
11Vibrations and Stability at the Bulk and at the Interface
The idea of Lindstedt’s method is in presenting the frequency in the form of
2
3
…ω=ω+εω +ε ω+εω +
(2.31)
and obtaining the iterative equations for the frequency in addition to those
for x. Many other methods for non-linear vibration analysis are discussed in
the literature (Rand 2005; Meirovitch 1986).
2.4 Bifurcations, Catastrophes, and Chaos
As we discussed in the preceding section, there are several qualitative ways
in which a system can become unstable. There is a “soft” loss of stability
when the state of equilibrium bifurcates and adjacent states become new
stable states of equi ...