An introduction to the phenomena which are encountered in systems which vibrate under the influence of parametric and nonlinear effects. These aspects are discussed in the context of mechanical engineering, although applications or circumstances outside mechanical engineering within which particular effects have been observed have been included. The book does not assume prior knowledge of this area and contains some examples of parametric instability problems and aspects of non-linear vibrations. Several equations, including the virtual work and Lagrange equations, are analyzed and derived and there is a brief review of parametric systems, with references for further reading. There are also sections dealing with the kinematics and the derivation of the equations of motion for a parametrically excited cantilever beam where combined bending and torsional motion is possible and a final section on chaos is included.
...recommend this book to the applied community as a valuable source of practical examples of parametric excitations, treated in a modern fashion. - Mathematical Reviews; [Cartmell] has successfully presented the usually complicated and difficult subjects of parametric and nonlinear vibrations in a concise, clear and easy-to-understand manner - Choice
Part 1 Linear vibrations in mechanical engineering: classification of vibration problems; fundamentals of vibrating mechanical systems; the conservative single degree of freedom model; the non-conservative single degree of freedom model; practical uses for single degree of freedom models; transients and impulses in single degree of freedom systems; systems with more than one degree of freedom; continuous systems. Part 2 Parametric vibrations in linear vibrating systems: stability considerations; some simple physical systems; analysis of governing equations; further investigations into parametric phenomena. Part 3 Non-linear vibrations in forced and parametrically excited systems; large deflection non-linearities; material and structural configuration non-linearities. Part 4 Non-linear vibrations in autoparametric systems: two mode interaction in a coupled beam system; application to vibration absorption; multi-modal autoparametric interactions. Part 5 Phase plane concepts and chaotic vibrations: an introduction to the phase plane; a summary of fundamental phase plane concepts; chaos in vibrating systems.
Number Of Pages: 242
Published: 30th June 1990
Publisher: Chapman and Hall
Country of Publication: GB
Dimensions (cm): 23.5 x 15.88
Weight (kg): 0.45