Yin Fang

Publication Date


Document Type


First Advisor

Gupta, Abhijit

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mechanical Engineering


Bolted joints--Vibration--Mathematical models; Vibration--Mathematical models; Printed circuits--Mathematical models


One of the most typical supports for the printed circuit boards is a bolted joint.Un- derstanding the properties of bolted joints is necessary before a vibration analysis of circuit boards can be made. A bolted joint typically used to support printed circuit boards made of copper clad epoxy fiber glass is analyzed in this thesis. The bolted joint is modeled by appropriate linear and torsional springs. In order to isolate the bolted joint without being concerned about the elastic properties of the circuit board, a beam is made with an aluminum box channel attached to a beam made of copper clad fiber glass epoxy. This box beam attachment makes the beam very rigid in bending. The stiffness values are estimated by applying experimental modal analysis data to the beam model. Another experiment using Linear Variable Differential Transformer (LVDT) is performed to verify the results. Rayleigh damping is used to model the damping provided by the joint These damping parameters are obtained from experimental modal damping ratios. Finally, a different size beam, but with the same bolted joint, is used to compare theoretical and experimental natural frequencies and damping ratios.


Includes bibliographical references (pages 24)


vi, 24 pages




Northern Illinois University

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