me863outline_s04 - ME863NonlinearOscillationsSpring2004...

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ME 863 Nonlinear Oscillations Spring 2004 Outline of the Lecture Notes: 1. Introduction to Nonlinear Vibration 2. Linearization Time-variant autonomous systems Local stability of hyperbolic (real parts of eigenvalues are nonzero) fixed point governed by eigenvalues (NM 3.2.1) Phase portraits 3. Conservative Systems: Period of Free Vibration Phase portraits, x' vs. x by energy methods (NM 1.2, 2.1-2. .2) Elliptic integral method for period (NM 2.2) Regular perturbation fails: secular terms (NM 2.3.1) Lindstedt's method: allow frequency to be amplitude dependent (NM 2.3.2) Harmonic-balance method (NM 2.3.4) Period indeed is amplitude dependent (NM 2.4) 4. Limit Cycles Polar coordinates Hopf bifurcation Multiple scales introduced in analyzing Rayleigh's equation Averaging: variation of constants viewpoint (NM 3.3.4) Relaxation oscillations (NM 3.3.4, 3.5) Friction-induced vibration: piecewise linearity and stick-slip Bendixson's criterion for the nonexistence of limit cycles
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me863outline_s04 - ME863NonlinearOscillationsSpring2004...

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