Abstract
This theoretical and experimental work deals with the power law evolution followed by the natural frequency of a hanging, heavy and flexible plate as a function of its length . When the plate length is small enough, it behaves as an elastic plate whose weight can be neglected: it is well known that evolves as a function of . 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, , just like hanging chains. These two power laws depend on the ratio , where 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.
Keywords:
natural frequency; elastic plate; power law