The solution of natural frequency equations by relaxation methods
The application of Dr. R. V. Southwell's relaxation method1,2 to the solution of natural frequency equations for systems with a finite number of degrees of freedom is discussed in this article. The first object is to discuss the conditions under which the procedure converges. It is shown that two criteria can be given, such that if the one is satisfied, the procedure converges to the highest mode, and, if the other is satisfied, to the lowest. This is of more than purely theoretical interest: for it is shown that the possibility of finding the highest mode directly can be used to simplify considerably the process of finding further modes. 1. The criteria of convergence. The equations to be solved will be written in the form