Chap. 9] SEISMIC METHODS 461 



involved. The procedure is to drive the specimen with impulses of con- 

 tinuously varying frequency until maximum amplitude is obtained. With 

 sufficient accuracy, this resonance frequency may be considered equal to 

 the natural frequency. Measurements of a complete resonance curve give 

 interesting information on the damping within the specimen. 



Transverse vibration tests: These tests''" are the dynamic equivalent of the 

 tests referred to on page 459. They may be applied to bars supported on 

 one end or on both ends. As was stated in connection with eq. (9-17), 

 the natural frequency, wo of an elastic system oscillating with the load 

 m is given by 



where the spring constant, or force per unit deflection P/d, 



c = i^' (9-26W 



for a bar clamped on one end. For slabs suspended between two points* 

 similar relations may be worked out from the formulas previously given 

 for the static deflection. 



The above relations hold only if the mass may be considered as concen- 

 trated on one end. The transverse frequency of unloaded bars clamped 

 on one end is given by 



wo = 



9(7) 4/ R ^^^^ *^^ circular [radius r]) 



and 



0)0 



""2^(1) 1/5 (for the rectangular) 



(9-26c) 



sections, a being the dimension of the side in the plane of oscillation. For 

 the fundamental, n is 1.875; for the first harmonic, 4.694; \/E/5 is known 

 as the "bar" velocity (see eq. [9-29a]). 



Torsional vibrations: The specimens under tests are suspended in a ver- 

 tical position and are loaded with a disk whose moment of inertia K is 

 known or may be determined. This method is well adapted to long-drill 

 cores. The general relation for the period of a torsional system is T = 

 27r '\jKll^p , where I is the length of the specimen and J p the polar 



^«G. Grime, Phil. Mag,, 20, 304 (1935), 23, 96 (1937). W. H. Swift, Phil. Mag., 

 2, 351-368 (Aug., 1926). 



