System modeling and modification via modal analysis

Abstract

A new method is developed for experimentally determining the system parameters of a structure that is suitable for implementation in microprocessor-based systems. It uses single degree-of-freedom models to describe a multi-degree-of-freedom system. The system is assumed to be describable by a linear, proportionally and lightly damped, lumped parameter model. Two types of damping models, viscous and structural damping, are provided.

The effective mass, stiffness, and damping are obtained by fitting the experimental data in the inverse Nyquist plane. The effective mass, stiffness, and damping are convertible to global modal mass, stiffness, and damping through normal mode corrections. Then a physical space mathematical model may be assembled from the modal properties for complete and truncated modal vector system descriptions. Therefore, this method will deal with the general case where the number of degree-of-freedom exceeds the number of identified modes.

After a mathematical model is developed, different ways of modifying the structure analytically are investigated. This modified model is used to predict the new dynamic characteristics of the modified structure due to changes in its mass, stiffness, or damping properties. There are three ways that modifications can be made. They are: l) modifications made in the physical coordinates model; 2) modifications made in both the physical and modal coordinates models; and 3) modifications made in the modal coordinates model. The last way is found to be the most efficient way; therefore, model modifications should be done totally in modal spaces, modal space I and II. The derivation of mass, stiffness, and damping modification matrices for general structure is also presented.

The resonance specification and frequency response function synthesis are two useful techniques that aid in system modification and are, therefore, included. A resonant peak can be shifted to another frequency by making certain modifications to the structure, thus avoiding undesired vibration. The resonance specification will determine the amount of physical change needed. It is not practical to store all the frequency response function measurements of a structure during testing. Therefore, a frequency response function synthesis is needed, such that any one can be synthesized from the model developed.

A theoretical three degree-of-freedom system and two experimental systems--a square plate and a C-clamp--were used to verify the techniques developed.