AN ITERATIVE TECHNIQUE BASED ON THE DUNKERLEY METHOD FOR DETERMINING THE NATURAL FREQUENCIES OF VIBRATING SYSTEMS

The principle underlying the Dunkerley method of obtaining the smallest natural frequency for a multi-degree-of-freedom elastic system is extended by an iterative procedure to simultaneously determine all the frequencies of that system. In obtaining the higher frequencies, the first iteration of the procedure is akin to the Paipetis extension of the Dunkerley method. The method is found to converge quickly when the frequencies are not close to each other, but converges slowly otherwise. For multiplicities or close frequencies, a simple modification of the initial step reinstitutes quick convergence. The method is applied to several classical lumped parameter problems to demonstrate its usefulness. © 1991.