This theoretical and experimental work deals with the power law evolution followed by the natural frequency f 0 of a hanging, heavy and flexible plate as a function of its length L. When the plate length L is small enough, it behaves as an elastic plate whose weight can be neglected: it is well known that f 0 evolves as a function of L − 2. Nevertheless, when the plate length is increased, the mass has to be taken into account, and the previous evolution is not valid anymore. In the case of long elastic plates, f 0 ∼ L − 1 / 2, just like hanging chains. These two power laws depend on the ratio L / L c, where L c is a critical length that writes as a function of the plate mass and the flexural rigidity. After the theory is developed and the plate motion equation is solved using a Galerkin expansion, we find the theoretical evolution of the natural frequencies as a function of length. Experiments were performed with three distinct materials and the natural frequency was systematically measured for a wide length interval. Our data points fit the above-mentioned limit cases and the intermediate case was calculated thanks to our Galerkin expansion.
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