A First Course In Vibrations And Waves

A First Course in Vibrations and Waves

A First Course in Vibrations and Waves

The study of vibrations and waves is central to physics and engineering disciplines.This text contains a detailed treatment of vibrations and waves at an introductory level suitable for second and third year students. It builds on first year physics and emphasizes understanding of vibratory motion and waves based on first principles. Since waves appear in almost all branches of physics and engineering, readers will be exposed to many different types of waves; this study aims to draw together their similarities, by examining them in a common language. The book is divided into three parts: Part I contains a preliminary chapter that serves as a review of relevant ideas of mechanics and complex numbers. Part II is devoted to a detailed discussion of vibrations of mechanical systems. This part covers simple harmonic oscillator, coupled oscillators, normal coordinates, beaded string, continuous string, and Fourier series. It concludes with a presentation of stationary solutions of driven finite systems. Part III is concerned with waves, focusing on the discussion of common aspects of all types of waves, and the applications to sound, electromagnetic, and matter waves are illustrated. Finally, relevant examples are provided at the end of the chapters to illustrate the main ideas, and better the reader's understanding.

Vibrations and Waves in Continuous Mechanical Systems

The subject of vibrations is of fundamental importance in engineering and technology. Discrete modelling is sufficient to understand the dynamics of many vibrating systems; however a large number of vibration phenomena are far more easily understood when modelled as continuous systems. The theory of vibrations in continuous systems is crucial to the understanding of engineering problems in areas as diverse as automotive brakes, overhead transmission lines, liquid filled tanks, ultrasonic testing or room acoustics. Starting from an elementary level, Vibrations and Waves in Continuous Mechanical Systems helps develop a comprehensive understanding of the theory of these systems and the tools with which to analyse them, before progressing to more advanced topics. Presents dynamics and analysis techniques for a wide range of continuous systems including strings, bars, beams, membranes, plates, fluids and elastic bodies in one, two and three dimensions. Covers special topics such as the interaction of discrete and continuous systems, vibrations in translating media, and sound emission from vibrating surfaces, among others. Develops the reader’s understanding by progressing from very simple results to more complex analysis without skipping the key steps in the derivations. Offers a number of new topics and exercises that form essential steppingstones to the present level of research in the field. Includes exercises at the end of the chapters based on both the academic and practical experience of the authors. Vibrations and Waves in Continuous Mechanical Systems provides a first course on the vibrations of continuous systems that will be suitable for students of continuous system dynamics, at senior undergraduate and graduate levels, in mechanical, civil and aerospace engineering. It will also appeal to researchers developing theory and analysis within the field.