Publication Date

1995

Document Type

Dissertation/Thesis

First Advisor

Gupta, Abhijit

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mechanical Engineering

LCSH

Harmonic functions; Modal analysis

Abstract

Existing element types available in finite element codes typically utilize polynomial shape functions which define the displacement field in the problem of interest. The polynomial shape functions serve the purpose adequately in static analysis where the displacements and the stresses in a structure are of primary interest. These shape functions give rise to increasing inaccuracy as the higher modes of vibration are investigated in the typical modal analysis of a structure. It will be shown that harmonic shape functions yield better results for frequencies and mode shapes for the higher modes with same element count. The higher modes are typically of interest in the determination of structural frequencies in quartz crystals. Problems involving axial vibrations of a bar and transverse vibrations of beams have been investigated to validate the use of harmonic shape functions. A comparative analysis has been made between results predicted by the harmonic interpolation functions and polynomial interpolation functions using same number of nodes.

Comments

Includes bibliographical references (leaf [88])

Extent

xiii, 122 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

Download

Share

COinS