Vibration localization of simplified mistuned cyclic structures undertaking external harmonic force

Critical fatigue problems often occur in mistuned cyclic structures since their forced vibration responses are often much larger than those of perfectly tuned structures. Therefore, it is of great importance to predict the forced vibration responses of mistuned cyclic structures for their safe and reliable designs. In this paper, a simplified model for mistuned cyclic structures is chosen to investigate vibration localization phenomena. The effects of mistuning, stiffness coupling, and damping on the variations of maximum forced vibration responses of the model are examined through numerical study. It is found that strong vibration localization occurs under certain relations among mistuning, stiffness coupling, and damping. It is also found that the maximum forced vibration response asymptotically increases as the number of repeated subcomponents of the cyclic structure increases.     

Vibration mechanism of a mistuned bladed-disk

For coupling vibration of the mistuned bladed-disk in aeroengine, the vibration differential equation of the system is established using component-mode synthesis methods. Experimental mode analysis and mode correction are used to calculate some low-order modes of tuned blade and the disk with cone-flange. The models of actual mistuned bladed-disk is constructed by exerting some small perturbation on the mode stiffness of blades. The forced vibration experimentation of an actual mistuned bladed-disk in non-rotating status is carried out to verify the vibration model and calculation formulae. The results show that excessive vibration response of a single blade is caused by blade mistuning, and the random mistuning distribution of a small frequency difference is more profitable than other arrangements for depressing the maximal vibration level of the hapless blade. In this study, the better natural frequency difference amplitude of blades and the right working frequency range of aeroengine are also suggested according to the result analysis of several numerical calculations.     

An electro-mechanical impedance model of a cracked composite beam with adhesively bonded piezoelectric patches

A model of a laminated composite beam including multiple non-propagating part-through surface cracks as well as installed PZT transducers is presented based on the method of reverberation-ray matrix (MRRM) in this paper. Toward determining the local flexibility characteristics induced by the individual cracks, the concept of the massless rotational spring is applied. A Timoshenko beam theory is then used to simulate the behavior of the composite beam with open cracks. As a result, transverse shear and rotatory inertia effects are included in the model. Only one-dimensional axial vibration of the PZT wafer is considered and the imperfect interfacial bonding between PZT patches and the host beam is further investigated based on a Kelvin-type viscoelastic model. Then, an accurate electro-mechanical impedance (EMI) model can be established for crack detection in laminated beams. In this model, the effects of various parameters such as the ply-angle, fibre volume fraction, crack depth and position on the EMI signatures are highlighted. Furthermore, comparison with existent numerical results is presented to validate the present analysis.     

CRACK DETECTION IN BEAM-TYPE STRUCTURES USING FREQUENCY DATA

A practical method to non-destructively locate and estimate size of a crack by using changes in natural frequencies of a structure is presented. First, a crack detection algorithm to locate and size cracks in beam-type structures using a few natural frequencies is outlined. A crack location model and a crack size model are formulated by relating fractional changes in modal energy to changes in natural frequencies due to damage such as cracks or other geometrical changes. Next, the feasibility and practicality of the crack detection scheme are evaluated for several damage scenarios by locating and sizing cracks in test beams for which a few natural frequencies are available. By applying the approach to the test beams, it is observed that crack can be confidently located with a relatively small localization error. It is also observed that crack size can be estimated with a relatively small size error.     

CRACK IDENTIFICATION IN VIBRATING BEAMS USING THE ENERGY METHOD

An energy-based numerical model is developed to investigate the influence of cracks on structural dynamic characteristics during the vibration of a beam with open crack(s). Upon the determination of strain energy in the cracked beam, the equivalent bending stiffness over the beam length is computed. The cracked beam is then taken as a continuous system with varying moment of intertia, and equations of transverse vibration are obtained for a rectangular beam containing one or two cracks. Galerkin's method is applied to solve for the frequencies and vibration modes. To identify the crack, the frequency contours with respect to crack depth and location are defined and plotted. The intersection of contours from different modes could be used to identify the crack location and depth.     

离心压缩机级内三维粘性流动数值分析

本文介绍了用时间推进法进行离心压缩机级内全三维粘性流场的计算方法．该方法是作者在已完成的求解孤立叶排Ｎ－Ｓ方程的计算程序的基础上发展的，通过使用周向非均匀的叶排间隙混合平面概念来考虑离心叶轮与扩压器之间的相互影响，并依据质量守恒原则，对下游的进口气流角进行了修正，以保证了上下游叶排在相容的流动特性下工作．完成了离心压缩机级（包括叶轮与扩压器）三维粘性定常流场的计算及性能预测．应用本文所发展的程序，对某高炉鼓风机的叶轮及其叶片扩压器进行了计算．     

压缩理想气体和实际气体的离心式叶轮流场分析

本文对压缩理想气体和实际气体的离心式叶轮作了流场分析。分析使用流线曲率法。实际气体的热力学是基于作者提出的通用状态方程和Ｓｃｈｕｌｅｓ的多变分析。对一个压缩理想气体的叶轮作了实验测量。分析结果比较表明，压缩理想气体和实际气体时叶轮中速度分布是不同的，且压缩实际气体时，叶轮出口参数不同于压缩理想气体时的计算和实测结果。     

SIMPLIFIED MODELS FOR THE LOCATION OF CRACKS IN BEAM STRUCTURES USING MEASURED VIBRATION DATA

A new simplified approach to modelling cracks in beams undergoing transverse vibration is presented. The modelling approach uses Euler-Bernoulli beam elements with small modifications to the local flexibility in the vicinity of cracks. This crack model is then used to estimate the crack locations and sizes, by minimizing the difference between the measured and predicted natural frequencies via model updating. The uniqueness of the approach is that the simplified crack model allows the location and damage extent to be estimated directly. The simplified crack model may also be used to generate training data for pattern recognition approaches to health monitoring. The proposed method has been illustrated using the experimental data on beam examples.     

Crack detection in single-crystalline silicon wafers using impact testing

This paper presents acoustic measurements obtained by mechanically exciting vibratory modes in single-crystalline silicon wafers with hairline periphery cracks of different type and location. The data presented shows a dependence of natural frequencies, peak amplitudes and damping levels of four audio vibration modes in the frequency range up to 1000 Hz on crack type and crack location. Data from defective wafers exhibit lower natural frequencies, higher damping levels, and lower peak amplitudes. The results suggest an impact test method may be useful for solar cell crack detection and quality control.     

Coupled horizontal and vertical bending vibrations of a stationary shaft with two cracks

This paper investigates the coupled bending vibrations of a stationary shaft with two cracks. It is known from the literature that, when a crack exists in a shaft, the bending, torsional, and longitudinal vibrations are coupled. This study focuses on the horizontal and vertical planes of a cracked shaft, whose bending vibrations are caused by a vertical excitation, in the clamped end of the model. When the crack orientations are not symmetrical to the vertical plane, a response in the horizontal plane is observed due to the presence of the cracks. The crack orientation is defined by the rotational angle of the crack, a parameter which affects the horizontal response. When more cracks appear in a shaft, then the coupling becomes stronger or weaker depending on the relative crack orientations. It is shown that a double peak appears in the vibration spectrum of a cracked or multi-cracked shaft.Modeling the crack in the traditional manner, as a spring, yields analytical results for the horizontal response as a function of the rotational angle and the depths of the two cracks. A 2×2 compliance matrix, containing two non-diagonal terms (those responsible for the coupling) serves to model the crack. Using the Euler–Bernoulli beam theory, the equations for the natural frequencies and the coupled response of the shaft are defined. The experimental coupled response and eigenfrequency measurements for the corresponding planes are presented. The double peak was also experimentally observed.     

Analytical modeling and vibration analysis of internally cracked rectangular plates

This study proposes an analytical model for nonlinear vibrations in a cracked rectangular isotropic plate containing a single and two perpendicular internal cracks located at the center of the plate. The two cracks are in the form of continuous line with each parallel to one of the edges of the plate. The equation of motion for isotropic cracked plate, based on classical plate theory is modified to accommodate the effect of internal cracks using the Line Spring Model. Berger?s formulation for in-plane forces makes the model nonlinear. Galerkin?s method used with three different boundary conditions transforms the equation into time dependent modal functions. The natural frequencies of the cracked plate are calculated for various crack lengths in case of a single crack and for various crack length ratio for the two cracks. The effect of the location of the part through crack(s) along the thickness of the plate on natural frequencies is studied considering appropriate crack compliance coefficients. It is thus deduced that the natural frequencies are maximally affected when the crack(s) are internal crack(s) symmetric about the mid-plane of the plate and are minimally affected when the crack(s) are surface crack(s), for all the three boundary conditions considered. It is also shown that crack parallel to the longer side of the plate affect the vibration characteristics more as compared to crack parallel to the shorter side. Further the application of method of multiple scales gives the nonlinear amplitudes for different aspect ratios of the cracked plate. The analytical results obtained for surface crack(s) are also assessed with FEM results. The FEM formulation is carried out in ANSYS.     

非设计工况下低比速泵叶轮内不稳定流动和湍流度试验

采用两维激光流速仪，在非设计工况下对三种泵叶轮不稳定流动和湍流度进行了测试，结果表明：叶轮内不稳定流动和湍流度受旋转和曲率及入流状态的综合影响，呈十分复杂的空间分布，偏离设计点时湍流强度和流动脉动与叶轮内流场相互关联，相对于设计工况都更要高些。     

Thresholds for the detection of inharmonicity in complex tones

Thresholds were measured for the detection of inharmonicity in complex tones. Subjects were required to distinguish a complex tone whose partials were all at exact harmonic frequencies from a similar complex tone with one of the partials slightly mistuned. The mistuning which allowed 71% correct identification in a two-alternative forced-choice task was estimated for each partial in turn. In experiment I the fundamental frequency was either 100, 200, or 400 Hz, and the complex tones contained the first 12 harmonics at equal levels of 60 dB SPL per component. The stimulus duration was 410 ms. For each fundamental the thresholds were roughly constant when expressed in Hz, having a mean value of about 4 Hz (range 2.4-7.3 Hz). In experiment II the fundamental frequency was fixed at 200 Hz, and thresholds for inharmonicity were measured for stimulus durations of 50, 110, 410, and 1610 ms. For harmonics above the fifth the thresholds increased from less than 1 Hz to about 40 Hz as duration was decreased from 1610-50 ms. For the lower harmonics (up to the fourth) threshold changed much less with duration, and for the three shorter durations thresholds for each duration were roughly a constant proportion of the harmonic frequency. The results suggest that inharmonicity is detected in different ways for high and low harmonics. For low harmonics the inharmonic partial appears to "stand out" from the complex tone as a whole. For high harmonics the mistuning is detected as a kind of "beat" or "roughness," presumably reflecting a sensitivity to the changing relative phase of the mistuned harmonic relative to the other harmonics.(ABSTRACT TRUNCATED AT 250 WORDS)     

THE DYNAMIC STIFFNESS MATRIX METHOD IN FORCED VIBRATION ANALYSIS OF MULTIPLE-CRACKED BEAM

The dynamic behaviour of a beam with numerous transverse cracks is studied. Based on the equivalent rotational spring model of crack and the transfer matrix for beam, the dynamic stiffness matrix method has been developed for spectral analysis of forced vibration of a multiple cracked beam. As a particular case, when the excitation frequency is close to zero, the solution for static response of beam with an arbitrary number of cracks has been obtained exactly in an analytical form. In general case, the effect of crack number and depth on the dynamic response of beam was analyzed numerically.     

弯曲母线离心叶轮设计方案比较、分析

为了探讨叶型弯曲不同分布对叶轮效率的影响,本文使用三元粘性数值模拟方法,对几个具有弯曲母线的离心叶轮进行了分析比较,在减损机理、特别是设计准则方面进行了摸索和探讨。     

Free vibration analysis of beams and frames with multiple cracks for damage detection

The problem of calculating the natural frequencies of beams with multiple cracks and frames with cracked beams is studied. The natural frequencies are obtained using a new method in which a rotational spring model is used to represent the cracks. For beams, dynamic stiffness matrices of order 4 are obtained in a recursive manner, according to the number of cracks, by applying partial Gaussian elimination. The Wittrick–Williams algorithm is used to compute the natural frequencies in the resulting transcendental eigenvalue problem. Published numerical examples for cracked beams are used for validation. The global dynamic stiffness matrix of a frame with multiply cracked members is then assembled. A published two bay frame example is used to evaluate the new method. The effect of changing the location of a crack in a two bay two storey frame is studied numerically, giving insight into the inverse problem of damage detection.     

离心压气机叶轮的"可控涡"设计及其CFD比较分析

根据准三维气动没计方法,用Bezier曲线构造叶轮子午流道,样条曲线控制环量沿子午面流线的分布规律,气动设计离心式叶轮。通过CFD数值模拟对设计叶轮性能分析比较,结果表明利用准三维设计与三维流动分析相结合的途径是一种比较方便实用的设计方法,且控制参数(环量)的给定未必一定受库塔条件的限制。     

高比转速离心压气机叶轮的设计及其三维流场分析

利用三维数值模拟计算(CFD)技术进行了100 kW微型燃气轮机的高比转速离心压气机叶轮的设计与内部流动的数值模拟与分析,得到了相应的特性曲线与主要气动参数分布。根据数值模拟分析,设计的100 kW微型燃气轮机高比转速离心压气机叶轮具有较高的效率和较宽广且平坦的工作特性,可以满足微燃机总体设计对压气机的要求。流道内存在复杂的跨音速流动现象。在下一步工作中,有必要优化设计叶轮几何型线,提高压气机效率。     

The use of roving discs and orthogonal natural frequencies for crack identification and location in rotors

A variety of approaches that have been developed for the identification and localisation of cracks in a rotor system, which exploit natural frequencies, require a finite element model to obtain the natural frequencies of the intact rotor as baseline data. In fact, such approaches can give erroneous results about the location and depth of a crack if an inaccurate finite element model is used to represent an uncracked model. A new approach for the identification and localisation of cracks in rotor systems, which does not require the use of the natural frequencies of an intact rotor as a baseline data, is presented in this paper. The approach, named orthogonal natural frequencies (ONFs), is based only on the natural frequencies of the non-rotating cracked rotor in the two lateral bending vibration x–z and y–z planes. The approach uses the cracked natural frequencies in the horizontal x–z plane as the reference data instead of the intact natural frequencies. Also, a roving disc is traversed along the rotor in order to enhance the dynamics of the rotor at the cracked locations. At each spatial location of the roving disc, the two ONFs of the rotor–disc system are determined from which the corresponding ONF ratio is computed. The ONF ratios are normalised by the maximum ONF ratio to obtain normalised orthogonal natural frequency curves (NONFCs). The non-rotating cracked rotor is simulated by the finite element method using the Bernoulli–Euler beam theory. The unique characteristics of the proposed approach are the sharp, notched peaks at the crack locations but rounded peaks at non-cracked locations. These features facilitate the unambiguous identification and locations of cracks in rotors. The effects of crack depth, crack location, and mass of a roving disc are investigated. The results show that the proposed method has a great potential in the identification and localisation of cracks in a non-rotating cracked rotor.     

A numerical study on the flow and sound fields of centrifugal impeller located near a wedge

Centrifugal fans are widely used and the noise generated by these machines causes one of the serious problems. In general, the centrifugal fan noise is often dominated by tones at blade passage frequency and its higher harmonics. This is a consequence of the strong interaction between the flow discharged from the impeller and the cut-off in the casing. However, only a few researches have been carried out on predicting the noise because of the difficulty in obtaining detailed information about the flow field and considering the scattering effect of the casing. The objective of this study is to understand the generation mechanism of sound and to develop a prediction method for the unsteady flow field and the acoustic pressure field of the centrifugal impeller. A discrete vortex method is used to model the centrifugal impeller and a wedge and to calculate the flow field. The force of each element on the blade is calculated by the unsteady Bernoulli equation. Lowson's method is used to predict the acoustic source. In order to consider the scattering and diffraction effects of the casing, Kirchhoff-Helmholtz boundary element method (BEM) is developed. The source of Kirchhoff-Helmholtz BEM is newly developed, so the sound field of the centrifugal fan can be obtained. A centrifugal impeller and wedge are used in the numerical calculation and the results are compared with the experimental data. Reasonable results are obtained not only for the peak frequencies but also for the amplitudes of the tonal sound. The radiated acoustic field shows the diffraction and scattering effect of the wedge.