A structured approach to design-for-frequency problems using the Cayley-Hamilton theorem.

Patrick Dumond,Natalie Baddour

doi:10.1186/2193-1801-3-272

Abstract

An inverse eigenvalue problem approach to system design is considered. The Cayley-Hamilton theorem is developed for the general case involving the generalized eigenvalue vibration problem. Since many solutions exist for a desired frequency spectrum, a discussion of the required design information and suggestions for including structural constraints are given. An algorithm for solving the inverse eigenvalue design problem using the generalized Cayley-Hamilton theorem is proposed. A method for solving partially described systems is also specified. The Cayley-Hamilton theorem algorithm is shown to be a good design tool for solving inverse eigenvalue problems of mechanical and structural systems.

Highlights

In mechanical and structural system design, engineers are often faced with the task of designing systems which either have natural frequencies which must fall outside a specific range or operate at exactly certain frequencies
In this paper, we considered a tool that can be used for discrete design-for-frequency engineering problems
An engineer would generally prefer a direct approach to design-for-frequency when designing a mechanical or structural system, rather than a heuristic trial-by-error approach

Summary

Introduction

In mechanical and structural system design, engineers are often faced with the task of designing systems which either have natural frequencies which must fall outside a specific range or operate at exactly certain frequencies. These design problems can be considered as eigenvalue problems, since the eigenvalues are used to determine the natural frequencies (frequency spectrum) of the system. If specific natural frequencies are sought, empirical or iterative methods are used to modify the system’s physical parameters until the desired eigenvalues are obtained. This approach is both time consuming and indirect. A better approach would be to design the system directly from the natural frequencies

Results

Discussion

Conclusion