Singular Equations of Waves and Vibrations
Singular Equations of Waves and Vibrations

Author: Marian Apostol

Publisher: Cambridge Scholars Publishing

Published: 2023-04-17

Total Pages: 199

ISBN-13: 1527504972

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This book presents an exploration of the wave and vibration equation in one, two and three dimensions, with emphasis on singular solutions. The distinction between the wave treatment and the vibration treatment is particularly discussed with the causality principle being the leading principle for waves in this context. The necessity of regularization of the singular solutions is presented whilst the scattered waves are differentiated from the reflected (and refracted) waves, according to Huygens principle. The physical content of the wave equation is underlined. Relevant applications are included and some more exotic phenomena are discussed, such as pulses, tsunami and storm breakers, the ringing of bells and the collapsing of towers, and classical waves and vibrations in an elastic half-space or a sphere. This book is oriented to students, instructors, teachers, researchers in physics and applied mathematics, as well as engineers and other practitioners of mathematical physics.

Partial Differential Equations
Partial Differential Equations

Author: Walter A. Strauss

Publisher: John Wiley & Sons

Published: 2007-12-21

Total Pages: 467

ISBN-13: 0470054565

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Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Nonlinear Oscillations of Hamiltonian PDEs
Nonlinear Oscillations of Hamiltonian PDEs

Author: Massimiliano Berti

Publisher: Springer Science & Business Media

Published: 2007-10-01

Total Pages: 191

ISBN-13: 0817646809

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Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. The text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.

Almost Periodic Oscillations and Waves
Almost Periodic Oscillations and Waves

Author: Constantin Corduneanu

Publisher: Springer Science & Business Media

Published: 2009-04-29

Total Pages: 313

ISBN-13: 0387098194

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This text is well-designed with respect to the exposition from the preliminary to the more advanced and the applications interwoven throughout. It provides the essential foundations for the theory as well as the basic facts relating to almost periodicity. In six structured and self-contained chapters, the author unifies the treatment of various classes of almost periodic functions, while uniquely addressing oscillations and waves in the almost periodic case. This is the first text to present the latest results in almost periodic oscillations and waves. The presentation level and inclusion of several clearly presented proofs make this work ideal for graduate students in engineering and science. The concept of almost periodicity is widely applicable to continuuum mechanics, electromagnetic theory, plasma physics, dynamical systems, and astronomy, which makes the book a useful tool for mathematicians and physicists.

Time-dependent and Vibration Problems
Time-dependent and Vibration Problems

Author: Carlos A. Brebbia

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 273

ISBN-13: 364282398X

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This series has been developed in response to the interest shown in boundary ele ments by scientists and engineers. Whilst Volume 1 was dedicated to basic principles and applications, this book is concerned with the state of the art in the solution of time-dependent problems. Since papers have recently been published on this im portant topic it is time to produce a work of a more permanent nature. The volume begins with a chapter on the Fundamentals of Boundary Integral Equation Methods in Elastodynamics. After reviewing the basic equations of elasto dynamics, the wave equation and dynamic reciprocal theorems are stated and the direct and indirect boundary element formulations are presented. Eigenvalue problems are discussed together with the case of the Fourier transformations. Several applications illustrate the effectiveness of the technique for engineering. Chapter 2 examines some of the various boundary integral equation formulations available for elastodynamic problems. In particular the displacement-traction for mulation is compared with the displacement-potential case. The special character istics of the elastodynamics fundamental solutions are discussed in detail and a criti cal comparison with the elastostatics case is presented. While the chapter is not meant to be a complete review of the work in the field, the original presentation of the problem and the suggestions for further work make an important contribu tion to the development of the method.

Regular and Chaotic Oscillations
Regular and Chaotic Oscillations

Author: Polina S. Landa

Publisher: Springer Science & Business Media

Published: 2012-11-12

Total Pages: 401

ISBN-13: 3540452524

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This text maps out the modern theory of non-linear oscillations. The material is presented in a non-traditional manner and emphasises the new results of the theory - obtained partially by the author, who is one of the leading experts in the area. Among the topics are: synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration on modification of characteristics and behaviour of the non-linear systems.

Nonlinear Physics, from Vibration Control to Rogue Waves and Beyond
Nonlinear Physics, from Vibration Control to Rogue Waves and Beyond

Author: Attilio Maccari

Publisher: Cambridge Scholars Publishing

Published: 2023-02-13

Total Pages: 309

ISBN-13: 1527588181

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This textbook is devoted to nonlinear physics, using the asymptotic perturbation method as a mathematical tool. The theory is developed systematically, starting with nonlinear oscillators, limit cycles and their bifurcations, followed by iterated nonlinear maps, continuous systems, nonlinear partial differential equations (NPDEs) and culminating with infinite-period bifurcation in the nonlinear Schrodinger equation and fractal and chaotic solutions in NPDEs. A remarkable feature of the book is its emphasis on applications. It offers several examples, and the scientific background is explained at an elementary level and closely integrated with the mathematical theory. In addition, it is ideal for an introductory course at the senior or first-year graduate level.

Vibration of Continuous Systems
Vibration of Continuous Systems

Author: Singiresu S. Rao

Publisher: John Wiley & Sons

Published: 2007-02-09

Total Pages: 744

ISBN-13: 0471771716

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Broad, up-to-date coverage of advanced vibration analysis by the market-leading author Successful vibration analysis of continuous structural elements and systems requires a knowledge of material mechanics, structural mechanics, ordinary and partial differential equations, matrix methods, variational calculus, and integral equations. Fortunately, leading author Singiresu Rao has created Vibration of Continuous Systems, a new book that provides engineers, researchers, and students with everything they need to know about analytical methods of vibration analysis of continuous structural systems. Featuring coverage of strings, bars, shafts, beams, circular rings and curved beams, membranes, plates, and shells-as well as an introduction to the propagation of elastic waves in structures and solid bodies-Vibration of Continuous Systems presents: * Methodical and comprehensive coverage of the vibration of different types of structural elements * The exact analytical and approximate analytical methods of analysis * Fundamental concepts in a straightforward manner, complete with illustrative examples With chapters that are independent and self-contained, Vibration of Continuous Systems is the perfect book that works as a one-semester course, self-study tool, and convenient reference.

Singular Equations of Waves and Vibrations
Singular Equations of Waves and Vibrations

Author: MARIAN. APOSTOL

Publisher:

Published: 2023-07

Total Pages: 0

ISBN-13: 9781527504967

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This book presents an exploration of the wave and vibration equation in one, two and three dimensions, with emphasis on singular solutions. The distinction between the wave treatment and the vibration treatment is particularly discussed with the causality principle being the leading principle for waves in this context. The necessity of regularization of the singular solutions is presented whilst the scattered waves are differentiated from the reflected (and refracted) waves, according to Huygens principle. The physical content of the wave equation is underlined. Relevant applications are included and some more exotic phenomena are discussed, such as pulses, tsunami and storm breakers, the ringing of bells and the collapsing of towers, and classical waves and vibrations in an elastic half-space or a sphere. This book is oriented to students, instructors, teachers, researchers in physics and applied mathematics, as well as engineers and other practitioners of mathematical physics.