Vibration of Structures and Machines

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.