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Abstrak :
This book can be utilized for a variety of courses, including junior and senior-level vibration and linear mechanical analysis courses. The author connects, by means of a rigorous, yet intuitive approach, the theory of vibration with the more general theory of systems. The book features : aseven-step modeling technique that helps structure the rather unstructured process of mechanical-system modeling, a system-theoretic approach to deriving the time response of the linear mathematical models of mechanical systems, the modal analysis and the time response of two-degree-of-freedom systems. The first step on the long way to the more elaborate study of multi-degree-of-freedom systems, using the Mohr circle, simple, yet powerful simulation algorithms that exploit the linearity of the system for both single- and multi-degree-of-freedom systems, examples and exercises that rely on modern computational toolboxes for both numerical and symbolic computations as well as a Solutions Manual for instructors, with complete solutions of a sample of end-of-chapter exercises. Chapters 3 and 7, on simulation, include in each “Exercises” section a set of miniprojects that require code-writing to implement the algorithms developed in these chapters.

Abstrak :
Energy methods in dynamics is a textbook based on the lectures given by the first author at Ruhr University Bochum, Germany. Its aim is to help students acquire both a good grasp of the first principles from which the governing equations can be derived, and the adequate mathematical methods for their solving. Its distinctive features, as seen from the title, lie in the systematic and intensive use of Hamilton's variational principle and its generalizations for deriving the governing equations of conservative and dissipative mechanical systems, and also in providing the direct variational-asymptotic analysis, whenever available, of the energy and dissipation for the solution of these equations. It demonstrates that many well-known methods in dynamics like those of Lindstedt-Poincare, Bogoliubov-Mitropolsky, Kolmogorov-Arnold-Moser (KAM), Wentzel–Kramers–Brillouin (WKB), and Whitham are derivable from this variational-asymptotic analysis. This second edition includes the solutions to all exercises as well as some new materials concerning amplitude and slope modulations of nonlinear dispersive waves.

Abstrak :
This monograph presents an introduction to Harmonic Balance for nonlinear vibration problems, covering the theoretical basis, its application to mechanical systems, and its computational implementation. Harmonic Balance is an approximation method for the computation of periodic solutions of nonlinear ordinary and differential-algebraic equations. It outperforms numerical forward integration in terms of computational efficiency often by several orders of magnitude. The method is widely used in the analysis of nonlinear systems, including structures, fluids and electric circuits. The book includes solved exercises which illustrate the advantages of Harmonic Balance over alternative methods as well as its limitations. The target audience primarily comprises graduate and post-graduate students, but the book may also be beneficial for research experts and practitioners in industry.

Abstrak :
In many plants, vibration and noise problems occur due to fluid flow, which can greatly disrupt smooth plant operations. These flow-related phenomena are called flow-induced vibration. This book explains how and why such vibrations happen and provides hints and tips on how to avoid them in future plant design. The world-leading author team doesn?t assume prior knowledge of mathematical methods and provides the reader with information on the basics of modeling. The book includes several practical examples and thorough explanations of the structure, the evaluation method and the mechanisms to aid understanding of flow-induced vibrations.

Abstrak :
Mathematics is a grand subject in the way it can be applied to various problems in science and engineering. To use mathematics, one needs to understand the physical context. The author uses mathematical techniques along with observations and experiments to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow. Equal emphasis is placed on the mathematical formulation of the problem and the interpretation of the results. In the sections on mechanical vibrations and population dynamics, the author emphasizes the nonlinear aspects of ordinary differential equations and develops the concepts of equilibrium solutions and their stability. He introduces phase plane methods for the nonlinear pendulum and for predator-prey and competing species models. Haberman develops the method of characteristics to analyze the nonlinear partial differential equations that describe traffic flow. Fan-shaped characteristics describe the traffic situation that occurs when a traffic light turns green and shock waves describe the effects of a red light or traffic accident. Although it was written over 20 years ago, this book is still relevant. It is intended as an introduction to applied mathematics, but can be used for undergraduate courses in mathematical modeling or nonlinear dynamical systems or to supplement courses in ordinary or partial differential equations.