Vibrations in Mechanical Systems - Maurice Roseau

Vibrations in Mechanical Systems

Analytical Methods and Applications

(Autor)

Buch | Softcover
XIV, 515 Seiten
2011 | 1984
Springer Berlin (Verlag)
978-3-642-64879-3 (ISBN)
117,69 inkl. MwSt
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The familiar concept described by the word "vibrations" suggests the rapid alternating motion of a system about and in the neighbourhood of its equilibrium position, under the action of random or deliberate disturbing forces. It falls within the province of mechanics, the science which deals with the laws of equilibrium, and of motion, and their applications to the theory of machines, to calculate these vibrations and predict their effects. While it is certainly true that the physical systems which can be the seat of vibrations are many and varied, it appears that they can be studied by methods which are largely indifferent to the nature of the underlying phenomena. It is to the development of such methods that we devote this book which deals with free or induced vibrations in discrete or continuous mechanical structures. The mathematical analysis of ordinary or partial differential equations describing the way in which the values of mechanical variables change over the course of time allows us to develop various theories, linearised or non-linearised, and very often of an asymptotic nature, which take account of conditions governing the stability of the motion, the effects of resonance, and the mechanism of wave interactions or vibratory modes in non-linear 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.-

Erscheint lt. Verlag 6.10.2011
Übersetzer H.L.S. Orde
Zusatzinfo XIV, 515 p.
Verlagsort Berlin
Sprache englisch
Maße 178 x 254 mm
Gewicht 995 g
Themenwelt Naturwissenschaften Physik / Astronomie Allgemeines / Lexika
Schlagworte Complex System • eigenfrequency • eigenvalue • Elasticity • Equilibrium • Invariant • Kinematics • linear differential equation • linear oscillation • Mechanics • Potential • reflection • Relative Motion • scattering • Solution • Vibration
ISBN-10 3-642-64879-7 / 3642648797
ISBN-13 978-3-642-64879-3 / 9783642648793
Zustand Neuware
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