Flexural resonant frequencies of thin rectangular cantilever plates

Knowledge of the flexural vibration frequencies of thin rectangular cantilever plates forms the basis for numerous applications in sensing and instrumentation. Despite the seemingly simple nature of the problem, an accurate formula for the fundamental resonant-frequency that is valid for all aspect ratios and Poisson's ratios is notably lacking in the literature. In this article, we present such a result using a variational and singular perturbation formulation. This yields a simple analytical formula that exhibits a maximum error of 2%.