Engineers apply mathematics and science to solve problems. In a traditional undergraduate engineering curriculum, a student begins an academic career by taking courses in mathematics and basic sciences such as chemistry and physics. A student begins to develop problem-solving skills in basic engineering science courses. For a mechanical engineering student, these courses include statics, dynamics, mechanics of solids, fluid mechanics, and thermodynamics. In such courses, students learn to apply basic laws of nature, constitutive equations, and equations of state to develop solutions to abstract engineering problems.

     Vibrations is one of the first courses where students learn to apply the knowledge obtained from mathematics and basic engineering science courses to solve practical problems. Indeed the problem-solving skills developed in a vibrations course are as valuable as the knowledge of the subject of vibrations. Solution of practical problems in vibrations requires modeling of physical systems. A system is abstracted from its surroundings. Assumptions appropriate to the system are made. Basic engineering science and mathematics are applied to derive a mathematical model. The resulting solution is used to learn about system behavior that could be used in applications such as design. The reader of this text will learn about vibrations by using such a problem-solving approach.

     An application of vibration analysis is in engineering design. Design principles are developed using analysis of model one-degree-of-freedom systems. Design applications are presented for multi-degree-of-freedom systems and continuous systems. Many examples and homework problems have a design flavor.

     This book is intended as a text in a junior or senior level undergraduate course in vibrations. It could be used in a course populated by both undergraduate and beginning graduate students. The prerequisites for such a course should include courses in statics, dynamics, mechanics of materials, and mathematics through differential equations. Some material usually covered in a fluid mechanics course is used, but this material can be omitted without loss of continuity.

     An overview of the modeling procedure is presented in Chapter 1 (This material can be omitted if students have background in system dynamics). Two methods of dynamic analysis are presented and used throughout the book. The free-body diagram method is based on D'Alembert's principle. An energy method that includes the effect of nonconservative forces is presented as an alternative and is preferred in modeling multi-degree-of-freedom systems.

     Chapters 2 through 4 focus on vibrations of linear one-degree-of-freedom systems while Chapters 5 through 7 focus on vibrations of multi-degree-of-freedom-systems. Chaper 8 presents methods of reducing unwanted vibrations of discrete linear systems. Chapter 9 provides a brief overview of continuous systems. Chapter 10 introduces the reader to the finite-element method, while Chapter 11 focuses on linear vibrations.

     While the structure of the second edition is similar to that of the first edition, there is much new in the second edition. The use of complex algebra in the analysis of the forced response of discrete systems has been added. Free and forced vibrations of multi-degree-of-freedom systems with a general damping matrix are now presented. Many new examples are presented. Approximately one-third of the end-of-chapter problems are new for this edition. An appendix containing answers to selected problems has been added.

     Chapter 10, "Finite-Element Method," is new. Engineering students are usually exposed to the finite-element method during undergraduate studies, but rarely are exposed to its application to vibrations problems. This chapter is a welcome addition for those who have previously studied the finite-element method, although it is self-contained in that the method is developed by using the assumed modes method and Lagrange's equations.

     Examples throughout the book use MATLAB for numerical computation, symbolic computation and visualization of result. MATLAB script files are consistent with Student Edition of MATLAB, Version 5. The accompanying CD, titled VIBES II, contains all script files presented in the text as well as other script files used for a variety of vibrations applications. Problems using MATLAB are presented at the end of each chapter. Many problems require use of the VIBES II files to solve vibrations problems while others require the development of a MATLAB script file.Users are encouraged to explore the files and develop their own applications. A list of files summarizing their applications is available by printing the text file LIST.TXT.

     MATLAB and similar software are used as tools in vibration analysis. Indeed, they are powerful tools, easy to use for computation and visualization. While it is important to understand how the mathematics used in solving a problem is performed, complex computations often obscure the use of the results. The use of MATLAB allows the focus to be on the modeling, analysis, and design aspects of a problem, rather than computational considerations.

     The author acknowledges the support and encouragement of Jonathan Plant, Senior Sponsoring Editor, during preparation of the second edition and the help of John Corrigan, formerly of McGraw-Hill, during the preparation of the first edition. The help of former students Ken Kuhlmann, Mark Pixley, and Ashish Choski is greatly appreciated. Many valuable comments and suggestions were provided during preparation of the first and second editions by Donald Adams, University of Wyoming; Atila Ertas, Texas Tech University; Andrew Hansen, University of Wyoming; Eugene I. Rivin, Wayne State University; S.C. Sinha, Auburn University; Robert Steidel, University of California-Berkeley; J. Kim Vandiver, Massachusetts Institute of Technology; Dr. Aldo Ferri, Georgia Institute of Technology; Peter Philliou, Wentworth Institute of Technology; Richard Alexander, Texas A&M University; H.Nayeb-Hashemi, Northeastern University; Bala Balachandran, University of Maryland; William Webster, Kettering Institute, and Nester Sanchez, University of Texas at San Antonio. Finally the author expresses appreciation to his wife, Seala Fletcher-Kelly, and his son Graham, for their patience and support.

S. Graham Kelly
July 30, 1999