Haitao Liao
CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.3, pp. 155-187, 2014, DOI:10.3970/cmes.2014.103.155
Abstract The improved constrained optimization harmonic balance method(COHBM) is presented to solve the Duffing oscillator with time delayed term. Within the framework of the proposed method, the analytical gradients of the objective function and nonlinear quality constraints with respect to optimization variables are formulated and the sensitivity information of the Fourier coefficients can also obtained. The general formulas of the geometrically nonlinear and time delayed terms are analytically derived, which makes the calculations of nonlinear differential equations in the frequency domain easily. A stability analysis method based on the analytical formulation of the nonlinear equality constraints is presented for the nonlinear… More >
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