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2020 | Buch

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Mechanical Vibrations

An Introduction

verfasst von: Prof. György Szeidl, Dr. László Péter Kiss

Verlag: Springer International Publishing

Buchreihe : Foundations of Engineering Mechanics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book presents a unified introduction to the theory of mechanical vibrations. The general theory of the vibrating particle is the point of departure for the field of multidegree of freedom systems. Emphasis is placed in the text on the issue of continuum vibrations. The presented examples are aimed at helping the readers with understanding the theory.This book is of interest among others to mechanical, civil and aeronautical engineers concerned with the vibratory behavior of the structures. It is useful also useful for students from undergraduate to postgraduate level. The book is based on the teaching experience of the authors.

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Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The necessary kinematic relations with an emphasis on rigid body motions are all covered. Then the equivalence of the effective forces to the external forces, the principle of impulse and momentum as well as the principle of work and energy are presented in the text. Proofs are, sometimes, omitted or are left for problems to be solved.

György Szeidl, László Péter Kiss

Chapter 2. Impact

Abstract

The collision between two bodies, which occurs in a very short time period and during which the two bodies exert relatively large impulsive forces on each other (if there are no constraints these forces are much greater than the forces exerted on the two bodies by other bodies—then the effects of the former forces can be neglected) is called impact. The properties of this phenomenon and the solution procedures are covered here.

György Szeidl, László Péter Kiss

Chapter 3. Some Vibration Problems

Abstract

Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. Within the framework of the linear theory the classical vibration problems of single degree of freedom system are considered and the solutions are also presented.

György Szeidl, László Péter Kiss

Chapter 4. Introduction to Multidegree of Freedom Systems

Abstract

Lagrange’s equation of the second are established for a system of particles first. They can, however, be applied to deriving equations of motion for such systems which involve rigid bodies as well. Special emphasis is laid on spring mass systems with two degrees of freedom. Solutions are presented for various free and forced vibration problems concerning systems wit two degrees of freedom. It is also shown how to tune a system to avoid resonance.

György Szeidl, László Péter Kiss

Chapter 5. Some Problems of Multidegree of Freedom Systems

Abstract

The general theory of multidegree of freedom system is considered. The eigenvalue problem that provides the eigenfrequencies for a vibrating finite degree of freedom system is also presented. It is shown what properties these eigenvalue problems have including the fundamental characteristics of the eigenvalues and eigenvectors. Some simple solution procedures are suggested. The concept of the Rayleigh quotient is introduced. Finally the case of forced vibrations is investigated.

György Szeidl, László Péter Kiss

Chapter 6. Some Special Problems of Rotational Motion

Abstract

Special problems of rotational motion. The most important properties of a flywheel, which can be used to store kinetic energy and to make the rotational motion smoother by reducing the speed of fluctuations, are discussed. Stability problems caused by a change in the load torque is also investigated. If the shaft is not rigid further problems occur. Laval’s theorem and the gyroscopic effect of the rotational motion are also considered.

György Szeidl, László Péter Kiss

Chapter 7. Systems with Infinite Degrees of Freedom

Abstract

Vibration problems of systems with infinite degrees of freedom are considered. First the longitudinal vibrations of rods. Then solutions are presented for the transverse vibration of a string and for the torsional vibrations of rods with circular cross section. This is followed by a detailed analysis for the transverse vibrations of beams.

György Szeidl, László Péter Kiss

Chapter 8. Eigenvalue Problems of Ordinary Differential Equations

Abstract

Eigenvalue problem of ordinary differential equations is considered. We present the definition of the Green functions and reduce some eigenvalue problems to homogeneous Fredholm integral equation with the Green function as kernel. A solution algorithm is suggested by the use of which numerical solutions are given for some vibration problems of circular plates subjected to constant radial in plane load and for the vibratory behavior of beams loaded by an axially force.

György Szeidl, László Péter Kiss

Chapter 9. Eigenvalue Problems of Ordinary Differential Equation Systems

Abstract

Eigenvalue problems of ordinary differential equation systems are discussed. The concept of the Green function matrix is introduced. By utilizing the Green function matrices the eigenvalue problems described by ordinary differential equation systems can be reduced to eigenvalue problems governed by homogeneous Fredholm integral equation systems. The solution algorithm presented in Chapter 8 is generalized for such eigenvalue problems. The applications are related to the vibration problems of Timoshenko beams.

György Szeidl, László Péter Kiss

Chapter 10. Eigenvalue Problems Described by Degenerated Systems of Ordinary Differential Equations

Abstract

Vibration problems of curved beams with a centerline of constant radius are governed by degenerated differential equation systems. Here we provide a definition for the Green function matrices concerning the degenerated differential equation systems. These matrices are determined for pinned-pinned, fixed-fixed and pinned-fixed heterogeneous curved beams. By utilizing the Green function matrices the eigenvalue problems that describe the vibratory behavior of these beams are reduced to Fredholm integral equation systems. Numerical solutions are also presented in graphical format.

György Szeidl, László Péter Kiss

Backmatter

Titel: Mechanical Vibrations
verfasst von: Prof. György Szeidl
Dr. László Péter Kiss
Copyright-Jahr: 2020
Verlag: Springer International Publishing
Electronic ISBN: 978-3-030-45074-8
Print ISBN: 978-3-030-45073-1
DOI: https://doi.org/10.1007/978-3-030-45074-8

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