Aeroelastic Analysis of a Transonic Fan Blade with Low Hub-to-Tip Ratio including Mistuning Effects

This paper presents a comprehensive investigation of aeroelastic stability for a high aft-swept transonic fan blade with low hub-to-tip ratio. The evolution of the blade’s aeroelastic stability in the first bending modes is studied. A 3D flutter computation representing today’s industry standard is performed. Steady state flow field and motion-induced unsteady pressures acting on the blade have been determined by a 3D Reynolds-Averaged Navier-Stokes (RANS) equations with a standard k-ε turbulence model. A weakly coupled (one-way) method has been employed to describe the interaction between fluid and structure. The results of aerodynamic damping indicate a significant shock-driven risk. To increase the flutter margin by a viable method, a statistical mistuned aeroelastic stability investigation has been performed. It has been found that alternately intentional mistuning with a small blade frequency offset stabilizes the system effectively. However, as the standard deviation of random mistuning reaches some critical values, the introduction of alternately intentional mistuning does not provide any additional stabilizing effects.

Influence of Non-uniform Parameter of Bolt Joint on Complexity of Frequency Characteristics of Cylindrical Shell

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.

Research on mode localization of reticulated shell structures

Reticulated shell structures （RSSs） are characterized as cyclically periodic structures. Mistuning of RSSs will induce structural mode localization. Mode localization has the following two features： some modal vectors of the structure change remarkably when the values of its physical parameters （mass or stiffness） have a slight change; and the vibration of some modes is mainly restricted in some local areas of the structure. In this paper, two quantitative assessment indexes are introduced that correspond to these two features. The first feature is studied through a numerical example of a RSS, and its induced causes are analyzed by using the perturbation theory. The analysis showed that internally, mode localization is closely related to structural frequencies and externally, slight changes of the physical parameters of the structure cause instability to the RSS. A scaled model experiment to examine mode localization was carried out on a Kiewit single-layer spherical RSS, and both features of mode localization are studied. Eight tests that measured the changes of the physical parameters were carried out in the experiment. Since many modes make their contribution in structural dynamic response, six strong vibration modes were tested at random in the experimental analysis. The change and localization of the six modes are analyzed for each test. The results show that slight changes to the physical parameters are likely to induce remarkable changes and localization of some modal vectors in the RSSs.

Vibration Characteristics of Mistuned Bladed Disks

The finite element models of blade, disk and bladed disk are built up by finite element software ANSYS. The natural frequencies of the single blade, the whole bladed disk and the bladed disk with only one sector by cyclic symmetry boundary have been calculated. Then, based on the results above, a structure dynamic model of multiple degree-of-freedom （MDOF） systems is established to simulate the bladed-disk assembly. Solve the motion equation by using the Runge-Kutta Method （Gill Method）. The dynamic response of the MDOF system is achieved. As for the given mistuning patterns, the vibration responses of bladed disks are calculated. The results have been compared and analyzed, and the optimum pattern is selected.

Application of Improved Hybrid Interface Substructural Component Modal Synthesis Method in Vibration Characteristics of Mistuned Blisk

The large and complex structures are divided into hundreds of thousands or millions degrees of freedom（DOF） when they are calculated which will spend a lot of time and the efficiency will be extremely low. The classical component modal synthesis method （CMSM） are used extensively, but for many structures in the engineering of high-rise buildings, aerospace systemic engineerings, marine oil platforms etc, a large amount of calculation is still needed. An improved hybrid interface substructural component modal synthesis method（HISCMSM） is proposed. The parametric model of the mistuned blisk is built by the improved HISCMSM. The double coordinating conditions of the displacement and the force are introduced to ensure the computational accuracy. Compared with the overall structure finite element model method（FEMM）, the computational time is shortened by23.86%–31.56%and the modal deviation is 0.002%–0.157% which meets the requirement of the computational accuracy. It is faster 4.46%–10.57% than the classical HISCMSM. So the improved HISCMSM is better than the classical HISCMSM and the overall structure FEMM. Meanwhile, the frequency and the modal shape are researched, considering the factors including rotational speed, gas temperature and geometry size. The strong localization phenomenon of the modal shape’s the maximum displacement and the maximum stress is observed in the second frequency band and it is the most sensitive in the frequency veering. But the localization phenomenon is relatively weak in 1st and the 3d frequency band. The localization of the modal shape is more serious under the condition of the geometric dimensioning mistuned. An improved HISCMSM is proposed, the computational efficiency of the mistuned blisk can be increased observably by this method.

应用于几何失谐叶盘振动分析的考虑预应力的模态综合法（英文）

The importance of mistuning analysis lies on understanding the vibration characteristics of the bladed disk.Previous works generally ignored the nonlinear effect of prestress,which increase the gap between the actual results and research results.In this paper,a unique way to address the reduced-order model is presented,where disk and each blade component is attached as individual substructures with free-interface component mode synthesis considering prestress.The influence of nonlinear inertial effect on mistuning characteristics of rotors is compared with linear inertial effect.Results show that ignoring nonlinearity of the rotational speed,the influence of speed on mode localization may be different from the true situation.

Research on vibration suppression of a mistuned blisk by a piezoelectric network

The work aims to provide a further investigation of the dynamic characteristics of an integral bladed disk（also called ‘blisk＇） with a Parallel Piezoelectric Network（PPN）. The PPN is constructed by parallelly interconnecting the piezoelectric patches distributed in the blisk. Two kinds of PPN are considered, namely mono-periodic PPN and bi-periodic PPN. The former has a piezoelectric patch in each sector, and the later has one patch every few sectors. The vibration suppression performance of both kinds of PPN has been studied through modal analysis, forced response analysis, and statistical analysis. The research results turn out that the PPN will only affect mechanical frequencies near the electrical frequency clusters slightly, and the bi-periodic PPN will make the nodal diameter spectrum of the modes more complex, but the amplitude corresponding to the new nodal diameter component is much smaller than that of the nodal diameter component corresponding to the mono-periodic system. The mechanical coupling between the blades and the disk plays an important role in the damping effect of the PPN, and it should be paid attention to in applications. The mono-periodic PPN can effectively suppress the amplitude magnification of the forced response induced by the mistuning of the blisk; meanwhile, it can mitigate the vibration localization of the mistuned electromechanical system. If piezoelectric patches are set only in part of the sectors, the bi-periodic PPN still has a vibration suppression ability, but the effect is related to the number and spatial distribution of the piezoelectric patches.