912 MISCELLANEOUS GEOPHYSICAL METHODS [Chap. 12 



A. Vibration Recording (Free Vibrations) 



1. Vibrations of buildings and other structures. Free vibrations occur in 

 buildings and other structures (bridges, water tanks, dams) as a result of 

 wind gusts, earthquakes, traffic vibrations, blasting, and other industrial 

 activity. Observations of free vibrations usually have to depend on the 

 random occurrence of such agencies; only when the structures are small 

 (water tanks, bridge models) may the initial deflections be produced by 

 pullbacks with predetermined load. Vibrations are recorded with vibro- 

 graphs or seismographs of moderate magnification, equipped with mechani- 

 cal or optical recorders. It is advantageous to make measurements on 

 various portions of a structure in both horizontal and vertical directions, 

 so that various vibration modes in the planes of symmetry and the varia- 

 tion of amplitude with height may be obtained. When a multiplicity of 

 records has to be secured simultaneously, electrical seismographs with 

 central recording are preferred to mechanical instruments. In this work, 

 moderate magnifications ranging from 200 to 1500 are sufficient; natural 

 instrument periods vary from 1 to 3 seconds; damping should be nearly 

 critical. Observations are arranged to yield natural frequencies and 

 damping (in at least two directions) and variation of vibration amplitude 

 with height. 



For buildings whose ratio of height to width is great, flexural vibrations 

 are most important. In the opposite case, where the width is much greater 

 than the height, flexure is unimportant and shear predominates. When 

 the ratio of height to width is between 3 and 4, both kinds of vibrations 

 will be encountered. Torsional vibrations may also occur. In addition 

 to the fundamental, several harmonics are generally observed. If shear 

 predominates,^^ the ratios of the translational and torsional fundamental 

 periods to higher mode periods should be near 3, 5, and 7 (for a building 

 on rigid foundation). When flexure predominates, the translational period 

 ratios should be near 6.2, 17.5, 34.6, and so on. Observations on com- 

 pleted buildings are of value in establishing a reference file for future use, 

 particularly when such measurements have been made on buildings that 

 have been through an earthquake. In this manner, the damage done may 

 be correlated with the frequency response of both building and ground. 



Before construction is commenced, the natural frequency of a building 

 may be calculated if it has a simple geometric form. It is more satisfac- 

 tory, however, to determine the natural frequency on a model by a pull- 

 back test (free vibration) or from the response on a shaking table (forced 

 vibration). 



2. Free ground vibrations. Free ground vibrations are produced by 



n U. S. Coast & Geod. Surv., Spec. Pub. No. 201, 51 (1936). 



