Vibration of Structures and Machines Practical Aspects

The aim of this book is to address important practical aspects of nonlinear vibration analysis. It presents cases rarely discussed in the existing literature on vibration that are problems of considerable interest for researchers and practical engineers, such as rotor dynamics and torsional vibration of engines. The book can be used not only as a reference, but also as a graduate-level text, as it develops the subject from its foundations and contains problems and solutions for each chapter. The book begins with a discussion of vibrations in linear systems with one degree of freedom, providing a mathematical and physical basis for the subsequent chapters. Linear systems with many degrees of freedom serve to introduce the modal analysis of vibrations as well as some useful computational procedures. The book then turns to continuous linear systems, discussing both analytical solutions that provide physical insights as well as discretization techniques that supply tools for actual computation. The discussion of nonlinear vibrations includes a treatment of chaotic vibrations and other new insights. The book concludes with detailed discussions of the dynamics of rotating and reciprocating machinery. In this new edition the notation has been modernized, the classical approach to vibration and the modern approach through dynamical systems theory have been integrated; the material on control and active systems has been completely rewritten and material relevant to mechatronics has been added.

1 Discrete Linear Systems.- 1.1 Systems with a single degree of freedom.- 1.2 Systems with many degrees of freedom.- 1.3 Lagrange equations.- 1.4 State space.- 1.5 Free behaviour.- 1.6 Uncoupling of the equations of motion: Space of the configurations.- 1.7 Uncoupling of the equations of motion: State space.- 1.8 Excitation due to the motion of the constraints..- 1.9 Forced oscillations with harmonic excitation.- 1.10 Systems with structural damping.- 1.11 Systems with frequency-dependent parameters...- 1.12 Coordinate transformation based on Ritz vectors..- 1.13 Structural modification.- 1.14 Parameter identification.- 1.15 Laplace transforms, block diagrams, and transfer functions.- 1.16 Response to nonharmonic excitation.- 1.17 Short account of random vibrations.- 1.18 Concluding examples.- 1.19 Exercises.- 2 Continuous Linear Systems.- 2.1 General considerations.- 2.2 Beams and bars.- 2.3 Flexural vibration of rectangular plates.- 2.4 Propagation of elastic waves in taut strings and pipes.- 2.5 The assumed-modes methods.- 2.6 Lumped-parameters methods.- 2.7 The finite element method.- 2.8 Reduction of the number of degrees of freedom...- 2.9 Exercises.- 3 Nonlinear Systems.- 3.1 Linear versus nonlinear systems.- 3.2 Equation of motion.- 3.3 Free oscillations of the undamped system.- 3.4 Forced oscillations of the undamped system.- 3.5 Free oscillations of the damped system.- 3.6 Forced oscillations of the damped system.- 3.7 Parametrically excited systems.- 3.8 An outline of chaotic vibrations.- 3.9 Exercises.- 4 Dynamic Behaviour of Rotating Machinery.- 4.1 Rotors and structures.- 4.2 Fields of instability.- 4.3 The linear Jeffcott rotor.- 4.4 Model with four degrees of freedom: Gyroscopic effect.- 4.5 Dynamic study of rotors with many degrees of freedom.- 4.6 Nonisotropic systems.- 4.7 Introduction to nonlinear rotor dynamics.- 4.8 Rotors on hydrodynamic bearings (oil whirl and oil whip).- 4.9 Flexural vibration dampers.- 4.10 Signature of rotating machinery.- 4.11 Rotor balancing.- 4.12 Exercises.- 5 Dynamic Problems of Reciprocating Machines.- 5.1 Specific problems of reciprocating machines.- 5.2 Equivalent system for the study of torsional vibrations.- 5.3 Computation of the natural frequencies.- 5.4 Forced vibrations.- 5.5 Torsional instability of crank mechanisms.- 5.6 Dampers for torsional vibrations.- 5.7 Experimental measurement of torsional vibrations.- 5.8 Axial vibrations of crankshafts.- 5.9 Short outline on balancing of reciprocating machines.- 5.10 Exercises.- 6 Short Outline on Controlled and Active Systems.- 6.1 General considerations.- 6.2 Control systems.- 6.3 Controlled linear systems.- 6.4 Modal approach to structural control.- 6.5 Dynamic study of rotors on magnetic bearings.- 6.6 Exercises.- A Solution Methods.- A.1 General considerations.- A.2 Solution of linear sets of equations.- A.3 Computation of eigenfrequencies.- A.4 Solution of nonlinear sets of equations.- A.5 Numerical integration in time of the equation of motion.