CIRCULAR CLAMPED PLATE 



43 



where / = thickness of the plate, in centimeters, 



R = radius of the plate up to the clamping boundary, in centimeters, 



p = density, in grams per cubic centimeters, 



<x = Poisson's ratio, and 



^= Young's modulusjin dynes per square centimeter. See Table 3. L 



fri= s.ogfoi 



[21=3.43(01 



f3i=4..95foi 



fi2=5.98foi 



f2a=a74fo 



fi3=ll,9foi 



Fig. 3.4. Modes of vibration of a clamped circular plate. Shaded segments are displaced 

 in opposite phase to unshaded. 



The fundamental frequency is with the circumference as a node and a 

 maximum displacement at the center. 



The frequency of the next two overtones with nodal circles. Fig. 3.45 

 and 3.4C, are, 



/02 = 3.91/ox 



/o3 = 8.75/oi 



The frequencies of the first, second and third overtones with nodal diame- 

 ters are 



/n = 2.09/01 



fn = 3.43/01 



/31 = 4.95/01 

 These nodes are shown in Figs. 3.4D, 3AE and 3.4i^. 



