A symbolic algorithm for the automatic computation of multitone-input harmonic balance equations for nonlinear systems. (English) Zbl 1170.70002
Summary: We develop a symbolic algorithm for the automatic generation of harmonic balance equations for multitone input for a class of nonlinear differential systems with polynomial nonlinearities. Generalized expressions are derived for the construction of balance equations for a defined multitone signal form. Procedures are described for determining combinations for a given output frequency from the desired set obtained from box truncated spectra and their permutations to automate symbolic algorithm. An application of method is demonstrated using the well-known Duffing-van der Pol equation. Then the obtained analytical results are compared with numerical simulations to show the accuracy of the approach. We also investigate the computation times for both the numerical solutions of equations versus the number of frequency components and the symbolic generation of the equations versus the power of nonlinearity.
MSC:
| 70-08 | Computational methods for problems pertaining to mechanics of particles and systems |
| 70K40 | Forced motions for nonlinear problems in mechanics |
| 68W30 | Symbolic computation and algebraic computation |
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