Research On Quasi-three-dimensional Dynamic Modeling Method And Vibration Characteristics Of Rotating Functionally Graded Blades

Turbomachinery blades,especially for the aero engine and gas turbine,endure severe steady and unsteady loads during their operational life,such as centrifugal force,thermal load and airflow force.It is of great significance to study the dynamic behaviors of blades under various steady and unsteady loads for the safety design of the blades.With the advancement of material technology,composite materials with the advantages of light weight,corrosion resistance,high-temperature resistance,high specific strength and stiffness and strong designability,have been gradually applied in the design of gas turbine blades and show great utilization potentiality.In order to improve the dynamic design level of composite blades and avoid the vibration fatigue damage of composite blades caused by resonance,this work focuses on the functionally graded composite blades and studies the dynamic modeling method of the composite blade under complex factors based on the existing vibration theory of composite blade.Several complex factors such as rotational effect,complex geometric shape,non-uniform material distribution,high-temperature thermal load and geometric nonlinearity are considered.The influence laws and mechanisms of different complex factors on the dynamic characteristics of composite blades are explored.This study aims to provide theoretical and methodological support for the structural dynamic optimization design of gas turbine composite blades.The main research work is as follows:In order to meet the modeling requirements of high precision,high efficiency and high applicability for composite blades with complex factors,a quasi-three-dimensional dynamic modeling method of the composite blade under elastic boundary conditions is proposed.This method uses Carrera’s high-order intercept fitting technique to fit the transverse displacement function of the blade structure.Classical theory and first-order shear deformation theory can be regarded as two special cases.The boundary conditions of the blade structure are transformed into a quantizable form based on the penalty function method,realizing the parametric simulation of the classical and elastic boundary conditions.The vibration displacement variables of the blade structure are constructed by the generalized spectral function,and the unique mass and stiffness nuclear matrices corresponding to the vibration equations of the blade structure are obtained based on the energy variational principle.The structure theories can be obtained by iterating the same nuclear matrix,thus realizing a unified description of the loworder and high-order theories.Numerical verification results show that the proposed method achieves an effective balance between computational accuracy and solving efficiency by controlling the theoretical order of the model.As for the vibration problem of functionally graded blades with a high aspect ratio,a quasithree-dimensional dynamic model of rotating functionally graded beams is established.According to the kinematic equation of the rotating beam,the centrifugal stiffening effect,rotational softening effect and Coriolis effect caused by the rotational motion are considered.The vibration governing equation of the rotating functionally graded beam is derived based on the energy variational method.Taking the isotropic and functionally graded beams as examples,the convergence and correctness of the theoretical model for the non-self-adjoint vibration system are verified by comparing it with literature data.On this basis,the influences of the rotating speed,material parameters,presetting angle and hub-radius ratio on the vibration characteristics of the rotating functionally graded beams are systematically studied.Regarding the vibration problem of small aspect ratio pre-twisted functionally graded blades,quasi-three-dimensional dynamic models of rotating pre-twisted functionally graded plates and shells are established.The initial centrifugal stress field due to the high rotating speed is solved separately by two centrifugal stress solving methods,direct integration of centrifugal forces and static analysis under centrifugal forces.The additional potential energy of the centrifugal prestress effect is obtained by introducing the complete second-order nonlinear strain terms in the frame of the curvilinear coordinate system.The vibration governing equations of the pre-twisted blades are obtained based on the Hamilton principle.The modal tests of the pre-twisted shell-type blades are carried out.By comparing the theoretical results with the literature data,numerical results and experimental data,the correctness and effectiveness of the theoretical model are verified.On this basis,the applicability of the two methods for solving the centrifugal stress field in the dynamic modeling of rotating pre-twisted blades is evaluated.The influence mechanisms of the rotational speed,centrifugal shear stress,material parameters and structural parameters on the vibration characteristics of rotating pretwisted functionally graded blades are explored.Considering the high-temperature thermal load environment of turbine blades,the vibration characteristics of functionally graded sandwich blades under thermal environment are studied.According to the heat conduction equation and thermal boundary conditions,the temperature distribution that occurred within the blade is determined.The constitutive equation of functionally graded sandwich blades in thermal environment is derived taking into consideration the thermal strains.A quasi-static analysis of the pre-twisted functionally graded sandwich blade enduring both the centrifugal and thermal loads is carried out to accurately predict the initial thermo-mechanical stresses.The thermo-mechanical prestress effect is considered in the total energy functional by introducing the high-order nonlinear strain terms.The vibration equations of the rotating composite blades under thermal environment are derived by using the Hamilton principle.The convergence and correctness of the dynamic model are verified.The influences of the temperature rise,rotating speed,structural parameters and material parameters on the vibration characteristics of the composite blades are investigated.Considering the geometrical nonlinear initial deformation of blades at a high rotating speed,the vibration characteristics of high-speed rotating pre-twisted functionally graded blades are studied.Based on the principle of virtual work,the nonlinear steady equilibrium equations of the pre-twisted shell-type blade subjected to a high centrifugal load are derived.The Newton-Raphson method is used to solve the initial nonlinear deformation of the pretwisted shell-type blade.Taking the nonlinear deformed blade as the starting position of vibration and considering the effect of centrifugal prestress effect,the vibration characteristics of the nonlinear deformed pre-twisted shell-type blades are analyzed.On the basis of verifying the correctness of the theoretical model,the influences of the rotational speed,hub-radius ratio,pre-twisted angle and presetting angle on the vibration characteristics of the shell-type blades are investigated.The influence mechanism of nonlinear structural deformation on the vibration characteristics of rotating pre-twisted blades is explored.The ranges of applicability of the linear and nonlinear models are assessed for the dynamic analysis of high-speed rotating shelltype blades.