Abstract
The phase plane δ-method is known as a graphical method on the phase plane. This method may be classified into three algorithms (standard, averaged and dotted δ-method) and their fundamental properties are discussed; i.e. accuracy, stability and convergence, in order to use this method for the numerical method of dynamic analysis. These three algorithms are examined by several numerical examples and dynamic responses are compared with those computed by Newmark's β method. Conclusions are as follows; (1) When applied to a linear single-degree-of-freedom system, each method is reduced to the recurrence formula. So the dynamic response can be computed without drawback. Each algorithm of the phase plane δ-method is more useful than Newmark's β method both in amplitude and phase. Especially, dotted δ-method shows the most useful properties. (2) When applied to a non-linear system, each method requires a recurrsive computation. Both dotted and averaged δ-method have more rapid convergence than Newmark's β method by far.
