum system for separate measurements of large amplitude rotations was implemented at the end of the 1980s at the Institute of the Physics of the Earth in Moscow, Russia, using commercially available pendulum instruments. The system was tested using a basic shake table and later successfully applied to measurements in the near field of two large underground nuclear explosions. In this article I updated and generalized the approach to measuring translational and large amplitude rotational motion formulated in previous publications (Graizer, 1989; Graizer et al., 1989). Numerical testing demonstrated that using a combination of pendulums for measuring rotations may be limited for recording relatively large amplitudes of rotations of the order of 10-4 and higher for the two-pendulum system of about 100 cm size.




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