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Linear vibrations is a topic of central interest in numerous fields of engineering and is widely applicable to civil, mechanical, aerospace, and biomedical engineering. This book deals with the elements of the theory of linear vibrations and its applications.The theory of linear vibrations is systematically developed starting from the basics. In a systematic manner, the author deals with single-degree of freedom systems before progressing to the more complex multi-degree of freedom systems. Topics such as Laplace transforms, complex frequency responses, elements of feedback control and aspects of time-delayed control and its applications are discussed at the end. A set of graded problems, to exercise the understanding of the student, is provided at the end of each chapter. Numerous illustrative examples are provided in each chapter alongside the development of the theory. In addition, there are two chapters specifically devoted to illustrative examples and applications.By including topics from stability and control theory, the book aims to provide the student with a broader view of the application areas to which the theory is germane. It is meant to be a text for a one semester, first course, on the subject, suitable for seniors and/or first year graduate students in engineering. Applied mathematicians will also find this book useful.Linear vibrations is a topic of central interest in numerous fields of engineering and is widely applicable to civil, mechanical, aerospace, and biomedical engineering. This book deals with the elements of the theory of linear vibrations and its applications.
The theory of linear vibrations is systematically developed starting from the basics. In a systematic manner, the author deals with single-degree of freedom systems before progressing to the more complex multi-degree of freedom systems. Topics such as Laplace transforms, complex frequency responses, elements of feedback control and aspects of time-delayed control and its applications are discussed at the end. A set of graded problems, to exercise the understanding of the student, is provided at the end of each chapter. Numerous illustrative examples are provided in each chapter alongside the development of the theory. In addition, there are two chapters specifically devoted to illustrative examples and applications.
By including topics from stability and control theory, the book aims to provide the student with a broader view of the application areas to which the theory is germane. It is meant to be a text for a one semester, first course, on the subject, suitable for seniors and/or first year graduate students in engineering. Applied mathematicians will also find this book useful.
List of contents
Basic Mechanics, Single Degree of Freedom Systems.- Undamped Single Degree of Freedom (SDOF) Systems, Free Vibrations.- Damped SDOF Systems, Free Vibrations.- Harmonic Excitation of Damped SDOF Systems, Resonance.- Isolation of Instruments and Foundations, Motion Sensing Instrumentation.- Response of Damped SDOF Systems to General Excitations.- Damping in Structural and Mechanical Systems, Viscous, Structural, Bouc-Wen, and Coulomb Damping.- Illustrative Examples and Applications of SDOF Systems.- Laplace Transforms, Complex Frequency Response; Elements of Structural Feeddback Control, Time-Delayed Control.- Two Degree of Freedom Systems, Eigenvalues, Mode Shapes, Modal Frequencies.- Classically and non-classically Damped Multi-degree of Freedom Systems(MDOF).- generalized coordinates, Lagrange's Equations, Linearization, and Equivalent linearization; Stability, Examples.- Elements of Feedback Control of MDOF Systems.- Illustrative Examples and Applications of MDOF Systems.- An Introduction to Continuous Systems
