Vibrations of free square plates: part I. Normal vibrating modes

Abstract

After a brief historical note, the paper describes the result of systematic observations which have been made on the normal vibrations of free square plates. The nodal systems are divided into seven classes and their further recognition is effected by the application of given rules. The natural vibration frequencies found by measurement are in fair agreement with Ritz's calculations. The relative frequencies of the higher partials agree with Chladni's observation that they are proportional to m2+n2. For values of m and n exceeding three, it is found that the frequencies, relatively to the gravest I| I tone taken as unity, are given roughly by ¾ (m2+n2).