A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the ra...A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the radially symmetric motion of the pre-strained sheet are obtained.The conditions of cavitated bifurcation that describe cavity formation and motion with time at the axial line of the pre-strained sheet are proposed,that is to say,a circular cavity will form if the suddenly applied radial tensile load exceeds a certain critical value;dynamically,it is proved that the formed cavity will present a nonlinearly periodic oscillation,which is essentially different from the singular periodic oscillation of the formed cavity in an incompressible hyperelastic solid sphere.Numerical simulations show the effects of prescribed radial tension,material parameter and tensile load on critical ten-sile load describing cavity formation and periodic oscillation of the pre-strained circular sheet.展开更多
Model uncertainty directly affects the accuracy of robust flutter and limit-cycle-oscillation (LCO) analysis. Using a data-based method, the bounds of an uncertain block-oriented aeroelastic system with nonlinearity a...Model uncertainty directly affects the accuracy of robust flutter and limit-cycle-oscillation (LCO) analysis. Using a data-based method, the bounds of an uncertain block-oriented aeroelastic system with nonlinearity are obtained in the time domain. Then robust LCO analysis of the identified model set is performed. First, the proper orthonormal basis is constructed based on the on-line dynamic poles of the aeroelastic system. Accordingly, the identification problem of uncertain model is converted to a nonlinear optimization of the upper and lower bounds for uncertain parameters estimation. By replacing the identified memoryless nonlinear operators by its related sinusoidal-input describing function, the Linear Fractional Transformation (LFT) technique is applied to the modeling process. Finally, the structured singular value(μ) method is applied to robust LCO analysis. An example of a two-degree wing section is carded out to validate the framework above. Results indicate that the dynamic characteristics and model uncertainties of the aeroelastic system can be depicted by the identified uncertain model set. The robust LCO magnitude of pitch angle for the identified uncertain model is lower than that of the nominal model at the same velocity. This method can be applied to robust flutter and LCO prediction.展开更多
The nonlinear aeroelastic system of an airfoil with an external store was investigated,with emphasis on the bounds of limit cycle oscillations(LCOs).Based on the equivalent linearization,an approach was proposed to ca...The nonlinear aeroelastic system of an airfoil with an external store was investigated,with emphasis on the bounds of limit cycle oscillations(LCOs).Based on the equivalent linearization,an approach was proposed to calculate the bounds on LCOs over the full flight envelope.The bounds are determined directly without solving LCOs one by one as the flow speed varies.The presented approach can provide us with the maximal LCO amplitudes and the lower threshold for flow speed beyond which LCOs may arise.Numerical examples show that the obtained bounds are in nice agreement with numerical simulation results.The speed threshold can be predicted to a relative error less than 0.1%,and the maximal LCO amplitude to about 3%.The influences of the system parameters on the speed threshold for speed were investigated efficiently by the proposed approach.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.10872045, 10721062)the Program for New Century Excellent Talents in University (Grant No.NCET-09-0096)the Fundamental Research Funds for Central Universities (Grant No.DC10030104)
文摘A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the radially symmetric motion of the pre-strained sheet are obtained.The conditions of cavitated bifurcation that describe cavity formation and motion with time at the axial line of the pre-strained sheet are proposed,that is to say,a circular cavity will form if the suddenly applied radial tensile load exceeds a certain critical value;dynamically,it is proved that the formed cavity will present a nonlinearly periodic oscillation,which is essentially different from the singular periodic oscillation of the formed cavity in an incompressible hyperelastic solid sphere.Numerical simulations show the effects of prescribed radial tension,material parameter and tensile load on critical ten-sile load describing cavity formation and periodic oscillation of the pre-strained circular sheet.
基金supported by the National Natural Science Foundation of China (Grant Nos. 90716006 and 10902006)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20091102110015)the Innovation Foundation of BUAA for PhD Graduates
文摘Model uncertainty directly affects the accuracy of robust flutter and limit-cycle-oscillation (LCO) analysis. Using a data-based method, the bounds of an uncertain block-oriented aeroelastic system with nonlinearity are obtained in the time domain. Then robust LCO analysis of the identified model set is performed. First, the proper orthonormal basis is constructed based on the on-line dynamic poles of the aeroelastic system. Accordingly, the identification problem of uncertain model is converted to a nonlinear optimization of the upper and lower bounds for uncertain parameters estimation. By replacing the identified memoryless nonlinear operators by its related sinusoidal-input describing function, the Linear Fractional Transformation (LFT) technique is applied to the modeling process. Finally, the structured singular value(μ) method is applied to robust LCO analysis. An example of a two-degree wing section is carded out to validate the framework above. Results indicate that the dynamic characteristics and model uncertainties of the aeroelastic system can be depicted by the identified uncertain model set. The robust LCO magnitude of pitch angle for the identified uncertain model is lower than that of the nominal model at the same velocity. This method can be applied to robust flutter and LCO prediction.
基金supported by the National Natural Science Foundation of China(Grant Nos.11002088,11272361)the Innovation Foundation for PhD Graduates of SYSU
文摘The nonlinear aeroelastic system of an airfoil with an external store was investigated,with emphasis on the bounds of limit cycle oscillations(LCOs).Based on the equivalent linearization,an approach was proposed to calculate the bounds on LCOs over the full flight envelope.The bounds are determined directly without solving LCOs one by one as the flow speed varies.The presented approach can provide us with the maximal LCO amplitudes and the lower threshold for flow speed beyond which LCOs may arise.Numerical examples show that the obtained bounds are in nice agreement with numerical simulation results.The speed threshold can be predicted to a relative error less than 0.1%,and the maximal LCO amplitude to about 3%.The influences of the system parameters on the speed threshold for speed were investigated efficiently by the proposed approach.
