Swept sine testing of rotor-bearing system for damping estimation

Many types of rotating components commonly operate above the first or second critical speed and they are subjected to run-ups and shutdowns frequently. The present study focuses on developing FRF of rotor bearing systems for damping estimation from swept-sine excitation. The principle of active vibration control states that with increase in angular acceleration, the amplitude of vibration due to unbalance will reduce and the FRF envelope will shift towards the right (or higher frequency). The frequency response function (FRF) estimated by tracking filters or Co-Quad analyzers was proved to induce an error into the FRF estimate. Using Fast Fourier Transform (FFT) algorithm and stationary wavelet transform (SWT) decomposition FRF distortion can be reduced. To obtain a theoretical clarity, the shifting of FRF envelope phenomenon is incorporated into conventional FRF expressions and validation is performed with the FRF estimated using the Fourier Transform approach. The half-power bandwidth method is employed to extract damping ratios from the FRF estimates. While deriving half-power points for both types of responses (acceleration and displacement), damping ratio (ζ) is estimated with different approximations like classical definition (neglecting damping ratio of order higher than 2), third order (neglecting damping ratios with order higher than 4) and exact (no assumptions on damping ratio). The use of stationary wavelet transform to denoise the noise corrupted FRF data is explained. Finally, experiments are performed on a test rotor excited with different sweep rates to estimate the damping ratio.     

Non-linear vibrations of cables considering loosening

A cable cannot resist the axial compressive force that may be induced during large amplitude vibrations. In this paper, the effect of cable loosening on non-linear vibrations of flat-sag cables is discussed by using the finite difference method that can express cable loosening. In the present method, flexural rigidity and damping of the cable are considered in the equations of motion of a cable in order to handle the numerical instability. The effect of cable loosening is evaluated explicitly in the present paper. Furthermore, non-linear vibration properties are evaluated for various parameters under periodic and step vertical loading. The effect of cable loosening on response under vertical periodic time-varying load is small and it is possible for the sag-to-span ratio to roughly equal the ratio for modal transition. The loosening under the vertical step loading in the direction opposite to the gravity appears at almost the same sag-to-span ratio.     

Spectral and perturbation analysis for ultrasonic guided waves

The influence of damage on waves propagating in complex geometry waveguides is investigated through a numerical model formulated by combining the Spectral Finite Element Method and Perturbation Techniques. The resulting numerical tool allows efficient computation of the wave propagation response and the analysis of the effects of damages of various extent and location. The dynamic behavior of the damaged waveguides is described through a general higher order model which couples different waves thus allowing the prediction of mode conversion phenomena. Arbitrary cross-section can be considered through Finite Element (FE) discretization according to well-established Semi-Analytical Finite Element (SAFE) procedures. Two types of damages which allow the application of perturbation theory are considered: a small localized reduction of the thickness and a reduction of material stiffness and density. A validation by comparison with a Finite Element Model as well as numerical examples are presented to illustrate the model capabilities.     

Three-dimensional non-linear coupling and dynamic tension in the large-amplitude free vibrations of arbitrarily sagged cables

This paper presents a model formulation capable of analyzing large-amplitude free vibrations of a suspended cable in three dimensions. The virtual work-energy functional is used to obtain the non-linear equations of three-dimensional motion. The formulation is not restricted to cables having small sag-to-span ratios, and is conveniently applied for the case of a specified end tension. The axial extensibility effect is also included in order to obtain accurate results. Based on a multi-degree-of-freedom model, numerical procedures are implemented to solve both spatial and temporal problems. Various numerical examples of arbitrarily sagged cables with large-amplitude initial conditions are carried out to highlight some outstanding features of cable non-linear dynamics by accounting also for internal resonance phenomena. Non-linear coupling between three- and two-dimensional motions, and non-linear cable tension responses are analyzed. For specific cables, modal transition phenomena taking place during in-plane vibrations and ensuing from occurrence of a dominant internal resonance are observed. When only a single mode is initiated, a higher or lower mode can be accommodated into the responses, making cable spatial shapes hybrid in some time intervals.     

Accurate identification of the frequency response functions for the rotor-bearing-foundation system using the modified pseudo mode shape method

In this paper, an identification technique in the dynamic analyses of rotor-bearing-foundation systems called the pseudo mode shape method (PMSM) was improved in order to enhance the accuracy of the identified dynamic characteristic matrices of its foundation models. Two procedures, namely, phase modification and numerical optimisation, were proposed in the algorithm of PMSM to effectively improve its accuracy. Generally, it is always necessary to build the whole foundation model in studying the dynamics of a rotor system through the finite element analysis method. This is either unfeasible or impractical when the foundation is too complicated. Instead, the PMSM uses the frequency response function (FRF) data of joint positions between the rotor and the foundation to establish the equivalent mass, damping, and stiffness matrices of the foundation without having to build the physical model. However, the accuracy of the obtained system's FRF is still unsatisfactory, especially at those higher modes. In order to demonstrate the effectiveness of the presented methods, a solid foundation was solved for its FRF by using both the original and modified PMSM, as well as the finite element (ANSYS) model for comparisons. The results showed that the accuracy of the obtained FRF was improved remarkably with the modified PMSM based on the results of the ANSYS. In addition, an induction motor resembling a rotor-bearing-foundation system, with its housing treated as the foundation, was taken as an example to verify the algorithm experimentally. The FRF curves at the bearing supports of the rotor (armature) were obtained through modal testing to estimate the above-mentioned equivalent matrices of the housing. The FRF of the housing, which was calculated from the equivalent matrices with the modified PMSM, showed satisfactory consistency with that from the modal testing.     

Vibration control by recursive time-delayed acceleration feedback

This paper presents a theoretical basis of time-delayed acceleration feedback control of linear and nonlinear vibrations of mechanical oscillators. The control signal is synthesized by an infinite, weighted sum of the acceleration of the vibrating system measured at equal time intervals in the past. The proposed method is shown to have controlled linear resonant vibrations, low-frequency non-resonant vibrations, primary and 1/3 subharmonic resonances of a forced Duffing oscillator. The concept of an equivalent damping and natural frequency of the system is also introduced. It is shown that a large amount of damping can be produced by appropriately selecting the control parameters. For some combinations of the control parameters, the effective damping factor of the system is shown to be inversely related to the time-delay in the small delay limit. Selection of the optimum control parameters for controlling the forced and free vibrations is discussed. It is shown that forced vibration is best controlled by unity recursive gain and smaller values of the time-delay parameter. However, the transient response can be optimally controlled by suitably selecting the time delay depending upon the gain. The delay values for the optimal forced response may be different from that required for the optimum transient response. When both are important, a suboptimal choice of the delay parameters with unity recursive gain is recommended.     

基于近场辐射声压信号的索力识别方法*

为准确、快速获取拉索结构索力,该文提出利用结构近场固定位置辐射声压信号对拉索进行索力测试的方法。基于动力学理论推导出结构振动加速度响应与其近场辐射声压响应的线性比例关系,并根据希尔伯特-黄变换推导了声压响应信号与结构频率的关系。对单根拉索依次施加3种不同工况的初始张拉力,并对结构中心表面处施加一瞬时脉冲力,使拉索受迫振动发声,通过对结构近场范围内拉索振动辐射声压进行测量,进而获得不同工况下不同位置声压响应信号,并探讨了在有高斯噪声干扰情况下通过希尔伯特-黄变换方法获取拉索固有频率的可靠性。数值模拟分析验证了该方法能较为准确地得到拉索固有频率并利用索力计算实用公式有效地计算出索力值,为实际工程中拉索索力测试提供了一种新的简单有效的方法。     

Prediction of uncertain frequency response function bounds using polynomial chaos expansion

A probabilistic method is developed to predict the uncertainty bounds on Frequency Response Functions (FRFs) developed from Finite Element models. A non-intrusive Polynomial Chaos Expansion (PCE) method is used to predict uncertainty regression models of the various parameters that make up a curvefit of the FRF: natural frequencies, damping ratios, complex amplitudes, mass and stiffness residuals, by making use of an efficient Latin Hypercube technique. These uncertainty models are then combined to efficiently determine PDFs of the parameters and also the uncertainty bounds of the FRFs. The approach is demonstrated using two examples; a simple beam containing uncertainty in Young's Modulus, and a full-scale aircraft composite wing model containing uncertainties in both Young's modulus and the shear modulus. The results were compared with Monte Carlo Simulation (MCS) and it was found that the parameter PDFs and FRF error bounds obtained using a 2nd-order PCE model agreed very well whilst requiring significantly less computation.     

Exact analytical formula for Voigt spectral line profile

An analytical formula for the Voigt spectral line profile has been derived. The obtained formula is the solution of the second-order differential equation of the Voigt profile. The obtained results using the new analytical formula are in perfect agreement with the published results obtained by numerical calculation methods for a wide range of the line damping parameter (a) . The accuracy of the obtained formula is found to be 100% for all ranges of the line damping parameter (a).     

Power law damping parameter identification

The parameter estimation of a nonlinear power damping system is studied. The parameter identification method used here assumes a priori the equation of motion describing the system dynamics. The method, which is based on the measured data (acceleration), was applied to the free and forced vibrations.The identification procedure was found to be robust on the guessed value of parameters at the numerical experimentation. The parameter values were estimated with a good accuracy for both modes of system operation (free and forced) if only the measured time history was sampled at a high enough rate for the noise level contained within. It was shown that the steady state of the harmonically excited system is not the best region for the parameter identification with this method.During the experimentation the method was applied to the free vibrations in different media (air and water). The results obtained by the parameter identification method were compared to the ones obtained by separate tests and good agreement was found. The identification procedure was found to work fine for all models under consideration and the models' responses correspond well to the measured acceleration time histories.     

Damping characteristics of a spray-deposited shape memory alloy beam

The damping characteristics of an Ni–Ti shape memory alloy (SMA) beam are theoretically and experimentally studied with interest in identifying an appropriate damping model for the material. The SMA beam is manufactured by a spray deposition method followed by heat treatment and found to have nanocrystalline structure in which damping capacity is high. The beam is then tested to obtain an impulse response and the frequency response function (FRF). By using the Hilbert transform technique it is shown that damping of the beam is almost amplitude independent in the tested range of displacement. It is also shown from the FRF that the damping of the spray-deposited shape memory alloy beam is well represented by a model including both linear viscous and hysteretic dampings.     

Prediction of vibrations induced by underground railway traffic in Beijing

This paper examines the problem of subway induced vibrations on line 4 of Beijing metro, which is currently under construction and is planned to pass in close proximity of the Physics Laboratory of Beijing University. The laboratory has a lot of equipment that is very sensitive to traffic induced vibrations and future operation of metro line 4 is a matter of concern. Hence, it is important to study the influence of subway induced vibrations inside the laboratory and to propose a viable solution to mitigate the vibrations. In this paper, the tunnel north of Chengfulu station is modelled using a coupled periodic FE-BE model and the free-field response due to moving trains is predicted. In addition, vibration measurements have been performed on the site of the Physics Laboratory to estimate the existing vibration levels due to road traffic. The predicted and measured vibrations are superimposed to assess the vibrations due to the combined effect of road and railway traffic in the vicinity of the Physics Laboratory. Apart from the numerical investigations, vibration measurements have also been performed on a similar site at line 1 of Beijing metro to substantiate the estimated results on metro line 4. Finally, it is studied how the vibrations can be controlled using a floating slab track, which is widely used as an effective measure of vibration isolation in tunnels. The efficiency of a 7.9 Hz floating slab track as a vibration countermeasure is assessed in this paper. This study demonstrates the applicability of the numerical model for the relevant assessment of subway induced vibrations and its use to study the performance of different track structures in the tunnel.     

正常星系光谱的一种谱线自动提取方法

正常星系的光谱是天体光谱谱线自动提取中最难处理的一种。文章针对正常星系光谱给出了一种新的谱线自动提取方法。首先,定义了两条光谱间的Max操作,Max操作的结果是生成了一条光谱,该光谱在每个波长处的强度取为在相应波长处强度较大的那一个光谱的强度;然后,通过迭代处理拟合连续谱,在每一步迭代中,先对原始光谱和前一步拟合出的连续谱进行Max操作,再对Max操作生成的光谱进行传统的连续谱拟合;最后,联合采用整体阈值处理和自适应的局部阈值处理提取谱线。实验结果表明：该方法的性能较之传统的小波方法有显著提高,这将对后续的基于谱线的光谱分类和参数测量非常有利。     

Nonlinear vibration of iced cable under wind excitation using three-degree-of-freedom model

High-voltage transmission line possesses a typical suspended cable structure that produces ice in harsh weather. Moreover, transversely galloping will be excited due to the irregular structure resulting from the alternation of lift force and drag force. In this paper, the nonlinear dynamics and internal resonance of an iced cable under wind excitation are investigated.Considering the excitation caused by pulsed wind and the movement of the support, the nonlinear governing equations of motion of the iced cable are established using a three-degree-of-freedom model based on Hamilton's principle. By the Galerkin method, the partial differential equations are then discretized into ordinary differential equations. The method of multiple scales is then used to obtain the averaged equations of the iced cable, and the principal parametric resonance-1/2 subharmonic resonance and the 2:1 internal resonance are considered. The numerical simulations are performed to investigate the dynamic response of the iced cable. It is found that there exist periodic, multi-periodic, and chaotic motions of the iced cable subjected to wind excitation.     

Response of plates with unconstrained layer damping treatment to random acoustic excitation,part II: Response evaluation

Theoretical and experimental investigations on the response of a plate with unconstrained layer damping treatment to random acoustic excitation have been carried out. The theoretical response evaluation consisted of determining the power spectral density of the acceleration response of the layered plate by the use of generalized harmonic analysis under a specific random acoustic excitation, with use being made of modal frequencies and associated loss factors estimated as described in Part I. A study was made on the contribution of cross coupling terms of the acceleration response for the two boundary conditions investigated: namely, all edges simply supported and all edges clamped. In the experimental investigation, plates with different damping layer thicknesses were subjected to high intensity random acoustic excitation generated by an exponential horn driven by an electropneumatic transducer. The acceleration responses were recorded and later analyzed to yield the power spectral densities. Experimental and theoretical results are compared.     

Dynamic analysis of ring-stiffened circular cylindrical shells

A numerical method is developed for the dynamic analysis of ring-stiffened circular cylindrical thin elastic shells. Only circular symmetric vibrations of the shell segments and radial and torsional vibrations of the rings are considered. The geometric and material properties of the shell segments and the rings may vary from segment to segment. Free vibrations or forced vibrations due to harmonic pressure loading are treated with the aid of dynamic stiffness influence coefficients for shell segments and rings. Forced vibrations due to transient pressure loading are treated with the aid of dynamic stiffness influence coefficients for shell segments and rings defined in the Laplace transform domain. The time domain response is then obtained by a numerical inversion of the transformed solution. The effect of external viscous or internal viscoelastic damping is also investigated by the proposed method. In all the cases, the dynamic problem is reduced to a static-like form and the “exact” solution of the problem is numerically obtained.     

Modelling of soil vibrations from railway tunnels

In densely populated areas such as the Netherlands, it is useful to predict railway traffic induced vibrations if a new railway line is to be built. A modular model, consisting of three sub-models is presented. The three sub-models are: the Static Deflection Model, the Track Model and the Propagation Model. The modular model takes into account all aspects, from the source to the propagation of waves through the soil. In order to investigate the dependence of the results on the accuracy of the model inputs, a parameter study has been performed with the third-sub model: the propagation model. For this study a Japanese metro tunnel has been modelled. Element size, soil stiffness, damping, boundary conditions and finite element method (FEM) software have been varied.     

双同轴电缆差分传输方式对干扰的抑制作用

传输线对信号的无失真传输是超宽带测量系统准确获得待测波形和量值的前提之一。基于带宽、功率容量、损耗、屏蔽性能、尺寸等诸多因素,在超宽带测量系统中经常选用同轴电缆作为传输线。指出采用单根同轴电缆传输信号时会引入干扰,分析了干扰形成的原因,通过数值模拟确认了干扰的存在和危害;提出采用两根共地同轴电缆共同传输信号并进行差分处理,可以有效消除传输线引入的干扰,分析了干扰消除的过程和原理,将原数值模拟模型中的单同轴电缆替换为双同轴电缆进行仿真计算,对比验证了双同轴电缆差分传输方式对干扰的有效抑制作用;对双同轴电缆差分传输结构进行了实验测试,结果表明,单根同轴电缆会引入较大的干扰信号,通过两根同轴电缆的共地连接、差分处理,可以有效消除干扰,达到高保真传输要求。     

Advances in testing the effect of acceleration on time dilation using a synchrotron Mössbauer source

New results, additional techniques and know‐how acquired, developed and employed in a recent HC‐1898 experiment at the Nuclear Resonance Beamline ID18 of ESRF are presented, in the quest to explore the acceleration effect on time dilation. Using the specially modified Synchrotron Mössbauer Source and KB‐optics together with a rotating single‐line semicircular Mössbauer absorber on the rim of a specially designed rotating disk, the aim was to measure the relative spectral shift between the spectra of two states when the acceleration of the absorber is anti‐parallel and parallel to the source. A control system was used for the first time and a method to quantify the effects of non‐random vibrations on the spectral shift was developed. For several runs where the effect of these vibrations was negligible, a stable statistically significant non‐zero relative shift was observed. This suggests the influence of acceleration on time.     

稀土掺杂固体发光材料的光谱分析

光谱分析是评价稀土发光材料光谱性质的主要依据,Judd-Ofelt(J-O)理论是光谱分析的基础。详述了采用J-O模型拟合三个强度参量和估算一些重要辐射参量的操作细节,讨论了相关公式的合理应用,总结了计算中误差的主要来源,并推荐了一种通过低温实验获得较可靠光谱参量的途径。建议采用透射光谱数据计算实验跃迁振子强度,吸收系数和吸收截面的计算应该扣除光反射、散射和基质本身吸收的影响,平均波数和平均波长的取值须考虑线形因子。并建议通过发射光谱的实测线形计算各波长的发射截面。由于J-O模型涉及许多近似和假设,计算结果误差较大,可能导致结果不可靠。通过分析指出,采用低温下测得的能级寿命和荧光分支比进行相关参量的估算可获得较可靠、较有意义的结果。