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Nonliear Vibrations- Incremental Harmonic Balance Method

  1. Nov 4, 2013 #1
    1. The problem statement, all variables and given/known data
    Consider the van del Pol equation
    [tex]\ddot{u}-ε(1-u^2)\dot{u}+u=0[\tex]
    Determine the limit cycle for ε=1 using the incremental harmonic balance method. Validate the result using numerical integration (e.g., Runge Kutta).



    2. Relevant equations
    It's incremental harmonic balance method. It's basically Newton-Raphson then a Galerkin's Procedure. I have a paper that describes the general procedure, but I can't even wrap my head around it. How are the limits for the Nc and Ns chosen or defined?

    There are too many equations for me to define here. I'm assuming you know what they are if you know IHB.


    3. The attempt at a solution

    The paper has already laid out the nondimensionlized equation and replaced x=x+Δx and ω=ω+Δω. I know it says not to say this, but I don't really have the background to solve something like this. I'm an undergraduate in a graduate class and it has gotten to a point where I just don't have the background. I've tried to find examples of someone actually carrying out this method step by step but can't find anything.
     
  2. jcsd
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