Civil Engineering Association

Vibration of Continuous Systems

IN-DEPTH INFORMATION ON THE VIBRATIONS OF CONTINUOUS SYSTEMS

Written by experts in the field, Vibrations of Continuous Systems expalins the vibrational behavior of basic structural components and elements. Several real-world applications in various fields, including acoustics and aerospace, mechanical, civil, and biomedical engineering, are highlighted. The book includes the derivation of the governing equations of motion and emphasizes the interplay between mathematics and physical understanding. Challenging end-of-chapter problems reinforce the concepts presented in this detailed guide.

COVERAGE INCLUDES:
Transverse vibrations of strings
Longitudinal and torsional vibrations of bars
Beam vibrations
Membrane vibrations
Plate vibrations
Shell vibrations
Vibrations of three-dimensional bodies
Vibrations of composite continuous systems

vibration of continuious systems

very structure or machine element in mechanical, civil, aerospace, marine, biomedical, automotive, or other engineering applications constitutes a continuous system. When subjected to an oscillating load, this system undergoes a vibratory behavior. Vibrations are an engineering concern in these applications because they may cause a catastrophic failure (complete collapse) of the machine or structure because of excessive stresses and amplitudes (resulting mainly from resonance) or because of material fatigue over a period of time. Documented examples are numerous. One of these is the collapse of the newly completed Tacoma Narrows Bridge in 1940, opened barely four months before, which swayed and collapsed in a 42-mile-per-hour wind undergoing a torsional mode resonance.
In addition, vibrations can cause difficulties to users either because of excessive amplitudes or because of manifesting themselves into noise (particularly at higher frequencies). Other applications of vibrations of continuous systems can be found in sound recognitions and
acoustical and music fields. Vibrations of continuous systems is an extremely interesting subject. Discovering theoretically how strings, rods, beams, plates, shells, and other continuous bodies vibrate—particularly, in what shapes and at what frequencies they vibrate freely—is fascinating.
And how they respond when subjected to fluctuating exciting forces and pressures is also interesting, and especially important in practical applications. Moreover, vibrations of continuous systems is an ideal subject to help understand the behaviors and meanings of partial differential equations and eigenvalue problems. The interplay between mathematics and physical understanding is emphasized throughout this book. Although this work has been written as a textbook to be used in classes, it is also suitable for independent study. Read carefully, the paragraphs follow as they would in a lecture. Students (or readers) should have beforehand at least a basic understanding of ordinary differential equations and, preferably, some background in the vibrations of discrete systems. Otherwise, they will need to dosupplementary reading in these subjects as they proceed. Some understanding of partial differential equations would also be beneficial.
Basic descriptions and explanations of vibrational concepts and phenomena are given in Chap. 1 (Introduction). This should be read carefully when beginning the book, and then read again as one progresses subsequently. Chapter 1 explains to the reader how the following chapters evolve as parts of a general development of the subject. Each chapter after the first has problems at its end. Most of them were used as homework problems in the classes taught by the first author. They are chosen so as to develop understanding of the topic by the student. Most of them require significant thought and time spent (more than one hour each). For most of them, use of a computer should reduce the time required, and improve accuracy. This book was initially written by the first author over a 30-year period. The second author wrote Secs 4.13 and 4.14 and Chap. 9, in addition to contributions to introductory sections of many chapters and his overall sponsorship and supervision of production of the whole manuscript. It is the result of the first author’s 50 years of research in the field of vibrations of continuous systems, and having taught a graduate-level course of the same title at Ohio State University for 35 years. His research in the field resulted in the monograph Vibration of Plates, published in 1969, which presented results (theoretical and experimental) from approximately 500 research papers and reports. Vibration of Shells, published in 1973, summarized approximately 1000 references. Sources worldwide in all languages were used. The first monograph has been cited many hundreds of times by others in their publications, the second one almost as many.
In addition, the first author supervised 40 Ph.D. dissertations and 20 M.Sc. theses, most of which dealt with the vibrations of continuous systems. The graduate student research, as well as collaboration with others, resulted in more than 100 published technical papers with the
first author on vibrations of continuous systems. This book is also the result of 20 years of experience in this field, mostly in industry, by the second author. During that time he published approximately 40 technical papers on the subject (in addition to a similar number in the area of automotive noise and vibration). The second author taught the material for about 10 years at Oakland and Mississippi State universities. He also published a book on Vibration of Laminated Shells and Plates in 2004 which reviewed hundreds of papers in the field and
is the first on the subject. The second author is also the co-author of two recent books on vehicle dynamics published in 2008 and 2009. He is supervising 10 graduate students (mostly Ph.D.s working on vibrations of continuous systems).While the first author wishes to thank all his graduate students for their contributions through the years, the second author wishes to
thank his current Ph.D. students M. Maleki, E. Asadi, W. Wang, and R. Wheeler for their help in preparing the manuscript.

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