Vibrations in Mechanical Systems

I. Forced Vibrations in Systems Having One Degree or Two Degrees of Freedom.- Elastic Suspension with a Single Degree of Freedom.- Torsional Oscillations.- Natural Oscillations.- Forced Vibrations.- Vibration Transmission Factor.- Elastic Suspension with Two Degrees of Freedom. Vibration Absorber.- Response Curve of an Elastic System with Two Degrees of Freedom.- Vehicle Suspension.- Whirling Motion of a Rotor-Stator System with Clearance Bearings.- Effect of Friction on the Whirling Motion of a Shaft in Rotation; Synchronous Precession, Self-sustained Precession.- Synchronous Motion.- Self-maintained Precession.- II. Vibrations in Lattices.- A Simple Mechanical Model.- The Alternating Lattice Model.- Vibrations in a One-Dimensional Lattice with Interactive Forces Derived from a Potential.- Vibrations in a System of Coupled Pendulums.- Vibrations in Three-Dimensional Lattices.- Non-Linear Problems.- III. Gyroscopic Coupling and Its Applications.- 1. The Gyroscopic Pendulum.- Discussion of the Linearised System.- Appraisal of the Linearisation Process in the Case of Strong Coupling.- Gyroscopic Stabilisation.- 2. Lagrange's Equations and Their Application to Gyroscopic Systems.- Example: The Gyroscopic Pendulum.- 3. Applications.- The Gyrocompass.- Influence of Relative Motion on the Behaviour of the Gyrocompass.- Gyroscopic Stabilisation of the Monorail Car.- 4. Routh's Stability Criterion.- 5. The Tuned Gyroscope as Part of an Inertial System for Measuring the Rate of Turn.- Kinematics of the Multigimbal Suspension.- a) Orientation of the Rotor.- b) Co-ordinates of an Intermediate Gimbal.- c) Relations Between the Parameters ? and ?.- The Equations of Motion.- Inclusion of Damping Terms in the Equations of Motion.- Dynamic Stability. Undamped System.- Frequencies of Vibrations of the Free Rotor.- Motion of the Free Rotor.- Case of a Multigimbal System Without Damping. The Tune Condition.- Examination of the Two-Gimbal System.- IV. Stability of Systems Governed by the Linear Approximation.- Discussion of the Equation Aq? + ??q? = 0.- Discussion of the Equation Aq? + ??q?+ Kq = 0.- Systems Comprising Both Gyroscopic Forces and Dissipative Forces..- 1. Case E = 0.- A Modified Approach in the Case of Instability.- 2. Case E ? 0.- Eigenmodes.- Rayleigh's Method.- Effect on the Eigenvalues of Changes in Structure.- An Example.- V. The Stability of Operation of Non-Conservative Mechanical Systems.- 1. Rolling Motion and Drift Effect.- 2. Yawing of Road Trailers.- 3. Lifting by Air-Cushion.- The Stationary Regime.- Case of an Isentropic Expansion.- Dynamic Stability.- VI. Vibrations of Elastic Solids.- I. Flexible Vibrations of Beams.- 1. Equations of Beam Theory.- 2. A Simple Example.- 3. The Energy Equation.- 4. The Modified Equations of Beam Theory; Timoshenko's Model.- 5. Timoshenko's Discretised Model of the Beam.- 6. Rayleigh's Method.- 6.1. Some Elementary Properties of the Spaces H1 (0, l), H2(0, l)..- 6.2. Existence of the Lowest Eigenfrequency.- 6.3. Case of a Beam Supporting Additional Concentrated Loads.- 6.4 Intermediate Conditions Imposed on the Beam.- 6.5 Investigation of Higher Frequencies.- 7. Examples of Applications.- 7.1. Beam Fixed at x = 0, Free at x = l.- 7.2. Beam Fixed at Both Ends.- 7.3. Beam Free at Both Ends.- 7.4. Beam Hinged at x = 0, Free at x = l.- 7.5. Beam Fixed at x= 0 and Bearing a Point Load at the Other End.- 7.6. Beam Supported at Three Points.- 7.7. Vibration of a Wedge Clamped at x = 0. Ritz's Method.- 7.8. Vibrations of a Supported Pipeline.- 7.9. Effect of Longitudinal Stress on the Flexural Vibrations of a Beam and Application to Blade Vibrations in Turbomachinery.- 7.10. Vibrations of Interactive Systems.- 8. Forced Vibrations of Beams Under Flexure.- 9. The Comparison Method.- 9.1. The Functional Operator Associated with the Model of a Beam Under Flexure.- 9.2. The Min-Max Principle.- 9.3. Application to Comparison Theorems.- 10. Forced Excitation of a Beam.- 10.1. Fourier's Method.-