Vibration analysis of a continuous system subject to generic forms of actuation forces and sensing devices

This work provides a general formulation to solve vibration problems for continuous systems with damping effects, including modal, transient, harmonic and spectrum response analyses. In modal analysis, the system eigenvalues and corresponding eigenfunctions can be determined. The orthogonal relations of eigenfunctions are shown. For transient, harmonic and spectrum analyses, the generic force/actuator functions and response/sensing operators are introduced, respectively, and used to derive the system response. The time domain response is obtained for transient analysis, the frequency response function is derived for harmonic analysis and statistical quantities of response variables due to random excitation are determined in spectrum analysis. The solution for each type of analysis can be formulated and expressed in a concise format in terms of generic force/actuator and response/sensor mode shape functions. In particular, one-dimensional beam and two-dimensional plate vibration analyses are illustrated by following the developed generic formulation. This work provides the complete analytical solutions of four types of vibration analyses for continuous systems and can be applied to other engineering structures as well.     

Estimation of interfacial forces in time domain for linear systems

A structural path rank ordering process under transient excitations requires a good knowledge of the interfacial path forces, which are difficult to directly measure. Four time domain methods to estimate the interfacial forces are proposed and comparatively evaluated with application to linear time-invariant, proportionally damped discrete systems. First, the transient response is derived by modal analysis and a direct time domain technique to calculate the interfacial forces is outlined. Next, the frequency domain estimation methods, based on the sub-system concept are reviewed, and an inverse Fourier transform scheme is introduced. An indirect method of estimating interfacial force in transient state is then developed through an inverse procedure of modal analysis. The sub-system approach is employed to obtain the interfacial forces based on the forced vibration response of the original system and modal data of the sub-system. Finally, an approximate time domain scheme is suggested that could be used only if the system properties are known or precisely estimated. Although the proposed indirect methods are designed for eventual experimental applications, this article provides numerical feasibility studies via a simple source-path-receiver system (with parallel vibration paths) that has five translational degrees of freedom. The proposed methods are compared under ideal impulse force excitation input and a periodic sawtooth load (without and with Gaussian noise) to observe the starting transients as well as subsequent motions and interfacial forces. Preliminary comparisons with a laboratory experiment are very promising.     

A recursive approach to prony parameter estimation

The Prony series method of fitting a series of complex exponentials to a time series can be applied to many acoustic and vibration signals. For example, in the analysis of a structure's response to transient excitation the Prony series method can be used to find the natural frequencies, damping ratios, amplitudes and relative phases of the modes of the structure. One of the main problems with this method is the need to calculate and invert matrices. In this paper an algorithm that combines the Prony series method with the recursive least squares algorithm is described. This eliminates the need to invert any matrices and also requires only part of the data to be available at one particular time. The method is applied to analyze a simulated structure's response and also to analyze the response of a beam to transient excitation.     

Transient energy density distribution of a rod under high-frequency excitation

Energy finite element analysis (EFEA) is an efficient way to solve high-frequency structural dynamics response problems. Up to now, EFEA has been used to deal with time-independent vibration problems. However, it is still necessary to understand the time dependent details of energy density distribution of a structure. To study the transient response of a rod under high-frequency sinusoidal excitation, the transient energy density governing equation for a rod is presented. The governing equation is solved, and the solution is verified using an analytical method. Example application to a rod is presented to illustrate the feasibility.     

Modal identification based on continuous wavelet transform and ambient excitation tests

This paper deals with the use of the continuous wavelet transform for modal identification from ambient vibration tests. The wavelet analysis of the free responses of a linear mechanical system has been used to estimate its natural frequencies, viscous damping ratios, and mode shapes, using either the modulus or the phase of the wavelet transform with “ridge” and “skeleton” notions. This technique is extended in this paper, to the response from ambient excitation tests based on the equivalent formulation between the free response and the correlation function of a linear mechanical system under stationary stochastic excitation. The main novelties involve the new formulation of continuous wavelet transform and the use of the singular value decomposition algorithm for ridges and skeleton detection under the noisy conditions of ambient vibration tests. A complete procedure for modal identification of ambient response, including these new formulations, is presented and then applied to numerical examples and experimental test to illustrate its validity.     

超声检测用压电换能器瞬态特性可控可调

超声检测用压电换能器瞬态特性主要包括瞬态空间响应和瞬态时间响应。本文通过调整控制换能器和激励源,实现瞬态空间响应和瞬态时间响应的某些特性的可控可调。其中包括在空间响应方面消除边缘波以获得平行声束和消除平面波以获得聚焦绳声束;在时间响应方面,调整换能器的背衬阻抗以获得可调首次波幅比和调整换能器结构和激励电信号以获得任意检测信号等。     

Reducing measurement time for a laser Doppler vibrometer using regressive techniques

In the last decade the laser Doppler vibrometer (LDV) has become a widely spread instrument for measuring vibrations. It often offers accurate measurements with a high spatial resolution. However, the measurement time of the LDV and especially for the scanning LDV is long. Therefore, reducing the measurement time is an attractive objective. A way to achieve this is to use a single sine excitation (on a resonance frequency). However, this technique has two major drawbacks: the inability to provide information on the damping and a operational deflection shape that can differ from the true mode shape. In this article two methods will be introduced to reduce measurement time without these defaults. In the first method introduced in this article a narrow band multisine is used as excitation signal and the measured vibration signal in the time domain is represented by a model using sines and cosines with these fixed narrow band frequencies. The coefficients of those sines and cosines are then estimated on a global scale by means of a least-squares estimator. An important advantage of this particular technique is that one does not have to measure a full period of the signal, reducing time. The second method accelerates the measurement time for scanning LDV measurements. Using the time domain sequence from each previous scan point and a limited number of time samples from the current scan point, the full time domain sequence of the current scan point can be estimated. Both these methods are a key benefit for in-line quality control, which can have upwards of 1000 spatial measurement locations. The proposed techniques will be validated on both simulations and experiments of varying complexity.     

Variation with distance of aircraft noise impact parameters

Recent developments in the use of statistical energy analysis for the prediction of vibration levels on spacecraft components have led to the need to measure the frequency averaged modal density. In the case of structural components having low damping it has been extremely difficult to make a successful measurement by using existing techniques. Success has usually been achieved by the addition of damping tape to the structure under test. The transient testing technique also requires extremely long data lengths on lightly damped structures, which can lead to a requirement for Fourier transforms considerably longer than normally available. In the technique described here random excitation and extremely short data lengths are used; the technique is shown to give good results on structures with no additional damping material, with a considerable saving in time and expense not only during the experimentation but also during data processing.     

基于温度激励的光纤陀螺光纤环瞬态特性检测

光纤陀螺基于萨尼亚克效应测量垂直于光纤环平面的敏感轴方向上的旋转分量。光纤环是光纤陀螺的核心部件,光纤环的缠绕质量直接影响着光纤陀螺的整体性能,对光纤环的缠绕质量全面检测十分必要。针对目前光纤环检测手段的局限性,提出了一种基于温度激励的光纤陀螺光纤环瞬态特性检测方法,全面表征了光纤环的缠绕质量。建立了光纤环柱面坐标三维计算模型,采用有限元方法定量分析光纤环不对称度和局部温度激励位置精度对光纤环瞬态响应的影响,同时开展了光纤环温度激励相应实验,实验结果与光纤环三维物理模型数值计算结果相一致,在理论和实验上验证了光纤环瞬态特性检测方法的可行性。     

A new blind fault component separation algorithm for a single-channel mechanical signal mixture

A vibration signal collected from a complex machine consists of multiple vibration components, which are system responses excited by several sources. This paper reports a new blind component separation (BCS) method for extracting different mechanical fault features. By applying the proposed method, a single-channel mixed signal can be decomposed into two parts: the periodic and transient subsets. The periodic subset is related to the imbalance, misalignment and eccentricity of a machine. The transient subset refers to abnormal impulsive phenomena, such as those caused by localized bearing faults. The proposed method includes two individual strategies to deal with these different characteristics. The first extracts the sub-Gaussian periodic signal by minimizing the kurtosis of the equalized signals. The second detects the super-Gaussian transient signal by minimizing the smoothness index of the equalized signals. Here, the equalized signals are derived by an eigenvector algorithm that is a successful solution to the blind equalization problem. To reduce the computing time needed to select the equalizer length, a simple optimization method is introduced to minimize the kurtosis and smoothness index, respectively. Finally, simulated multiple-fault signals and a real multiple-fault signal collected from an industrial machine are used to validate the proposed method. The results show that the proposed method is able to effectively decompose the multiple-fault vibration mixture into periodic components and random non-stationary transient components. In addition, the equalizer length can be intelligently determined using the proposed method.     

基于LabVIEW的振动信号分析系统设计

针对机械故障监测的需求,开发了振动信号分析系统。采用LabVIEW图形化开发工具,系统实现了振动信号分析流程和基本的信号分析方法,能够对振动信号进行预处理,并从时域、频域和时频域角度对其进行特征提取。完成了基于仿真信号和实测的公开振动数据集进行验证,实验结果表明,所开发的振动信号分析系统具备参数配置灵活、结果显示直观、扩展性强的优势,为基于振动测试的机械故障监测提供了基础平台。     

Nonlinear characterization with burst excitation of 1-3 piezocomposite transducers

Ultrasonic transducers made with 1-3 connectivity piezocomposites are frequently used in Medical applications and nondestructive testing. When the transducer is used for special applications as, for instance air-coupled transmission, it is necessary to compensate for the high difference of acoustic impedance between transducer and medium using high amplitude pulses to generate high acoustic signal. Thus, the nonlinear behavior of the transducer must be taken into account in similar application conditions. The newly developed method, which performs the nonlinear characterization with burst signal excitation near the thickness resonance frequency, is based on the measure of the current as well as the vibration velocity of the piezocomposite transducer. The current of the stationary response is measured before the end of the burst signal excitation. Burst excitation enables us to measure the nonlinear characterization without producing overheating in the transducers. The amplitude level dependence of mechanical losses tandelta(m) and the stiffness increases |Deltac/c(0)| have been studied, as well as the velocity dependence of a point of the transducer, measured with a laser vibrometer. In this method, the power level applied to the transducers can be higher than other nonlinear measurement methods, providing measurements of high accuracy.     

Ultrasonic transient bounded-beam propagation in a solid cylinder waveguide embedded in a solid medium

A semianalytical solution alternative and complementary to modal technique is presented to predict and interpret the ultrasonic pulsed-bounded-beam propagation in a solid cylinder embedded in a solid matrix. The spectral response to an inside axisymmetric velocity source of longitudinal and transversal cylindrical waves is derived from Debye series expansion of the embedded cylinder generalized cylindrical reflection/transmission coefficients. So, the transient guided wave response, synthesized by inverse double Fourier-Bessel transform, is expressed as a combination of the infinite medium contribution, longitudinal, transversal, and coupled longitudinal and transversal waveguide sidewall interactions. Simulated (f, 1/lambdaz) diagrams show the influence of the number of waveguide sidewall interactions to progressively recover dispersion curves. Besides, they show the embedding material filters specific signal portions by concentrating the propagating signal in regions where phase velocity is closer to phase velocity in steel. Then, simulated time waveforms using broadband high-frequency excitation show that signal leading portions exhibit a similar periodical pattern, for both free and embedded waveguides. Debye series-based interpretation shows that double longitudinal/transversal and transversal/longitudinal conversions govern the time waveform leading portion as well as the radiation attenuation in the surrounding cement grout. Finally, a methodology is deduced to minimize the radiation attenuation for the long-range inspection of embedded cylinders.     

Orientational relaxation of pheophorbide-a molecules in the ground and in the first excited state measured by transient dichroism spectroscopy

We report on transient dichroism spectroscopy carried out on pheophorbide-a in ethanol to measure the response time of the pump-beam induced anisotropy after selective excitation at high excitation levels. From the observed time behaviors of induced absorption, transient amplification, and of the bleaching signal, the orientational relaxation times of pheophorbide-a in the first excited singlet state and in the ground state were obtained separately to be 370 and 250 ps, respectively. It is found that pheophorbide-a behaves like a spherical rotor in the first excited state, while in the ground state randomization of molecules is dominated by the rotation around its quasi-symmetry axis. Because of rotation free measurement of ordinary transient absorption spectra fail in the case of ground state depletion, the observed orientational relaxation time of the ground state have to be taken into account to fit the bleaching kinetics obtained from transient absorption spectra very well to determine the intersystem crossing yield of pheophorbide-a to be 0.46.     

IN-SERVICE IDENTIFICATION OF NON-LINEAR DAMPING FROM MEASURED RANDOM VIBRATION

A non-linearly damped single-degree-of-freedom (s.d.o.f.) system under broadband random excitation is considered. A procedure for in-service identification of the damping characteristic from measured stationary response is described. The procedure is based on the stochastic averaging method. The explicit analytical solution is obtained for the integral equation, which relates the desired damping characteristics to the apparent force in the shortened equation for the slowly varying response amplitude, and thus to the measured probability density of the amplitude. The approach is of a non-parametric nature, which makes it convenient for testing hypotheses of damping mechanisms from measured random vibration data. Extensive results of numerical tests for the procedure are presented.     

Fluctuations of acoustic field in a granular medium

Results of an experimental study of sound propagation in a granular medium are presented. It is found that, in the case of excitation of a harmonic signal with a constant amplitude, the acoustic response of a single grain strongly varies in time. The dependence of the harmonic component amplitudes in the response spectrum on the level of signal excitation proves to be nonmonotonic and also strongly varies in time. The most intense fluctuations are observed in the subharmonic component of the propagating signal. The intensity fluctuation spectra of the harmonic components of the response are obtained for the frequency range of 10⁻⁴−10⁻¹ Hz. A possible mechanism that may be responsible for the slow fluctuations of an acoustic field in a granular medium is discussed.

     

Experimental study of the nonlinear dynamic characteristics of suspended taut steel cables using a 3-D motion analysis system

This paper presents an experimental study of the nonlinear dynamic characteristics of taut steel cables using a 3-D motion analysis system. In the experiment, the taut cables have one end fixed and the other end subject to harmonic vertical excitation. The 3-D motion analysis system can simultaneously record (with high resolution) the instant 3-D coordinates of the multiple markers fixed on a vibrating cable; this distinguishes it from other experimental systems used in vibration studies, in which the vibration of only one single point can be recorded during each individual testing. With the 3-D motion analysis system, this experimental study presents a distinctive interpretation of the dynamic characteristics of taut cables in spatial domain (based on the mode-shape information of the entire cable), in addition to one in time domain (based on real-time traces of one single point). This paper introduces the 3-D motion analysis system and experimental setup, discusses practical experimental procedures, and presents a detailed analysis of three sets of experimental vibration data of three taut steel cables with different small sags. The frequency response curves were obtained for three cables. For one of the three taut cables, more informative vibration data were recorded; this cable was studied in greater detail via modal analysis using a modal decomposition technique and nonlinear time-series analysis.     

Vibration of branched systems—A displacement excitation approach

Exact solutions for the free and forced torsional vibration of branched systems are obtained in terms of the modal parameters of the branches. The basic technique consists of first isolating the branches by clamping the system at the junction. The conditions necessary for the relaxation of the clamp are then obtained from the response of the system to a displacement excitation at the clamp. The vibration of branched engine installations in which repeated branch natural frequencies sometimes occur are given special attention. It is shown that the technique may be applied to the solution of the vibration problems of certain types of flexural systems.     

ADAPTIVE-PASSIVE ABSORBERS USING SHAPE-MEMORY ALLOYS

The adaptive-passive vibration absorber shows promise for combining the stability and low complexity of passive tuned absorbers with the robust performance of active vibration control schemes. Previous adaptive tuned vibration absorbers (ATVA) had been complex and bulky. Shape memory alloys (SMA), with their variable material properties, offer an alternative adaptive mechanism. Heating an SMA causes a change in the elastic modulus of the material. An ATVA using spring elements composed of three pairs of SMA wires and one pair of steel wires was constructed and tested. On-off actuation of the SMA elements created an ATVA with four discrete tuned frequencies. Characterization testing of the absorber showed variation of the natural frequency of the ATVA of approximately 15%. The ATVA was applied to a primary system and the frequency response of the system at various states of ATVA actuation was determined. Manual tuning of the ATVA actuation during a stepped-sine base excitation of the primary system showed a wider notch of attenuation than was possible with a non-adaptive absorber. Results of the tests indicate that an adaptive absorber incorporating SMA as a tuning element has potential as a simple, high-performance adaptive-passive technique for vibration control.