Determination of modal coupling in vibrating rectangular plates

In square isotropic plates, some of the degenerate mode pairs are split in frequency due to coupling between longitudinal and transverse strain (which might be called Poisson coupling), and the same splitting of degenerate modes can occur in rectangular orthotropic plates having a certain length/width ratio. We have studied this coupling in free plates of aluminum and spruce (quarter cut and skew cut) and determined Poisson's ratios from the frequency ratios of the ($\text{2,0±0,2}$) modes (called the x and ring modes by luthiers). The critical length/width ratio was found to be considerably greater (3·17) in the skew-cut spruce than in quarter-cut spruce (2·08), due to a smaller cross-grain elastic modulus and Poisson's ratio.