A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the...A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the non- linearity of the airfoil section＇s freeplay. There are two crit- ical speeds in the system, i.e., a lower critical speed, above which the system might generate limit cycle oscillation, and an upper critical one, above which the system will flutter. Then a Poincar6 map is constructed for the limit cycle os- cillations by using piecewise-linear solutions with and with- out contact in the system. Through analysis of the Poincar6 map, a series of equations which can determine the frequen- cies of period-1 limit cycle oscillations at any flight veloc- ity are derived. Finally, these analytic results are compared to the results of numerical simulations, and a good agree- ment is found. The effects of freeplay value and contact stiffness ratio on the limit cycle oscillation are also analyzed through numerical simulations of the original system. More- over, there exist multi-periods limit cycle oscillations and even complicated ＂chaotic＂ oscillations may occur, which are usually found in smooth nonlinear dynamic systems.展开更多
基金supported by the National Science Fund for Distinguished Young Scholars in China(11225212)the Young Teachers' Funds of Hunan Province,China
文摘A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the non- linearity of the airfoil section＇s freeplay. There are two crit- ical speeds in the system, i.e., a lower critical speed, above which the system might generate limit cycle oscillation, and an upper critical one, above which the system will flutter. Then a Poincar6 map is constructed for the limit cycle os- cillations by using piecewise-linear solutions with and with- out contact in the system. Through analysis of the Poincar6 map, a series of equations which can determine the frequen- cies of period-1 limit cycle oscillations at any flight veloc- ity are derived. Finally, these analytic results are compared to the results of numerical simulations, and a good agree- ment is found. The effects of freeplay value and contact stiffness ratio on the limit cycle oscillation are also analyzed through numerical simulations of the original system. More- over, there exist multi-periods limit cycle oscillations and even complicated ＂chaotic＂ oscillations may occur, which are usually found in smooth nonlinear dynamic systems.
