The aim of this book is to impart a sound understanding, both physical and mathematical, of the fundamental theory of vibration and its applications. The book presents in a simple and systematic manner techniques that can easily be applied to the analysis of vibration of mechanical and structural systems. Unlike other texts on vibrations, the approach is general, based on the conservation of energy and Lagrangian dynamics, and develops specific techniques from these foundations in clearly understandable stages. Suitable for a one-semester course on vibrations, the book presents new concepts in simple terms and explains procedures for solving problems in considerable detail.
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ISBN-13
978-1-4684-0362-6 (9781468403626)
DOI
10.1007/978-1-4684-0362-6
Schweitzer Klassifikation
1 Introduction.- 1.1 Basic Definitions.- 1.2 Elements of the Vibration Models.- 1.3 Dynamic Equations.- 1.4 Dynamics of Rigid Bodies.- 1.5 Linearization of the Differential Equations.- 1.6 Idealization of Mechanical and Structural Systems.- 2 Solution of the Vibration Equations.- 2.1 Homogeneous Differential Equations.- 2.2 Initial Conditions.- 2.3 Solution of Nonhomogeneous Equations with Constant Coefficients.- 2.4 Stability of Motion.- 3 Free Vibration of Single Degree of Freedom Systems.- 3.1 Free Undamped Vibration.- 3.2 Analysis of the Oscillatory Motion.- 3.3 Stability of Undamped Linear Systems.- 3.4 Torsional Systems.- 3.5 Equivalent Systems.- 3.6 Free Damped Vibration.- 3.7 Logarithmic Decrement.- 3.8 Structural Damping.- 3.9 Coulomb Damping.- 3.10 Negative Damping.- 3.11 Motion Control.- 3.12 Impact Dynamics.- 3.13 Concluding Remarks.- 4 Forced Vibration.- 4.1 Differential Equation of Motion.- 4.2 Forced Undamped Vibration.- 4.3 Resonance and Beating.- 4.4 Forced Vibration of Damped Systems.- 4.5 Rotating Unbalance.- 4.6 Base Motion.- 4.7 Measuring Instruments.- 4.8 Experimental Methods for Damping Evaluation.- 4.9 Concluding Remarks.- 5 Response to Nonharmonic Forces.- 5.1 Periodic Forcing Functions.- 5.2 Fourier Series.- 5.3 Determination of the Fourier Coefficients.- 5.4 Special Cases.- 5.5 Vibration Under Periodic Forcing Functions.- 5.6 Impulsive Motion.- 5.7 Response to an Arbitrary Forcing Function.- 5.8 Computer Methods in Nonlinear Vibration.- 6 Two Degree of Freedom Systems.- 6.1 Free Undamped Vibration.- 6.2 Matrix Equations.- 6.3 Damped Free Vibration.- 6.4 Undamped Forced Vibration.- 6.5 Vibration Absorber of the Undamped System.- 6.6 Forced Vibration of Damped Systems.- 6.7 The Untuned Viscous Vibration Absorber.- 6.8 Concluding Remarks.
