Basic Mechanical Vibrations

Basic Mechanical Vibrations

1st Edition - May 29, 1985

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  • Author: A J Pretlove
  • eBook ISBN: 9781483140612

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BASIC Mechanical Vibrations deals with vibrations and combines basic theory with the development of useful computer programs to make design calculations. The programs in the book are written in BASIC. This book is comprised of six chapters and begins with a brief introduction to computing, with special emphasis on the fundamentals of the BASIC computer language. The chapters that follow give concise elements of vibration theory followed by problem solving examples making use of BASIC programs. The vibration analysis of engineering systems, which may be modeled by a single degree of freedom, is presented. Simple systems with damping and no damping are considered, along with systems having two and several degrees of freedom. The final chapter is concerned with bending vibrations. The text includes some subroutines for performing simple matrix operations on two-dimensional arrays that can be used in vibration calculations. This monograph will be useful to engineers who need to make vibration design calculations and to students of mechanical engineering.

Table of Contents

  • Preface

    1 The BASIC Computer Language

    1.1 Computer Structure

    1.2 Peripherals

    1.3 Execution of BASIC Programs

    1.4 BASIC Programs

    2 Simple Systems with no Damping

    Essential Theory

    2.1 Equation of Free Motion

    2.2 Conservation of Energy

    2.3 Forced Motion: Resonance

    2.4 Earth Motion

    Worked Examples

    2.1 Compound Spring Stiffnesses

    2.2 Natural Frequency Calculation

    2.3 Forced Harmonic Motion

    2.4 Data Analysis from a Bridge Experiment

    2.5 Vibration Isolation


    3 Simple Systems with Damping

    Essential Theory

    3.1 Equation of Free Motion

    3.2 The Logarithmic Decrement

    3.3 Impulse Response Function

    3.4 Equation of Forced Motion

    3.5 Fourier Series Analysis

    3.6 Transient Forcing

    3.7 Rotating Machinery

    3.8 Earth Motion

    Worked Examples

    3.1 Quadratic Equations: Damping Ratio and Natural Frequency

    3.2 Polar Response Diagrams

    3.3 Transient Forcing: Step-By-Step Integration

    3.4 Transient Forcing: Duhamel's Integral


    4 Two Degree of Freedom Systems

    Essential Theory

    4.1 The Equation of Free Motion without Damping

    4.2 Coupling

    4.3 Principal Coordinates

    4.4 Damping and Stability

    4.5 Forced Vibration: the Vibration Absorber

    Worked Examples

    4.1 Vibration Properties of an Undamped 2-DOF System

    4.2 Natural Frequencies of a System with Vibration Absorber

    4.3 Free Motion of an Undamped 2-DOF System

    4.4 Forced Vibration of a Damped 2-DOF System


    5 Systems with Several Degrees of Freedom

    Essential Theory

    5.1 Stiffness Formulation

    5.2 Flexibility Formulation

    5.3 Simple Solutions to the Eigenvalue Problem

    5.4 Modal Orthogonality

    5.5 Forced Motion

    Worked Examples

    5.1 Matrix Multiplication

    5.2 Matrix Inversion

    5.3 Iteration Method for Eigenvalues

    5.4 Harmonic Forced Motion of an Undamped System


    6 Bending Vibrations

    Essential Theory

    6.1 The Differential Equation of Motion for a Uniform Beam

    6.2 Approximate Solution by Rayleigh's Method

    Worked Examples

    6.1 Natural Frequencies of Uniform Beams

    6.2 Mode Shapes for Uniform Beams

    6.3 Polynomials for Rayleigh's Method


    Further Reading


Product details

  • No. of pages: 128
  • Language: English
  • Copyright: © Butterworth-Heinemann 1985
  • Published: May 29, 1985
  • Imprint: Butterworth-Heinemann
  • eBook ISBN: 9781483140612

About the Author

A J Pretlove

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