Publication Date


Document Type


First Advisor

Gupta, Abhijit

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mechanical Engineering


Harmonic functions; Modal analysis


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.


Includes bibliographical references (leaf [88])


xiii, 122 pages




Northern Illinois University

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