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Study on the influence of joint parameters on nonlinear dynamics of a rotor system 研究关节参数对转子系统非线性动力学的影响
Pub Date : 2024-02-10 DOI: 10.1177/10775463241232752
Jin Chen, Kuan Lu, Weidong Zhu, Hui Cheng, Kaifu Zhang, Xiaohui Gu, Chao Fu
Aero-engine rotor system contains a variety of connectors such as bolts and bearings. However, the dynamic behaviors of the connection are complex in actual engineering. In this paper, the dynamic behavior of the rotor-bearing system with bolted joints and the influence of the parameters of the joints on it are clarified. The parameters include the bearing clearance and the deflection caused by the uneven bolt preload. A rotor-bearing model with bolted joints is established by using Lagrange equations. The bifurcation diagram is solved to explore the tendency of vibration of the system at different speeds by considering the Hertz contact force. Furthermore, the phase diagram, Poincaré map, time-domain steady-state response curve, and spectrum diagram are used to discuss the dynamic behaviors of the system specifically. The influence of the bearing clearance change and uneven bolt preload on the dynamic behaviors is investigated by using the bifurcation diagram. The result shows that the motion of the system is extremely complex, which includes chaotic motion. The Lyapunov exponent is then calculated to verify whether the system enters chaos. The correctness of the model is verified by comparing the result in this work with those in the literature. The model can clarify the dynamic behaviors of the system well and has high accuracy, which can provide the theoretical guidance for the design of rotor-bearing systems with bolted joints.
航空发动机转子系统包含各种连接件,如螺栓和轴承。然而,在实际工程中,连接的动态行为十分复杂。本文阐明了带有螺栓连接的转子-轴承系统的动态行为以及连接参数对其的影响。这些参数包括轴承间隙和螺栓预紧力不均匀引起的挠度。利用拉格朗日方程建立了带螺栓连接的转子轴承模型。考虑到赫兹接触力,通过求解分岔图来探索系统在不同速度下的振动趋势。此外,还利用相图、Poincaré 图、时域稳态响应曲线和频谱图来具体讨论系统的动态行为。利用分岔图研究了轴承间隙变化和不均匀螺栓预紧力对动态行为的影响。结果表明,系统的运动极其复杂,其中包括混沌运动。然后通过计算 Lyapunov 指数来验证系统是否进入混沌状态。通过将本研究的结果与文献中的结果进行比较,验证了模型的正确性。该模型能很好地阐明系统的动态行为,具有较高的精度,可为螺栓连接转子轴承系统的设计提供理论指导。
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引用次数: 0
Rolling bearing fault diagnosis based on multi-domain features and whale optimized support vector machine 基于多域特征和鲸鱼优化支持向量机的滚动轴承故障诊断
Pub Date : 2024-02-10 DOI: 10.1177/10775463241231344
Bing Wang, HuiMin Li, Xiong Hu, Wei Wang
Rolling bearing is an important rotating support component in mechanical equipment. It is very prone to wear, defects, and other faults, which directly affect the reliable operation of mechanical equipment. Its running condition monitoring and fault diagnosis have always been a matter of concern to engineers and researchers. A rolling bearing fault diagnosis technique based on multi-domain feature and whale optimization algorithm-support vector machine (MDF-WOA-SVM) is proposed. Firstly, recursive analysis is performed on vibration signal and the recursive features are employed as nonlinear recursive feature vector including recursive rate (RR), deterministic rate (DET), recursive entropy (RE), and diagonal average length (DAL). Then, a comprehensive multi-domain feature vector is constructed by combining three time-domain features including root mean square, variance, and peak to peak. Finally, whale optimization algorithm (WOA) is introduced to optimize the penalty factor C and kernel function parameter g to construct the optimal WOA-SVM model. The rolling bearing datasets of Jiangnan University is employed for instance analysis, and the results show that the 10-CV accuracy of the technique proposed is good with an accuracy of 99%. Compared with recursive features or time-domain features, multi-domain features are more accurate and comprehensive in describing characters of the signal. Some popular supervised learning models are also introduced for comparison including K-nearest neighbor (KNN) and decision tree (DT), and the result shows that the proposed method has a higher accuracy and certain advantages.
滚动轴承是机械设备中重要的旋转支撑部件。它极易出现磨损、缺陷等故障,直接影响机械设备的可靠运行。其运行状态监测和故障诊断一直是工程师和研究人员关注的问题。本文提出了一种基于多域特征和鲸鱼优化算法-支持向量机(MDF-WOA-SVM)的滚动轴承故障诊断技术。首先,对振动信号进行递归分析,采用递归特征作为非线性递归特征向量,包括递归率(RR)、确定率(DET)、递归熵(RE)和对角线平均长度(DAL)。然后,结合三个时域特征(包括均方根、方差和峰峰值),构建综合的多域特征向量。最后,引入鲸鱼优化算法(WOA)来优化惩罚因子 C 和核函数参数 g,从而构建最优的 WOA-SVM 模型。采用江南大学的滚动轴承数据集进行实例分析,结果表明所提技术的 10-CV 精度较好,准确率达 99%。与递归特征或时域特征相比,多域特征在描述信号特征方面更加准确和全面。此外,还引入了一些常用的监督学习模型进行比较,包括 K 近邻(KNN)和决策树(DT),结果表明所提出的方法具有更高的准确率和一定的优势。
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引用次数: 0
Automated structural parameter estimation of semi-rigid complex joints in a benchmark laboratory steel grid by experimental modal analysis 通过实验模态分析自动估算基准实验室钢网格中半刚性复杂接头的结构参数
Pub Date : 2024-02-09 DOI: 10.1177/10775463241232460
Milad Mehrkash, Erin Santini-Bell
The mechanical properties of joints may impact a system’s static and dynamic behavior. Since connections are usually complex, modeling their geometric details could take time and effort. Thus, joints of structures are often overlooked in model creation and calibration. Therefore, reliable analytical modeling of in-service structures requires accurate and efficient parameter estimation of the connections in their simplified models. However, joints are physically small parts of a system, and parameter estimation techniques may not be sufficiently sensitive to the variations of connections’ mechanical properties. This paper examines the finite element model updating of a laboratory steel grid focusing on the structural parameter estimation of its complex connections using modal data. The mechanical properties of the joints are parametrized by added mass and reduced rigidity. Therefore, several modified models with different combinations of heavier semi-rigid joints are developed. Each model is updated using two modal-based error functions, and the most representative updated model is selected. The results demonstrate how the grid modal outputs are influenced by updating the mass and stiffness of its connections. Moreover, mass and stiffness interactions of the grid joints in the parameter estimation procedure are illustrated. The updated models can efficiently simulate the structural behavior of the grid with increased confidence and reliability.
连接件的机械特性可能会影响系统的静态和动态行为。由于连接通常比较复杂,对其几何细节进行建模需要花费大量的时间和精力。因此,在模型创建和校准过程中,结构的连接处经常被忽略。因此,要对在役结构进行可靠的分析建模,就必须对其简化模型中的连接点进行准确有效的参数估计。然而,连接件是系统的物理小部件,参数估计技术可能对连接件机械性能的变化不够敏感。本文研究了实验室钢格栅的有限元模型更新,重点是利用模态数据估算其复杂连接的结构参数。连接件的力学性能是通过增加质量和降低刚度来参数化的。因此,开发了几种具有不同组合的较重半刚性连接的改进模型。使用两个基于模态的误差函数对每个模型进行更新,然后选择最具代表性的更新模型。结果表明了网格模态输出如何受到连接质量和刚度更新的影响。此外,还说明了参数估计过程中网格连接质量和刚度的相互作用。更新后的模型可以有效地模拟网格的结构行为,并提高其可信度和可靠性。
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引用次数: 0
Automated structural parameter estimation of semi-rigid complex joints in a benchmark laboratory steel grid by experimental modal analysis 通过实验模态分析自动估算基准实验室钢网格中半刚性复杂接头的结构参数
Pub Date : 2024-02-09 DOI: 10.1177/10775463241232460
Milad Mehrkash, Erin Santini-Bell
The mechanical properties of joints may impact a system’s static and dynamic behavior. Since connections are usually complex, modeling their geometric details could take time and effort. Thus, joints of structures are often overlooked in model creation and calibration. Therefore, reliable analytical modeling of in-service structures requires accurate and efficient parameter estimation of the connections in their simplified models. However, joints are physically small parts of a system, and parameter estimation techniques may not be sufficiently sensitive to the variations of connections’ mechanical properties. This paper examines the finite element model updating of a laboratory steel grid focusing on the structural parameter estimation of its complex connections using modal data. The mechanical properties of the joints are parametrized by added mass and reduced rigidity. Therefore, several modified models with different combinations of heavier semi-rigid joints are developed. Each model is updated using two modal-based error functions, and the most representative updated model is selected. The results demonstrate how the grid modal outputs are influenced by updating the mass and stiffness of its connections. Moreover, mass and stiffness interactions of the grid joints in the parameter estimation procedure are illustrated. The updated models can efficiently simulate the structural behavior of the grid with increased confidence and reliability.
连接件的机械特性可能会影响系统的静态和动态行为。由于连接通常比较复杂,对其几何细节进行建模需要花费大量的时间和精力。因此,在模型创建和校准过程中,结构的连接处经常被忽略。因此,要对在役结构进行可靠的分析建模,就必须对其简化模型中的连接点进行准确有效的参数估计。然而,连接件是系统的物理小部件,参数估计技术可能对连接件机械性能的变化不够敏感。本文研究了实验室钢格栅的有限元模型更新,重点是利用模态数据估算其复杂连接的结构参数。连接件的力学性能是通过增加质量和降低刚度来参数化的。因此,开发了几种具有不同组合的较重半刚性连接的改进模型。使用两个基于模态的误差函数对每个模型进行更新,然后选择最具代表性的更新模型。结果表明了网格模态输出如何受到连接质量和刚度更新的影响。此外,还说明了参数估计过程中网格连接质量和刚度的相互作用。更新后的模型可以有效地模拟网格的结构行为,并提高其可信度和可靠性。
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引用次数: 0
Investigation of a perturbation-based model updating approach for structural health and event monitoring 基于扰动的结构健康和事件监测模型更新方法研究
Pub Date : 2024-02-08 DOI: 10.1177/10775463241229477
Fabio von Coburg, Julius Westbeld, Erhard Buchmann, Philipp Höfer
With the intention to detect structural events, for example, occurrence of damage and assessing their severity under service, structural health and event monitoring proved itself as a reliable evaluation tool. While many algorithmic approaches exist, model-based monitoring offers the prominent advantage to enable extensive analysis of damage states based on a structural digital twin. In order to accurately replicate the dynamical behaviour of a real-world structure, inherent physical properties, for example, mass, stiffness and structural damping, of the digital twin might be corrected from nominal values. This can be achieved by numerical model updating procedures. In this study, the application of a model updating approach is presented to eliminate modal discrepancies. Based on the perturbated modal dynamic residual, an updating equation is formulated. Stiffness and mass correction terms with preserved orthogonality and symmetry conditions are determined by the method of least squares. A case study using computationally generated modal data is conducted, evaluating the numerical updating performance in terms of correction accuracy and reproduction of modal parameters. Finally, the transient structural response to an impulse excitation is compared between updated and reference model. The gathered results prove the method’s suitability as accurate and robust updating procedure, fostering its application in model-based monitoring frameworks.
结构健康和事件监测的目的是检测结构事件,例如在使用过程中发生的损坏并评估其严重程度,它已被证明是一种可靠的评估工具。虽然存在许多算法方法,但基于模型的监测具有突出优势,可以在结构数字孪生的基础上对损坏状态进行广泛分析。为了准确复制真实世界结构的动态行为,数字孪生结构的固有物理属性(如质量、刚度和结构阻尼)可能需要从标称值进行修正。这可以通过数值模型更新程序来实现。在本研究中,介绍了如何应用模型更新方法来消除模态差异。根据扰动模态动态残差,制定了一个更新方程。通过最小二乘法确定了具有保留正交性和对称性条件的刚度和质量修正项。利用计算生成的模态数据进行了案例研究,从修正精度和模态参数再现方面评估了数值更新的性能。最后,比较了更新模型和参考模型对脉冲激励的瞬态结构响应。收集到的结果证明了该方法作为精确、稳健的更新程序的适用性,促进了其在基于模型的监测框架中的应用。
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引用次数: 0
Investigation of a perturbation-based model updating approach for structural health and event monitoring 基于扰动的结构健康和事件监测模型更新方法研究
Pub Date : 2024-02-08 DOI: 10.1177/10775463241229477
Fabio von Coburg, Julius Westbeld, Erhard Buchmann, Philipp Höfer
With the intention to detect structural events, for example, occurrence of damage and assessing their severity under service, structural health and event monitoring proved itself as a reliable evaluation tool. While many algorithmic approaches exist, model-based monitoring offers the prominent advantage to enable extensive analysis of damage states based on a structural digital twin. In order to accurately replicate the dynamical behaviour of a real-world structure, inherent physical properties, for example, mass, stiffness and structural damping, of the digital twin might be corrected from nominal values. This can be achieved by numerical model updating procedures. In this study, the application of a model updating approach is presented to eliminate modal discrepancies. Based on the perturbated modal dynamic residual, an updating equation is formulated. Stiffness and mass correction terms with preserved orthogonality and symmetry conditions are determined by the method of least squares. A case study using computationally generated modal data is conducted, evaluating the numerical updating performance in terms of correction accuracy and reproduction of modal parameters. Finally, the transient structural response to an impulse excitation is compared between updated and reference model. The gathered results prove the method’s suitability as accurate and robust updating procedure, fostering its application in model-based monitoring frameworks.
结构健康和事件监测的目的是检测结构事件,例如在使用过程中发生的损坏并评估其严重程度,它已被证明是一种可靠的评估工具。虽然存在许多算法方法,但基于模型的监测具有突出优势,可以在结构数字孪生的基础上对损坏状态进行广泛分析。为了准确复制真实世界结构的动态行为,数字孪生结构的固有物理属性(如质量、刚度和结构阻尼)可能需要从标称值进行修正。这可以通过数值模型更新程序来实现。在本研究中,介绍了如何应用模型更新方法来消除模态差异。根据扰动模态动态残差,制定了一个更新方程。通过最小二乘法确定了具有保留正交性和对称性条件的刚度和质量修正项。利用计算生成的模态数据进行了案例研究,从修正精度和模态参数再现方面评估了数值更新的性能。最后,比较了更新模型和参考模型对脉冲激励的瞬态结构响应。收集到的结果证明了该方法作为精确、稳健的更新程序的适用性,促进了其在基于模型的监测框架中的应用。
{"title":"Investigation of a perturbation-based model updating approach for structural health and event monitoring","authors":"Fabio von Coburg, Julius Westbeld, Erhard Buchmann, Philipp Höfer","doi":"10.1177/10775463241229477","DOIUrl":"https://doi.org/10.1177/10775463241229477","url":null,"abstract":"With the intention to detect structural events, for example, occurrence of damage and assessing their severity under service, structural health and event monitoring proved itself as a reliable evaluation tool. While many algorithmic approaches exist, model-based monitoring offers the prominent advantage to enable extensive analysis of damage states based on a structural digital twin. In order to accurately replicate the dynamical behaviour of a real-world structure, inherent physical properties, for example, mass, stiffness and structural damping, of the digital twin might be corrected from nominal values. This can be achieved by numerical model updating procedures. In this study, the application of a model updating approach is presented to eliminate modal discrepancies. Based on the perturbated modal dynamic residual, an updating equation is formulated. Stiffness and mass correction terms with preserved orthogonality and symmetry conditions are determined by the method of least squares. A case study using computationally generated modal data is conducted, evaluating the numerical updating performance in terms of correction accuracy and reproduction of modal parameters. Finally, the transient structural response to an impulse excitation is compared between updated and reference model. The gathered results prove the method’s suitability as accurate and robust updating procedure, fostering its application in model-based monitoring frameworks.","PeriodicalId":508293,"journal":{"name":"Journal of Vibration and Control","volume":" 25","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139791960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Adaptive sliding mode control for vibration reduction on UAV carrying a payload 自适应滑动模式控制,用于减少携带有效载荷的无人飞行器的振动
Pub Date : 2024-02-06 DOI: 10.1177/10775463241231845
R. Geronel, Douglas D. Bueno
Unmanned aerial vehicles (UAVs) have been used to transport a variety of payloads, including medical materials, foods, and different electronic devices. This type of innovation generates important concerns regarding payload integrity, mainly when involving medical goods that can be affected by vibration. This paper presents the flight dynamics of suspended payload carried by an UAV, considering a flexible attachment between a quadrotor and its payload. Adaptive sliding mode control (ASMC) is proposed to enhance the trajectory tracking and consequently minimize the payload vibration. Adaptive coefficients are introduced to compensate the payload dynamics and uncertainties, which are computed for each proposed trajectory and cargo mass. The proposed adaptive control can efficiently compensate the extra dynamics and uncertainties caused by the attached payload, regardless of the chosen trajectory and weight of the cargo. A root mean square–based index is used to quantitatively evaluate the oscillations. The results show a significant attenuation of the undesired oscillations up to 27%, when the adaptive control is used. Therefore, the use of the proposed ASMC aims to guarantee an improved trajectory tracking and the attenuation of residual oscillations on the main state variables, allowing to be safely employed for transporting several types of medicines, including those sensitive to vibration and those that are dropped during a flight.
无人驾驶飞行器(UAV)已被用于运输各种有效载荷,包括医疗材料、食品和不同的电子设备。这种类型的创新引发了对有效载荷完整性的重要关注,主要是在涉及可能受振动影响的医疗物品时。考虑到四旋翼飞行器与其有效载荷之间的柔性连接,本文介绍了无人飞行器携带的悬挂有效载荷的飞行动力学。本文提出了自适应滑模控制(ASMC),以增强轨迹跟踪,从而最大限度地减少有效载荷的振动。为补偿有效载荷的动态和不确定性,引入了自适应系数,这些系数是针对每个拟议轨迹和货物质量计算得出的。无论选择的轨迹和货物重量如何,所提出的自适应控制都能有效地补偿附加有效载荷引起的额外动态和不确定性。使用基于均方根的指数对振荡进行定量评估。结果表明,在使用自适应控制时,不期望的振荡明显减弱,减弱幅度可达 27%。因此,使用所提出的 ASMC 可确保改进轨迹跟踪和减少主要状态变量上的残余振荡,从而可安全地用于运输多种类型的药品,包括对振动敏感的药品和在飞行过程中掉落的药品。
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引用次数: 0
Adaptive sliding mode control for vibration reduction on UAV carrying a payload 自适应滑动模式控制,用于减少携带有效载荷的无人飞行器的振动
Pub Date : 2024-02-06 DOI: 10.1177/10775463241231845
R. Geronel, Douglas D. Bueno
Unmanned aerial vehicles (UAVs) have been used to transport a variety of payloads, including medical materials, foods, and different electronic devices. This type of innovation generates important concerns regarding payload integrity, mainly when involving medical goods that can be affected by vibration. This paper presents the flight dynamics of suspended payload carried by an UAV, considering a flexible attachment between a quadrotor and its payload. Adaptive sliding mode control (ASMC) is proposed to enhance the trajectory tracking and consequently minimize the payload vibration. Adaptive coefficients are introduced to compensate the payload dynamics and uncertainties, which are computed for each proposed trajectory and cargo mass. The proposed adaptive control can efficiently compensate the extra dynamics and uncertainties caused by the attached payload, regardless of the chosen trajectory and weight of the cargo. A root mean square–based index is used to quantitatively evaluate the oscillations. The results show a significant attenuation of the undesired oscillations up to 27%, when the adaptive control is used. Therefore, the use of the proposed ASMC aims to guarantee an improved trajectory tracking and the attenuation of residual oscillations on the main state variables, allowing to be safely employed for transporting several types of medicines, including those sensitive to vibration and those that are dropped during a flight.
无人驾驶飞行器(UAV)已被用于运输各种有效载荷,包括医疗材料、食品和不同的电子设备。这种类型的创新引发了对有效载荷完整性的重要关注,主要是在涉及可能受振动影响的医疗物品时。考虑到四旋翼飞行器与其有效载荷之间的柔性连接,本文介绍了无人机携带悬挂有效载荷的飞行动力学。本文提出了自适应滑模控制(ASMC),以增强轨迹跟踪,从而最大限度地减少有效载荷的振动。为补偿有效载荷的动态和不确定性,引入了自适应系数,这些系数是针对每个拟议轨迹和货物质量计算得出的。无论选择的轨迹和货物重量如何,所提出的自适应控制都能有效地补偿附加有效载荷引起的额外动态和不确定性。使用基于均方根的指数对振荡进行定量评估。结果表明,在使用自适应控制时,不期望的振荡明显减弱,减弱幅度可达 27%。因此,使用所提出的 ASMC 可确保改进轨迹跟踪和减少主要状态变量上的残余振荡,从而可安全地用于运输多种类型的药品,包括对振动敏感的药品和在飞行过程中掉落的药品。
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引用次数: 0
A study on coupled edgewise and flapwise vibration modes of wind turbine blade 风力涡轮机叶片边缘和襟翼耦合振动模式研究
Pub Date : 2024-02-02 DOI: 10.1177/10775463241230573
M. U. Saram, Jianming Yang
The coupled flapwise and edgewise vibrations of a horizontal axis wind turbine blade (HAWT) are discussed in this paper. Kinetic and potential energies of the blade are evaluated with consideration of the effects of gravity and aerodynamic forces. Hamilton’s principle is employed to develop the nonlinear coupled modal equations of the blade. The coupling between the first order edgewise and the first two order of flapwise modes is considered. This leads to three equations with nonlinear terms. Multiple-scales perturbation method is employed to solve these equations. Furthermore, the numerical values of structural specifications of National Renewable Energy Laboratory (NREL) 5-MW reference wind turbine blade are used, for example. It is shown that first edgewise and first flapwise vibrations are dominant, while second flapwise mode of vibration is less significant in the case of transient responses. Energy transfer between resonant modes is observed in both internal and combination resonances. The amplitude–frequency curves and phase diagrams during primary and combination resonances are obtained for the steady-state responses. Combination and primary resonances are further examined by considering various factors such as geometric nonlinearity and aerodynamic force.
本文讨论了水平轴风力涡轮机叶片(HAWT)的襟翼和边缘耦合振动。考虑到重力和空气动力的影响,对叶片的动能和势能进行了评估。采用汉密尔顿原理建立叶片的非线性耦合模态方程。考虑了一阶边缘模态和前两阶襟翼模态之间的耦合。这就产生了三个非线性方程。采用多尺度扰动法求解这些方程。此外,还以美国国家可再生能源实验室(NREL)5 兆瓦参考风力涡轮机叶片的结构规格数值为例。结果表明,在瞬态响应情况下,第一边缘振动和第一襟翼振动占主导地位,而第二襟翼振动模式的影响较小。在内部共振和组合共振中都可以观察到共振模式之间的能量传递。在主共振和组合共振期间,获得了稳态响应的幅频曲线和相位图。考虑到几何非线性和空气动力等各种因素,对组合共振和主共振进行了进一步研究。
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引用次数: 0
A study on coupled edgewise and flapwise vibration modes of wind turbine blade 风力涡轮机叶片边缘和襟翼耦合振动模式研究
Pub Date : 2024-02-02 DOI: 10.1177/10775463241230573
M. U. Saram, Jianming Yang
The coupled flapwise and edgewise vibrations of a horizontal axis wind turbine blade (HAWT) are discussed in this paper. Kinetic and potential energies of the blade are evaluated with consideration of the effects of gravity and aerodynamic forces. Hamilton’s principle is employed to develop the nonlinear coupled modal equations of the blade. The coupling between the first order edgewise and the first two order of flapwise modes is considered. This leads to three equations with nonlinear terms. Multiple-scales perturbation method is employed to solve these equations. Furthermore, the numerical values of structural specifications of National Renewable Energy Laboratory (NREL) 5-MW reference wind turbine blade are used, for example. It is shown that first edgewise and first flapwise vibrations are dominant, while second flapwise mode of vibration is less significant in the case of transient responses. Energy transfer between resonant modes is observed in both internal and combination resonances. The amplitude–frequency curves and phase diagrams during primary and combination resonances are obtained for the steady-state responses. Combination and primary resonances are further examined by considering various factors such as geometric nonlinearity and aerodynamic force.
本文讨论了水平轴风力涡轮机叶片(HAWT)的襟翼和边缘耦合振动。考虑到重力和空气动力的影响,对叶片的动能和势能进行了评估。采用汉密尔顿原理建立叶片的非线性耦合模态方程。考虑了一阶边缘模态和前两阶襟翼模态之间的耦合。这就产生了三个非线性方程。采用多尺度扰动法求解这些方程。此外,还以美国国家可再生能源实验室(NREL)5 兆瓦参考风力涡轮机叶片的结构规格数值为例。结果表明,在瞬态响应情况下,第一边缘振动和第一襟翼振动占主导地位,而第二襟翼振动模式的影响较小。在内部共振和组合共振中都可以观察到共振模式之间的能量传递。在主共振和组合共振期间,获得了稳态响应的幅频曲线和相位图。考虑到几何非线性和空气动力等各种因素,对组合共振和主共振进行了进一步研究。
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引用次数: 0
期刊
Journal of Vibration and Control
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