The fundamental frequency of vibration of rectangular wood and plywood plates

Equations are derived expressing the frequency of vibration of rectangular wood and plywood plates in terms of elastic constants, dimensions and density. For supported edges, the solution is exact and gives the complete series of overtones. For clamped edges, the fundamental frequency is estimated by the approximate Rayleigh method, but evidence is presented which indicates that the errors introduced by the use of the Rayleigh method are, in fact, negligible. A method of measuring the frequencies is described; comparison of calculated with observed frequencies shows that the former are on the average about 23% high for clamped edges and about the same amount low for supported edges. This discrepancy is attributed to lack of correspondence between the experimental edge conditions and those assumed in the theoretical treatment. Finally, an empirical method, based on the rough proportionality between elastic constants and density of wood, is suggested and justified for obtaining approximate estimates of the fundamental frequencies in terms of plate dimensions only.