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The Mechanics Of Nonlinear Systems With Internal Resonances
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One of the most important features of nonlinear systems with several
degrees of freedom is the presence of internal resonances at certain
relations between natural frequencies of different modes. This
monograph is the first book devoted predominantly to internal
resonances in different mechanical systems including those of
practical importance.
The main purpose is to consider the internal resonances from the
general point of view and to elucidate their role in applied nonlinear
dynamics by using an efficient approach based on introducing the
complex representation of equations of motion (together with the
multiple scale method). Considered here are autonomous and
nonautonomous discrete two-degree-of-freedom systems, infinite chains
of particles, and continuous systems, including circular rings and
cylindrical shells. Specific attention is paid to the case of
one-to-one internal resonance in systems with cubic
nonlinearities. Steady-state and nonstationary regimes of motion,
interaction of the internal and external resonances at forced
oscillations, and bifurcations of steady-state modes and their
stability are systematically studied.
less
World Scientific; May 2006
276 pages; ISBN 9781860946820
Read online, or download in secure PDF format
276 pages; ISBN 9781860946820
Read online, or download in secure PDF format
