In this paper, Harmonic Balance based methods, namely Incremental Harmonic Balance Method and the method of Harmonic Balance with Alternating Frequency and Time traditionally used to compute periodic orbits of smooth nonlinear dynamical systems are employed to investigate dynamics of a non-smooth system, a piecewise linear oscillator with a play. The Incremental Harmonic Balance Method was used to compute the period one orbits including those exhibiting grazing and large impacts. The method of Harmonic Balance with Alternating Frequency and Time was implemented to calculate more complex orbits and multi stability. A good agreement between obtained approximate solutions and numerically calculated responses indicates robustness of the implemented HBMs, which should allow to effectively study the global dynamics of non-smooth systems.
|Number of pages||18|
|Journal||Communications in Nonlinear Science & Numerical Simulation|
|Early online date||4 Feb 2022|
|Publication status||Published - 1 May 2022|
The authors would like to acknowledge the financial support by NNSF of China (Nos. 11372282 and 10702065) and Scholarship of China; The National Secretariat of Science, Technology and Inno- vation of Ecuador (SENESCYT); The Escuela Superior Politcnica del Litoral of Ecuador (ESPOL).
- Piecewise linear oscillator with play
- Incremental Harmonic Balance Method
- Harmonic Balance with Alternative Frequency and Time
- Computation of periodic orbits