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Identification of resonant frequencies of rotating beams with the use of PZT crystals


Gyroscopic Effects Analysis in the Lagrangian Formulation of Rotating Beams


For rotating beams the frequency generally decreases as the curvature increases, and the reduction from the straight beam frequency increases as the rotating speed increases.


Usually, two counterrotating beams are collided continuously at a few points of the ring.


The model is used to investigate vibration attenuation in rotating beams using periodically distributed shunted piezoelectric patches.

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 The work summarized in this paper aims at improving the accuracy of rotor blade dynamics analysis,and that of its internal force calculation in particular,by the finite element method.A family of nonuniform rotating beam conforming elements is developed.Also,it is proposed how the internal force of the blade can be calculated directly from the node displacement by means of the dynamic stiffness matrix of the finite element("dynamic stiffness method" for short).In illustration the natural frequencies,mode... The work summarized in this paper aims at improving the accuracy of rotor blade dynamics analysis,and that of its internal force calculation in particular,by the finite element method.A family of nonuniform rotating beam conforming elements is developed.Also,it is proposed how the internal force of the blade can be calculated directly from the node displacement by means of the dynamic stiffness matrix of the finite element("dynamic stiffness method" for short).In illustration the natural frequencies,mode shapes and bending moments of a blade flapwise bending vibration have been calculated.Numerical results are presented for a typical case.The blade has discontinuosly varying bending stiffness and mass distribution along the spanwise direction.The nonuniform rotating beam conforming elements with displacement functions based respectively on the 3rd,5th and 7th order polynomial and the "dynamic stiffness method" are used in the calculation.The results show that the work has attained the predeterminate goal.  提高用有限元法进行桨叶动力分析、特别是动内力计算的精度是本文工作的主要目的。本文建立了变剖面旋转梁协调单元族;提出利用单元动刚度矩阵直接由节点位移计算桨叶内力(简称为计算内力的“动刚度法”)。作为例子,用所导出的不同精度的有限单元和建议的内力计算方法计算了具有不连续结构特性的变剖面桨叶弯曲振动固有频率、振型和模态内力。计算结果表明,工作可以达到预期的目的。  The main purpose of the work described in this paper is to improve the accuracy of rotor blade dynamics analysis, especially, that of internal force calculation by the finite element method. A family of nonuniform rotating beam confoming elements is developed. The explicit expressions for the geometrical stiffness matrices of tha elements with displacement functions based respectively on the 3rd, 5th and 7th order polynomical are given. This paper also presents a method'called "dynamic stiffness method"... The main purpose of the work described in this paper is to improve the accuracy of rotor blade dynamics analysis, especially, that of internal force calculation by the finite element method. A family of nonuniform rotating beam confoming elements is developed. The explicit expressions for the geometrical stiffness matrices of tha elements with displacement functions based respectively on the 3rd, 5th and 7th order polynomical are given. This paper also presents a method'called "dynamic stiffness method" by which the internal force can be calculated directly from the node displacement. As illustrative examples, the natural frequencies, mode shapes and bending moments of blade flapwise bending vibration are calculated. The results show that the purpose of the work can be achieved.  提高用有限无法进行桨叶动力分析、特别是内力计算的精度是本文工作的主要目的。本文建立了变剖面旋转梁协调单元族,给出了位移函数为三次、五次、七次幂多项式时变剖面旋转梁协调元的几何刚度矩阵显表达式。文中还提出了直接用节点位移计算内力的“动刚度法”。作为例子,用所给出的有限元和方法计算了桨叶弯曲振动固有频率、振型及模态弯矩。计算结果表明,工作可以达到预期的目的。  The continuous cooling transformation curve for 18Cr2Ni4WA steel hasbeen experimentally determined. The relationships between microstructuresobtained under different cooling rates with optical and electron microscopeandmechanical properties have been studied. The following conclusions may be drawn: (1) Microstructures and mechanical properties of the steel are controlledby cooling rate. Lath martensite, mixture martensite and bainite, bainite oreven all granular bainite have been obtained respectively under... The continuous cooling transformation curve for 18Cr2Ni4WA steel hasbeen experimentally determined. The relationships between microstructuresobtained under different cooling rates with optical and electron microscopeandmechanical properties have been studied. The following conclusions may be drawn: (1) Microstructures and mechanical properties of the steel are controlledby cooling rate. Lath martensite, mixture martensite and bainite, bainite oreven all granular bainite have been obtained respectively under different cooling rates. Martensite/retained austenite (M/A) island of certain amount andsizes are found in different microstructures stated above. (2) When the coolig time is about an hour from 900℃ to 270℃ the mainmicrostructure of steel is granular bainite and its overall properties are betterthan others. Compared with oil quenching, impact toughness a_k is increased by37%; fracture toughness J_(0.05), 105%; rotating beam fatigue limit σ_(1), 5%;impact fatigue life N_f, 33%; and crack propagation rate da/dN is lower. Butthe strength σ_b of 120 kg/mm~2 can still be assured (tempering temperature220℃). Therefore this quenching regime is the best one. (3) (M/A) islands of certain amount and sizes in microstructure canretard crack propagation effectively. According to this paper's experiments therelationship among impact fatigue life (N_f), diameter (D) of (M/A) islandand mean distance (λ) between (M/A) islands can be expressed by: Nf= 1/λ~(1.166)(λD)~0.213 (4) The relationship between fracture toughness K_(10), other mechanicalproperties and mean distance (λ) between (M/A) islands can be expressed by: K_(10)=2π/3·ε_f·E·σ_b·e~(n_2ψ)·λ (1/2)  本文测定了18Cr2Ni4WA钢奥氏体连续冷却转变曲线,分析了不同冷速下的显微组织,研究了冲击疲劳、旋转弯曲疲劳、断裂韧性和常规机械性能,讨论了组织和性能的关系。结果表明:该钢的显微组织依冷速不同可分别获得板条马氏体、板条马氏体和贝氏体、贝氏体、以至全部为粒状贝氏体。冷却时间约一小时得到以粒状贝氏体为主的组织,其综合机械性能优于其他组织。不同冷速的组织中均存在一定数量和尺寸的(M/A)岛,对疲劳裂纹扩展有阻碍作用,可提高疲劳寿命。   << 更多相关文摘 
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