Mechanical Vibrations: A Lecturebook
Edition: 1
Copyright: 2022
Pages: 440
Edition: 1
Copyright: 2022
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Mechanical Vibrations: A Lecturebook introduces the analysis of mechanical vibration systems by progressing from the fundamental equations of motion for discrete systems to the study of free and forced vibration responses in both discrete and continuous systems. It also covers practical applications and approximate solution methods used in vibration analysis. The appendices provide supporting material in calculus, complex numbers, relevant mathematical functions, dynamics, linear algebra, operator self-adjointness, a proof related to Lagrange’s equations, and transmissibility ratios.
About the Authors
Chapter I Equations of Motion for Discrete Systems
Chapter II Free Response of Discrete Systems
Chapter III Free Response of Continuous Systems
Chapter IV Forced Response of Discrete Systems
Chapter V Applications and Approximate Methods
Appendices
Appendix A: A Brief Review of Some Calculus Basics
Appendix B: Some Basic Operations with Complex Numbers
Appendix C: Functions Relevant to Vibration Analysis
Appendix D: Some Results from Dynamics
Appendix E: Some Results from Linear Algebra
Appendix F: Determining the Self-Adjointness of an Operator
Appendix G: A Needed Proof for Lagrange’s Equations
Appendix H: Transmissibility Ratios
Charles M. Krousgrill: Charles M. Krousgrill is a Professor in the School of Mechanical Engineer-ing at Purdue University. He received his M.S. in mechanical engineering from Purdue University in 1975, and his M.S. and Ph.D. in applied mechanics from the California Institute of Technology in 1976 and 1980, respectively. During his more than 30 years at Purdue University, few, if any, individuals have had a greater impact on the university’s undergraduate students and the institu-tion’s commitment to engineering education. Dr. Krousgrill’s efforts in this regard have garnered numerous awards and international accolades. To date, these include the Purdue University School of Mechanical Engineering’s Harry L. Solberg Best Teacher Award (eight times), the Purdue Uni-versity College of Engineering’s Potter Best Teacher Award (four times), the Purdue University Murphy Best Teacher Award, the 2010 Purdue University Helping Students Learn Award, the 2010 Purdue Alumni Association Special Boilermaker Award and the American Society of Engineering Education’s 2011 Archie Higdon Distinguished Educator Award – the de facto lifetime achieve-ment award for educational accomplishments in the field of mechanics. In January 2018, it was announced that Dr. Krousgrill had been awarded the named 150th Anniversary Professorship by Purdue University. Outside of the classroom, Dr. Krousgrill conducts research in the general areas of dynamics and mechanical vibration.
Jeffrey F. Rhoads: Jeffrey F. Rhoads is a Professor in the School of Mechanical Engineering at Purdue University and is affiliated with both the Birck Nanotechnology Center and Ray W. Herrick Laboratories at the same institution. He also serves as the Director of Practice for MEERCat Purdue: The Mechanical Engineering Education Research Center at Purdue University and the Associate Director of PERC: The Purdue Energetics Research Center. Dr. Rhoads received his B.S., M.S., and Ph.D. degrees, each in mechanical engineering, from Michigan State University in 2002, 2004, and 2007, respectively. Dr. Rhoads’ current research interests include the predictive design, analysis, and implementation of resonant micro/nanoelectromechanical systems (MEMS/NEMS) for use in chemical and biological sensing, electromechanical signal processing, and computing; the dynamics of parametrically-excited systems and coupled oscillators; the thermomechanics of energetic materials (including explosives, pyrotechnics, and propellants); additive manufacturing; and mechanics education. Dr. Rhoads is a Member of the American Society for Engineering Education (ASEE) and a Fellow of the American Society of Mechanical Engineers (ASME), where he serves on the Design Engineering Division’s Technical Committee on Vibration and Sound. Dr. Rhoads is a recipient of numerous research and teaching awards, including the National Science Foundation’s Faculty Early Career Development (CAREER) Award; the Purdue University School of Mechanical Engineering’s Harry L. Solberg Best Teacher Award (twice), the Robert W. Fox Outstanding Instructor Award, the and B.F.S. Schaefer Outstanding Young Faculty Scholar Award; the ASEE Mechanics Division’s Ferdinand P. Beer and E. Russell Johnston, Jr. Outstanding New Mechanics Educator Award; and the ASME C. D. Mote Jr., Early Career Award. In 2014, Dr. Rhoads was included in ASEE Prism Magazine’s 20 Under 40.
Mechanical Vibrations: A Lecturebook introduces the analysis of mechanical vibration systems by progressing from the fundamental equations of motion for discrete systems to the study of free and forced vibration responses in both discrete and continuous systems. It also covers practical applications and approximate solution methods used in vibration analysis. The appendices provide supporting material in calculus, complex numbers, relevant mathematical functions, dynamics, linear algebra, operator self-adjointness, a proof related to Lagrange’s equations, and transmissibility ratios.
About the Authors
Chapter I Equations of Motion for Discrete Systems
Chapter II Free Response of Discrete Systems
Chapter III Free Response of Continuous Systems
Chapter IV Forced Response of Discrete Systems
Chapter V Applications and Approximate Methods
Appendices
Appendix A: A Brief Review of Some Calculus Basics
Appendix B: Some Basic Operations with Complex Numbers
Appendix C: Functions Relevant to Vibration Analysis
Appendix D: Some Results from Dynamics
Appendix E: Some Results from Linear Algebra
Appendix F: Determining the Self-Adjointness of an Operator
Appendix G: A Needed Proof for Lagrange’s Equations
Appendix H: Transmissibility Ratios
Charles M. Krousgrill: Charles M. Krousgrill is a Professor in the School of Mechanical Engineer-ing at Purdue University. He received his M.S. in mechanical engineering from Purdue University in 1975, and his M.S. and Ph.D. in applied mechanics from the California Institute of Technology in 1976 and 1980, respectively. During his more than 30 years at Purdue University, few, if any, individuals have had a greater impact on the university’s undergraduate students and the institu-tion’s commitment to engineering education. Dr. Krousgrill’s efforts in this regard have garnered numerous awards and international accolades. To date, these include the Purdue University School of Mechanical Engineering’s Harry L. Solberg Best Teacher Award (eight times), the Purdue Uni-versity College of Engineering’s Potter Best Teacher Award (four times), the Purdue University Murphy Best Teacher Award, the 2010 Purdue University Helping Students Learn Award, the 2010 Purdue Alumni Association Special Boilermaker Award and the American Society of Engineering Education’s 2011 Archie Higdon Distinguished Educator Award – the de facto lifetime achieve-ment award for educational accomplishments in the field of mechanics. In January 2018, it was announced that Dr. Krousgrill had been awarded the named 150th Anniversary Professorship by Purdue University. Outside of the classroom, Dr. Krousgrill conducts research in the general areas of dynamics and mechanical vibration.
Jeffrey F. Rhoads: Jeffrey F. Rhoads is a Professor in the School of Mechanical Engineering at Purdue University and is affiliated with both the Birck Nanotechnology Center and Ray W. Herrick Laboratories at the same institution. He also serves as the Director of Practice for MEERCat Purdue: The Mechanical Engineering Education Research Center at Purdue University and the Associate Director of PERC: The Purdue Energetics Research Center. Dr. Rhoads received his B.S., M.S., and Ph.D. degrees, each in mechanical engineering, from Michigan State University in 2002, 2004, and 2007, respectively. Dr. Rhoads’ current research interests include the predictive design, analysis, and implementation of resonant micro/nanoelectromechanical systems (MEMS/NEMS) for use in chemical and biological sensing, electromechanical signal processing, and computing; the dynamics of parametrically-excited systems and coupled oscillators; the thermomechanics of energetic materials (including explosives, pyrotechnics, and propellants); additive manufacturing; and mechanics education. Dr. Rhoads is a Member of the American Society for Engineering Education (ASEE) and a Fellow of the American Society of Mechanical Engineers (ASME), where he serves on the Design Engineering Division’s Technical Committee on Vibration and Sound. Dr. Rhoads is a recipient of numerous research and teaching awards, including the National Science Foundation’s Faculty Early Career Development (CAREER) Award; the Purdue University School of Mechanical Engineering’s Harry L. Solberg Best Teacher Award (twice), the Robert W. Fox Outstanding Instructor Award, the and B.F.S. Schaefer Outstanding Young Faculty Scholar Award; the ASEE Mechanics Division’s Ferdinand P. Beer and E. Russell Johnston, Jr. Outstanding New Mechanics Educator Award; and the ASME C. D. Mote Jr., Early Career Award. In 2014, Dr. Rhoads was included in ASEE Prism Magazine’s 20 Under 40.