An optimum technique for determining elastic continuum dynamic response using modal analysis

A modal analysis method which minimizes a weighted error function for the differential equation of an elastic continuum is presented. The technique essentially determines optimum time functions for the modal amplifiers by a simple extremization step. The method reduces to a differential equation collocation method when the error weighting function is a Dirac delta function over the continuum space. By means of an example, the technique is shown to have the potential advantages of modal decoupling despite modal non-orthogality, increased accuracy and simplified implementation compared to a more standard approach such as Lagrange's equations. The method is shown to be equivalent to Lagrange's equations for the special case of orthogonal modes.