Beading and Dimpling Techniques to Improve the Vibration and Acoustic Characteristics of Plate ...

267 Pages·2016·9.8 MB·English

by  Nabeel Taiseer Alshabtat

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Nabeel Taiseer Alshabtat
Western Michigan University
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Alshabtat, Nabeel Taiseer, "Beading and Dimpling Techniques to Improve the Vibration and Acoustic
Characteristics of Plate Structures" (2011). Dissertations. 336.
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BEADING AND DIMPLING TECHNIQUES TO IMPROVE THE VIBRATION AND
ACOUSTIC CHARACTERISTICS OF PLATE STRUCTURES
by
Nabeel Taiseer Alshabtat
A Dissertation
Submitted to the
Faculty of the Graduate College
in partial fulfillment of the
requirements for the
Degree of Doctor of Philosophy
Department of Mechanical and Aeronautical Engineering
Advisor: Koorosh Naghshineh, Ph.D.
Western Michigan University
Kalamazoo, Michigan
August 2011
BEADING AND DIMPLING TECHNIQUES TO IMPROVE THE VIBRATION
AND ACOUSTIC CHARACTERISTICS OF PLATE STRUCTURES
Nabeel Taiseer Alshabtat, Ph.D.
Western Michigan University, 2011
A method of improving the vibroacoustic characteristics of beams and plates is
presented. This method is based on creating dimples or beads on the surface of the
structures. The proposed method couples the finite element method with an optimization
technique based on the genetic algorithm (GA). The improvement of the vibroacoustic
characteristics of beams and plates is achieved by two separate strategies. The first
strategy is optimizing the natural frequencies of beams and plates. The second strategy is
minimizing the sound radiation from such vibrating structures.
Optimizing the natural frequencies of some types of beams and simply supported
plates by creating dimples and beads on their surfaces is investigated. The simulation
results indicated that creating cylindrical dimples on simply-supported, free-free, and
cantilever beams decreases their fundamental frequencies, while creating dimples on a
clamped beam may increase its fundamental frequency. Furthermore, creating spherical
dimples or cylindrical beads on the surface of a simply-supported plate increases its
fundamental frequency. The change in plate fundamental frequency depends on dimple
location and size, as well as on bead location, size, and orientation. The optimal designs
of dimpled and beaded beams and plates are presented.
The reduction of the sound radiation from vibrating beams and plates by creating
dimples and beads is also investigated. The main effect of creating beads or dimples is
the significant change in the beam or plate mode shapes (especially the higher order
mode shapes). The change of the mode shape plays a significant role in the mechanism of
volume velocity cancellation, which causes a reduction in the sound power. Two cases of
optimization problems are considered: the first case is the minimization of the sound
power of a vibrating plate at a natural frequency, and the second is the minimization of
the sound power of a vibrating plate at a fixed frequency. The optimization examples
proved the efficiency of beading and dimpling techniques in designing quiet plates at a
specific frequency.

UMI Number: 3480285
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Copyright by
Nabeel Taiseer Alshabtat
2011
ACKNOWLEDGEMENTS
I would like to express the deepest appreciation to my advisor, Dr. Koorosh
Naghshineh, for his confidence, tolerance and support during the past four years. This
work could not have progressed as quickly as it did without the ideal working conditions
and computational tools which Dr. Koorosh Naghshineh brought together and made
readily accessible at the Western Michigan University Noise and Vibration Laboratory. I
am thankful also to Dr. Judah Ari-Gur for his valuable advice in modeling and
optimization. In addition, I would like to thank Dr. Peter Gustafson and Dr. Tarun Gupta
for their advice during the course of my research.
I would also like to thank my wife, Lara, and my sons Ahmad and Taiseer, whose
support has provided me with strength and conviction to conclude this project.
Lastly, I would like to thank my wonderful parents Taiseer and Gada for their
support throughout my educational studies. Their belief in my capacity to follow my
dreams and realize my potential as both a student and an individual has made this all
worthwhile.
Nabeel Taiseer Alshabtat
ii
TABLE OF CONTENTS
ACKNOWLEDGMENTS ii
LIST OF TABLES vi
LIST OF FIGURES viii
CHAPTER
1. INTRODUCTION AND OBJECTIVES 1
1.1 Introduction 1
1.2 Research Objectives 3
1.3 Dissertation Organization 4
2. PERTINENT LITERATURE AND RESEARCH MOTIVATION 5
2.1 Reinforcing Plate-Like Structures by Beading 5
2.2 Modification of Vibration Characteristics of Plate Structures 12
2.3 Review of Sound Radiation Modifications of Plate Structures 24
2.4 Research Motivation 36
3. BEAD AND DIMPLE FORMING 38
3.1 Embossing Forming 38
3.2 Bead Depth Limitations 41
3.3 Forming Limit Diagram and Semispherical Maximum Depth 44
4. INTRODUCTION TO STRUCTURAL OPTIMIZATION 50
4.1 General Concepts 50
4.2 Local and Global Minima 52
iii
Table of Contents-Continued
CHAPTER
4.3 Global Optimality and Convexity 52
4.4 Genetic Algorithms 55
5. OPTIMIZING THE NATURAL FREQUENCIES OF BEAMS VIA
DIMPLING TECHNIQUE 59
5.1 Beam Natural Frequencies Modification Methods 60
5.2 Dimpled Beam Modeling 63
5.3 Parametric Analysis 64
5.4 Stiffness Study 74
5.5 Optimization 79
5.6 Experimental Validation 88
5.7 Summary 95
6. OPTIMIZING THE NATURAL FREQUENCIES OF PLATES VIA
DIMPLING AND BEADING TECHNIQUES 97
6.1 Finite Element Modeling and Modal Analysis 98
6.2 Parametric Analysis 102
6.3 Optimization Ill
6.4 Summary 129
7. SOUND RADIATION MINIMIZATION 131
7.1 Structural Vibration 132
7.2 Sound Radiation from Vibrating Plate 133
7.3 Structural Acoustic Formulations 135
iv