Equivalent Nonlinearization of Nonlinear Systems to Random Excitations
The broadest class of solvable reduced Fokker-Planck equation is given and a new equivalent nonlinear method is presented to obtain an approximate probability density function for the response of a nonlinear oscillator to Gaussian white noise excitations. The method is based on the least meansquare criterion and Euler equation. It is shown that this method, which is simpler and more reasonable, generalizes Caughey’s method and gives the same results as Cai and Lin under purely additive excitations. Examples are given to show the applications of the method. In one of the examples, this method leads to a better approximation than that obtained from the energy dissipation criterion.
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