On Properties of Transfer Functions of a Flexible Structure

Abstract

A flexible arm is the distributed parameter system with infinite number of eigenvalues. Its transfer function can be calculated directly from the partial differential equation model by using the Laplace transformation. On the other hand, two approaches of the modal analysis; the unconstrained mode method and the constrained mode method are employed to construct infinite dimensional lumped parameter dynamical system models by expanding the elastic deformation, which make two kinds of transfer functions. We obtain three different but equivalent transfer functions for the same system. Comparison of these transfer functions yields relationships on eigenvalues and parameters of these systems. To this end, the distributed parameter model transfer function is expressed as a ratio of two transcendental entire functions and these are expanded in infinite products. It is shown that the poles of unconstrained model transfer function and zeros of the constrained model transfer function coincide with those of the distributed parameter transfer function respectively.