Turbo-machineries,as key components,have wide applications in civil,aerospace,and mechanical engineering.By calculating natural frequencies and dynamical deformations,we have explained the rationality of the series fo...Turbo-machineries,as key components,have wide applications in civil,aerospace,and mechanical engineering.By calculating natural frequencies and dynamical deformations,we have explained the rationality of the series form for the aerodynamic force of the blade under the subsonic flow in our earlier studies.In this paper,the subsonic aerodynamic force obtained numerically is applied to the low pressure compressor blade with a low constant rotating speed.The blade is established as a pre-twist and presetting cantilever plate with a rectangular section under combined excitations,including the centrifugal force and the aerodynamic force.In view of the first-order shear deformation theory and von-K′arm′an nonlinear geometric relationship,the nonlinear partial differential dynamical equations for the warping cantilever blade are derived by Hamilton’s principle.The second-order ordinary differential equations are acquired by the Galerkin approach.With consideration of 1:3 internal resonance and 1/2 sub-harmonic resonance,the averaged equation is derived by the asymptotic perturbation methodology.Bifurcation diagrams,phase portraits,waveforms,and power spectrums are numerically obtained to analyze the effects of the first harmonic of the aerodynamic force on nonlinear dynamical responses of the structure.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11372015,11832002,11290152,11427801,and 11972051)。
文摘Turbo-machineries,as key components,have wide applications in civil,aerospace,and mechanical engineering.By calculating natural frequencies and dynamical deformations,we have explained the rationality of the series form for the aerodynamic force of the blade under the subsonic flow in our earlier studies.In this paper,the subsonic aerodynamic force obtained numerically is applied to the low pressure compressor blade with a low constant rotating speed.The blade is established as a pre-twist and presetting cantilever plate with a rectangular section under combined excitations,including the centrifugal force and the aerodynamic force.In view of the first-order shear deformation theory and von-K′arm′an nonlinear geometric relationship,the nonlinear partial differential dynamical equations for the warping cantilever blade are derived by Hamilton’s principle.The second-order ordinary differential equations are acquired by the Galerkin approach.With consideration of 1:3 internal resonance and 1/2 sub-harmonic resonance,the averaged equation is derived by the asymptotic perturbation methodology.Bifurcation diagrams,phase portraits,waveforms,and power spectrums are numerically obtained to analyze the effects of the first harmonic of the aerodynamic force on nonlinear dynamical responses of the structure.
