This paper aims to investigate the wear evolution of contact interfaces and their impact on the nonlinear dynamics of anisotropic single-crystal blades. A modeling method for anisotropic blades is proposed, accompanied by a numerical simulation method that examines contact, friction, and wear behavior. Furthermore, a multi-scale dynamics solver is developed to analyze the behavior of anisotropic blades experiencing fretting wear. This method is applied to a shrouded single-crystal blade system, effectively predicting the wear behavior and its influence on the nonlinear response. Ultimately, the contributions of distinct anisotropic crystal orientations in single-crystal turbine blades to wear behavior and nonlinear dynamics are elucidated. It is determined that the nonlinear response, accounting for wear, is predominantly influenced by the angle beta.

The friction interface in friction-damped systems exhibits pronounced nonlinearity. Designing the critical structural parameters requires simultaneous consideration of multiple objective functions and extensive iterative computations for optimization evaluation. Therefore, a novel robust design approach for friction-damped systems enabling multi-objective simultaneous optimization is proposed. This approach integrates adaptive Polynomial Chaos Expansion (PCE) with multi-objective optimization techniques to efficiently design the critical parameters of friction-damped systems. The objective function is defined to ensure that the damping performance of the system adheres to specified robustness criteria under parameter uncertainty. This approach is applied to optimize critical parameters of simulated and real turbine blades with Underplatform Dampers (UPD), targeting both damping performance and robustness to parameter uncertainty. The Pareto front is obtained, and experiments validate the optimization results against test data. Results show that the predicted peak frequency and amplitude agree well with experiments. Considering design and contact uncertainties significantly improves the damping performance and robustness of the friction damper. Additionally, the study explores the robust design of UPD damping effects in actual turbine blades under various excitation levels. This approach has proven to be highly effective in maintaining lower blade amplitudes across diverse operating conditions.

Observations of a real aircraft engine shaft reveal that the rotor system is connected to the aircraft wing through a specifically oriented component, which is designed to couple axial and radial displacements. Although there have been many studies on the coupled vibration analysis of the disk-blade system, there are few reports on the cross-coupling mechanism caused by the asymmetric supports. With the aim of providing insight into a new cross-coupling phenomenon in the shaft-disk-blades system, a novel coupling model with asymmetric axial-radial supports is analytically formulated. Then the coupling model is validated by comparing the natural modal characteristics with the finite element model (FEM). At last, the new cross-coupling mechanism, induced by asymmetric radial supports, is investigated through analytical analysis and numerical investigations. In addition, a parametric study of the asymmetric support (stiffness and orientation) and disk location further highlighted the dynamic interaction of the subcomponents, revealing the roles of asymmetric radial supports in aggravating and mitigating cross-coupling vibration. The comparative analysis indicates that, in presence of an asymmetric axial-radial supporting structure, shaft axial and lateral mode will interact and further induce a new coupling with a flexible disc (0 and 1 ND) and blade bending modes simultaneously, giving rise to the so called “ARDMixedB”. The support asymmetry and disk location can determine the magnitude of dynamic coupling significantly, leading to mode mixing and exchange between axial and radial modes.

This study addresses the challenge of monitoring dynamic stresses in high-pressure turbine blades of aviation engines by designing a non-contact dynamic stress prediction method based on a BP neural network for rotating Disks. Firstly, the research focuses on a bladed disk, simulating blade tip displacement and blade root strain under various excitation conditions, and calculating stress outcomes using Hooke’s Law. Subsequently, an input-output neural network surrogate model is constructed with disk excitation conditions as inputs and blade tip displacement and monitoring point stress as outputs. Finally, the input and output data are divided into training and testing sets, and the surrogate model is trained and validated, ultimately establishing a non-contact dynamic stress prediction model for the disk under the influence of multi-parameter coupling. The data for building the neural network surrogate model is obtained through flat-bladed disk simulations, with model prediction errors within 6%.

Recent progress in aero-engine technologies has led to the widespread adoption of Nickel-based Single Crystal (SC) blades in turbine blade design. Firstly, this study explores the influence law of crystal orientation on the nonlinear dynamics of the nickel-based single-crystal shrouded bladed disk. Secondly, the research pays attention to the intricate changes in resonance amplitude corresponding to different crystal orientation angles. Ultimately, the surrogate models with different excitation forces are presented to achieve accurate prediction of the nonlinear dynamic response for a single-crystal bladed disk with arbitrary crystal orientations. An innovative approach has been proposed for predicting the nonlinear dynamics of the single crystal shrouded bladed disk. The method employs the multi-harmonic balance method to compute the nonlinear dynamics of the single-crystal shrouded bladed disk. Furthermore, dynamic response prediction method based on Kriging method is implemented to develop the surrogate models, which can predicts the nonlinear dynamics of the single crystal bladed disks under arbitrary crystal orientation accurately. Firstly, the numerical simulation indicates that the angles of crystal orientation play important roles in the nonlinear dynamics of the single crystal shrouded bladed disk. Then the surrogate model is constructed on the basis of the numerical results. Finally, the reliability of the surrogate models has been confirmed through various samples. The calculation results show that the effect of crystal orientation on nonlinear dynamic properties for single crystal bladed disk should be considered during the casting process. In this research, the significant influence of crystal orientation on the nonlinear behaviors of the single crystal shrouded bladed disk is analyzed. The primary objective of this work is to investigate the effect of the crystal orientations on the nonlinear responses and predict the responses amplitude for different crystal orientations. Unlike previous studies that have primarily focused on strength of single-crystal blades or bladed disks, this paper provides a comprehensive exploration of the nonlinear dynamic properties and the advanced predictive methodologies of tuned bladed disks under arbitrary crystal orientations. The results show that the effect of crystal orientation on the nonlinear response amplitude should be considered when casting the bladed disk to avoid high cycle fatigue.

In this paper, we proposed a frictional contact model for the tangential response of the contact plane within a thermal environment. Based on the Iwan model and Hertzian contact theory, the actual contact surface was considered a rigid smooth surface and an equivalent rough surface with different heights of micro-convex bodies with a uniformly distributed number to characterize the contact state of the contact surfaces. Additionally, an identification objective function was constructed based on the proposed friction model. The experimental data were taken as the initial values of the model parameters, and the values of the model parameters were identified through the least squares optimization algorithm, which verified the validity of the model. Finally, this paper examines how contact area, pressure, and the "blue brittleness" phenomenon of AISI1045 affect the friction characteristics of mechanical contact surfaces. This study offers theoretical guidance for accurately characterizing nonlinear friction assembly interfaces in thermal environments.

An effective method is developed in this study to identify the crystal orientation of Nickel-based single crystal turbine blade based on the influence law of crystal orientation on modal properties. Firstly, the calculation results obtained by using the high-fidelity model at the design points are referenced to construct the surrogate models of natural frequencies and normalized mode shapes based on the Kriging method. These surrogate models make it possible to determine the modal properties in any crystal orientation in a highly efficient way. Then, the 3D Scanning Laser Doppler Vibrometer (3D SLDV) technique is applied to the single crystal blade with unknown crystal orientation for obtaining the modal properties. It is also the first work to use 3D SLDV technique for experiment modal test on the single crystal blade to identify the crystal orientation. Finally, the objective function is constructed based on the modal properties obtained from surrogate model with respect to the result from the modal test of undefined single crystal blade. Artificial fish swarm algorithm (AFSA) is applied to continuously optimize the defined objective function for identifying the crystal orientation of single crystal blade. Compared with other methods for identifying the crystal orientation of single-crystal blades, the proposed method is able to obtain the crystal orientation accurately without the complicated test procedure and special test instruments. Meantime, the proposed method does not cause any damage to the single crystal blade. The high efficiency and high applicability of the proposed method are verified numerically, and then applied to a group of single crystal blades with unknown crystal orientations.

This paper proposed an effective method to predict the modal properties for single crystal blade with arbitrary crystal orientation. Firstly, the supermodel of single crystal blade is constructed to calculate the modal properties at the reference points. Then the surrogate models of natural frequencies and normalized mode shapes are constructed separately based on the Kriging method. Finally, the modal properties are predicted quickly when the crystal orientation is defined. The results show that the modal properties of single crystal blade in any crystal orientation within the limited range can be accurately predicted with high efficiency.

Underplatform dampers (UPDs) mitigate turbine blade vibrations in aeroengines through friction dissipation generated by the contact interface. However, in UPD design, uncertainties are often overlooked, including manufacturing discrepancies, excitation forces, and wear factors, leading to suboptimal predictions of structural dynamic responses. This study presents a dynamic model for the blade-UPD system with cyclic symmetric attributes, which simulates uncertainties using statistical methods. An efficient algorithm using adaptive techniques is proposed to construct polynomial chaos expansions (PCE) for precise and efficient uncertainty quantification (UQ) in turbine blades with UPDs. Further, the influence of single/multiple parameter uncertainties on the dynamic characteristics of the blade-UPD is explored. Sobol' indices are then employed to assess the sensitivity of uncertain factors to the vibration reduction properties of UPDs. The findings suggest that the new approach, which offers precise UQ at minimal computational cost, outperforms traditional methods like Ordinary Least Squares (OLS) and Sparse Least Angle Regression (LARS). Observations reveal a significant impact of parameter uncertainties on blade-UPD dynamic responses, which manifest as "resonance bands" and "frequency shifts" in some cases. Sensitivity analysis indicates noticeable variations in Sobol' indices for each uncertainty parameter as the excitation frequency changes. Specifically, the uncertainty in the friction coefficient demonstrates pronounced sensitivity to amplitude when slip occurs at the contact interface. Furthermore, the observed "drop" phenomenon in Sobol' indices is explained.

The coupling vibration of the blisk system has recently become an important area of research. The literature review indicates that the coupled behavior in the blisk system induces conspicuous distribution properties of modal frequencies of the blade-dominated family. However, this distribution rules and its evolution mechanism have not been fully interpreted in previous research. Therefore, present study will carry out three aspects of research work: In the first part, an analytical method has been developed to determine the coupling behavior between disk-dominated and blade-dominated families of modes for different blade number cases. The eigenvalue is firstly depicted as a function of the blade number to explain the distribution law of coupling modal frequencies. In the second part, experimental research is performed to exploit and verify the representative phenomenon in the blisk system. In the third part, a representative lumped-parameter (LP) model is proposed to simulate the blisk structure, and its analytical expressions of eigenvalue are formulated and discussed to explain the universality of the distribution rules of cycle blades’ coupling modes.

针对南京航空航天大学飞行器动力工程专业的专业基础课程-“机械振动学”的教学目标，文章提出“抛题”“解题”“拓题”“点题”及“巩固”五步式教学策略，在每个知识点的讲授过程中实现工程实例、问题引导和理论推导的有机结合，并通过实际教学案例论述了五步式教学策略的实施过程。教学实施结果表明，此教学策略可有助于教学目标的达成，教学效果提升明显。此外，文章展望了“机械振动学”课程授课方式的优化方向。

Analysis of the vibration reduction characteristics of shock absorbers is crucial for engines. In this study, the fractal theory was applied to the contact surface of an under-platform damper (UPD), and the influence of the excitation force in the same and opposite directions on the roughness of the contact surface was studied. First, based on fractal geometry theory (FGT), the roughness characterization method of a UPD contact surface was proposed. Then, the friction mechanical model of the rough contact surface was established by combining it with a 3D contact mechanical model. Furthermore, a finite element dynamic model of a blade with a UPD structure was set up. Next, the harmonic balance method was used to calculate the nonlinear response characteristics of a blade under different levels of contact surface roughness. Finally, the influence of the contact surface roughness on the vibration reduction ability of a UPD under different excitation modes was analyzed. According to the simulation results, as the contact surface became rougher, the vibration suppression ability of the UPD on the blade became stronger and stronger. With the change in the centrifugal force of the UPD and the amplitude of the same/reverse excitation force, the influencing law of the contact surface roughness on the vibration suppression ability of the UPD remained unchanged, indicating that the rougher the contact surface roughness, the better the vibration suppression effect.

In this paper, a contact slip mechanics model based on pressure distribution is developed, it is formed from multiple contact pairs and can define the contact behavior between contact interfaces. First, we establish the jointed structure's finite element model to calculate the contact interface's nodal pressure. Following this calculation, applying the cubic spline interpolation to the nodal pressure data, we obtain the contact surface pressure. Then using the theory of load equivalence, the contact surface pressure is converted into an equivalent load. The equivalent load is used as the normal pressure of the contact pairs place on the contact surface nodes. Subsequently, to verify the developed modeling approach, we establish a simplified blade model with the tenon-mortise structure for trial calculation. Finally, the nonlinear frictional force is linearized to solve the nonlinear differential equation by the incremental harmonic balance method (IHBM). The results show that the tenon-mortise contact surface exhibits micro-slip characteristics, which means that the pressure distribution characteristics of the contact surface are retained. The contact slip mechanics model developed in this paper is general which can be applied in modeling the contact surfaces of other joints.

Bolt connection is one of the main fixing methods of cylindrical shell structures. A typical bolted connection model is considered as a tuned system. However, in the actual working conditions, due to the manufacturing error, installation error and uneven materials of bolts, there are always random errors between different bolts. To investigate the influence of non-uniform parameters of bolt joint, including the stiffness and the distribution position, on frequency complexity characteristics of cylindrical shell through a statistical method is the main aim of this paper. The bolted joints considered here were simplified as a series of springs with random features. The vibration equation of the bolted joined cylindrical shell was derived based on Sanders’ thin shell theory. The Monte Carlo simulation and statistical theory were applied to the statistical analysis of mode characteristics of the system. First, the frequency and mode shape of the tuned system were investigated and compared with FEM. Then, the effect of the random distribution and the random constraint stiffness of the bolts on the frequency and mode shape were studied. And the statistical analysis on the natural frequencies was evaluated for different mistuned levels. And some special cases were presented to help understand the effect of random mistuning. This research introduces random theory into the modeling of bolted joints and proposes a reference result to interpret the complexity of the modal characteristics of cylindrical shells with non-uniform parameters of bolt joints.

The vibration reduction characteristics of the flexible blade with a dovetail joint and underplatform damper are studied in this paper. Considering the influence of the platform mass on the inherent characteristics of the blade, this paper regards the underplatform as a particle with mass. Moreover, two types of friction models are introduced on the contact interfaces of the blade. Meanwhile, the normal pressure of the contact interfaces will change with the rotating speed of the blade. Also, the dynamical equation for the rotating blade is established based on the finite element method. The nonlinear friction force on the contact interface is brought into the dynamical equation, and the vibration response of the blade is solved. The effects of the rotating speed, the initial preload, and the contact angle of the underplatform on the vibration reduction characteristic of the blade are investigated.

This paper focuses on the influence mechanism of cyclic blades on the dynamic coupling of a flexible shaft-disk-blade (FSDB) system through mathematical analysis and numerical simulation. Firstly, a coupling mechanism model of an FSDB unit is developed through a Lagrange method and the assumed mode method (AMM), after considering the coupling behavior among shaft bending, shaft torsion, disk vibration, and blade bending. The modal comparison results between the proposed model and FEM affirm the validity of the model. Then the analytical interpretation is explored by decomposing and discussing the diagonal coupling and cross-coupling matrices of the FSDB system. The mechanism discussion re-veals that the coupling matrices originate from the rigid and elastic motions of flexible disk and cyclic blades, indicating that the motions of cyclic blades play an important role in dynamic coupling. Therefore, the motions of cyclic blades are classified and analyzed, and their effects on natural frequencies (NFs) and critical speeds (CSs) are applied to fur-ther interpret and validate the dynamic coupling through numerical simulation. The nu-merical results indicate that motions of cyclic blades can increase, decrease, and eliminate the magnitude of dynamic coupling significantly.(c) 2022 Elsevier Inc. All rights reserved.

This paper aims to interpret the coupling modal properties of cyclic blades under impact–friction interactions and their evolution mechanism versus operating points. Therefore, a coupling analytical model of cyclic blades is developed based on a Lagrange method and the assumed mode method (AMM), after considering centrifugal stiffening, spin softening, stagger angle, and twist angle. Then a mixed modal analysis method (MMAM) for this analytical model is extended by combining the extended periodic motion concept (EPMC) with AMM. Wherein a classic alternating frequency/time method (AFT) and the continuation method are employed to overcome the numerical divergence problem. Then damped nonlinear normal modes (dNNMs), including eigenfrequencies, modal damping ratios, and mode shapes, of the coupling system with shroud joints are finally computed and discussed under different excitation levels and contact conditions through a modal synthesis algorithm. After that, the influence laws of centrifugal stiffening and spin softening on the dNNMs are explored to reveal its evolution mechanism versus operation speeds. Finally, the Campbell diagrams of dNNMs are successfully obtained to discuss the effects of the impact–friction coupling on critical speeds (CSs) of the shrouded blades system.

The present study's objectives are primarily to reveal the mistuning effects on the coupling system's non-linear vibration performance with a mechanical model of the flexible bladed disk system. And the sensitivities of the coupling system to different mistuning cases are also compared and estimated. Firstly, the tuned system's nonlinear characteristics are presented for providing a reference to interpret the nonlinear dynamics of the mistuning case. Then present analysis exploits the nonlinear response spectrum of the coupling system undergoing a series of parameter mistuning conditions. The numerical simulation reveals that the response characteristics of cycle blades exhibit perfect identity in the tuned system. When the parameter mistuning condition occurs, the identity characteristics are destroyed, especially the blade length mistuning case. The mistuning feature can also lead to new resonances at the modal frequency of flexible disk, which exhibits distinctive sensitivity to the different mistuning case. Besides, the vibration localization phenomenon occurs due to the broken cyclic periodicity of the bladed disk structure. Furthermore, enough attention should be paid to the coupling effects in the bladed disk system undergoing parameter mistuning in engineering practice. (C) 2021 Elsevier Ltd. All rights reserved.

This paper presents an investigation of the eigenvalues of veering and merging phenomena of a bladed disk system with contact features (an assembly bladed disk system). Of particular interest are the vibrational characteristics at rotational speed intervals at which the eigenvalue loci exhibit veering and merging phenomena. Furthermore, the current work attempts to investigate the interactions between the disk-dominated and blade-dominated families of modes in an assembly bladed disk system. In this regard, a representative model of an assembly bladed disk system is proposed, implementing an improved Euler-Bernoulli beam to model the rotating blade. The coupled equations of the bladed disk system are discretized using the modal functions which satisfy the eigenvalue problem. The change in modal properties of a blisk system with rotational speed is initially depicted to provide a reference for the analysis of a nonlinear system. Thereafter, the modal spectrum of the assembly bladed disk system is computed and analyzed by a frequency-domain method. Numerical analysis reveals that coupling interaction induces a series of eigenvalue veering and merging phenomena and that the modal frequencies at low rotational speeds are significantly affected by the nonlinearity of contact features. In particular, corresponding analysis of the mechanisms of these phenomena is presented. Furthermore, the present work also investigates the sensitivity of a low rotational speed interval and merging phenomena to several parameters. (C) 2020 Elsevier Ltd. All rights reserved.