Study On Nonlinear Vibrations Of Shallow Shell Structures Of Aeroengine Compressor Blades With Innovative Materials

The blades are important components of the aeroengine.The performance of the blades directly affects the performance,reliability and service life of the aero-engine.The blades realize the mutual transformation of the kinetic energy,thermal energy and pressure energy.The bearing condition is very complex and the working condition is very harsh.When the blades do work on the airflow,it will also cause the severe vibration for the blades,which is easy to generate large amplitude nonlinear vibration,and then induce serious safety accidents.If these complex nonlinear dynamic phenomena cannot be well controlled and avoided,the blades and the engine will be severely damaged.Therefore,in order to guide and modify the design of the compressor blades theoretically and practically,and then to suppress the vibrations of the blades,nonlinear dynamic modeling and analysis of the aeroengine compressor blades with high rotating speed by using the advanced nonlinear dynamic theory have important scientific significance and engineering value.In this thesis,considering the innovative materials,the aeroengine compressor blade is simplified as a rotating pretwisted shallow cylindrical shell.The linear and nonlinear dynamics characteristics of the rotating pretwisted shallow cylindrical shell are investigated.The strain-displacement relationship is derived by the Green strain tensor.The dynamic equations of rotating pretwisted shallow cylindrical shell with homogeneous materials,functionally graded materials and graphene platelets reinforced composite materials are established respectively.Then the linear and nonlinear vibrations of the above rotating pretwisted shallow cylindrical shells are investigated.The main contents of this thesis are given as follows:(1)Considering the effects of the presetting angle,pretwist angle and variable rotating speed,Green strain tensor is used to derive the strain-displacement relationship of the rotating pretwisted shallow cylindrical shell.Based on the first-order shear deformation theory,Hamilton principle and Galerkin method are utilized to derive the nonlinear equations of motion of the rotating pretwisted shallow cylindrical shell subjected to the impact load or the steady-state excitation.Transient responses of the system subjected to four different impact loads are investigated at first.Then,the effects of the damping coefficient,presetting angle and pretwist angle on nonlinear dynamic characteristics of the system subjected to the steady-state excitation are studied.(2)Nonlinear equations of motion of the rotating pretwisted shallow cylindrical shell contain coupling between linear stiffness terms.The method of multiple scales is used to obtain the averaged equations of the rotating pretwisted shallow cylindrical shell under two different primary resonances(the first mode and the second mode are excited respectively)in the case of 1:2 internal resonance.The effects of the detuning parameter,damping coefficient and excitation amplitude on amplitude-frequency responses and bifurcation behaviors of the system are studied.(3)Considering the effects of the presetting angle,pretwist angle and variable rotating speed,Green strain tensor is used to derive the strain-displacement relationship of the rotating pretwisted functionally graded material(FGM)shallow cylindrical shell.Based on the first-order shear deformation theory,Hamilton principle and Galerkin method are utilized to derive the nonlinear equations of motion of the rotating pretwisted FGM shallow cylindrical shell subjected to the impact load or the steady-state excitation.Transient responses of the system subjected to four different impact loads are investigated at first.Then,the effects of the excitation frequency,temperature and volume fraction index on nonlinear dynamic characteristics of the system subjected to the steady-state excitation are studied.(4)Considering the effects of the graphene reinforced material,presetting angle,pretwist angle and variable rotating speed,Green strain tensor is used to derive the strain-displacement relationship of the rotating pretwisted functionally graded graphene platelet reinforced composite(FG-GPLRC)shallow cylindrical shell.Based on the first-order shear deformation theory,Chebyshev-Ritz method is used to obtain the natural frequencies and mode shapes of the system.The effects of the graphene platelet(GPL)distribution pattern,GPL weight fraction,presetting angle,pretwisted angle and rotating speed on natural frequencies of the system are investigated.(5)Based on the mode shape obtained by the Chebyshev-Ritz method,Lagrange’s formulation is used to derive the nonlinear quations of motion of the rotating pretwisted FG-GPLRC shallow cylindrical shell.The effects of the Coriolis force,GPL distribution pattern,steady-state rotating speed and perturbation rotating speed amplitude on nonlinear dynamic characteristics of the system are investigated.(6)Considering the effects of the graphene coating layer and variable thickness,Green strain tensor is used to derive the strain-displacement relationship of the rotating pretwisted tapered composite shallow cylindrical shell with graphene coating layers.Based on the first-order shear deformation theory,Chebyshev-Ritz method is used to obtain the natural frequencies and mode shapes of the system.The effects of the GPL weight fraction,taper ratio,length-to-radius ratio,presetting angle,pretwist angle and rotating speed on natural frequencies of the system are investigated.