TY - JOUR
T1 - Computation of Periodic Orbits for Piecewise Linear Oscillator by Harmonic Balance Methods Communications in Nonlinear Science and Numerical Simulation
AU - Pei, Lijun
AU - Chong Escobar, Antonio Simon
AU - Pavlovskaia, Ekaterina
AU - Wiercigroch, Marian
N1 - Acknowledgments
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).
PY - 2021/12/24
Y1 - 2021/12/24
N2 - 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.
AB - 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.
KW - Piecewise linear oscillator with play
KW - Incremental Harmonic Balance Method
KW - IHBM
KW - Harmonic Balance with Alternative Frequency and Time
KW - HB-AFT
KW - Computation of periodic orbits
M3 - Article
JO - Communications in Nonlinear Science & Numerical Simulation
JF - Communications in Nonlinear Science & Numerical Simulation
SN - 1007-5704
ER -