Spectrum analysis of interval process model and its application in uncertain vibration analysis

In recent years, the authors have extended the traditional interval method into the time dimension to develop a new mathematical tool called the “interval process model” for quantifying time-varying or dynamic uncertainties. This model employs upper and lower bounds instead of precise probability distributions to quantify uncertainty in a parameter at any given time point. It is anticipated to complement the conventional stochastic process model in the coming years owing to its relatively low dependence on experimental samples and ease of understanding for engineers. Building on our previous work, this paper proposes a spectrum analysis method to describe the frequency domain characteristics of an interval process, further strengthening the theoretical foundation of the interval process model and enhancing its applicability for complex engineering problems. In this approach, we first define the zero midpoint function interval process and its auto/cross-power spectral density(PSD) functions. We also deduce the relationship between the auto-PSD function and the auto-covariance function of the stationary zero midpoint function interval process. Next, the auto/cross-PSD function matrices of a general interval process are defined, followed by the introduction of the concepts of PSD function matrix and cross-PSD function matrix for interval process vectors. The spectrum analysis method is then applied to random vibration problems, leading to the creation of a spectrum-analysis-based interval vibration analysis method that determines the PSD function for the system displacement response under stationary interval process excitations. Finally, the effectiveness of the formulated spectrum-analysis-based interval vibration analysis approach is verified through two numerical examples.

Analysis of vibration reduction characteristics and applicability of steel-spring floating-slab track

A coupled dynamics computation model for metro vehicles, along with a steel-spring floating-slab track, is developed based on the theory of vehicle-track coupled dynamics. Using the developed model, the influences of the thickness, length and mass of floating-slab, spring rate and its arrangement space, running speed, etc. on the time and frequency domain characteristics of steel-spring fulcrum force are analyzed. The applicability of steel-spring floatingslab track is discussed through two integrated example cases of metro and buildings possessing distinct natural vibra- tion characteristics. It is concluded that, it is quite significant, in the optimization modular design of the parameters of steel-spring floating-slab track, to take the matching relationship of both the amplitude-frequency characteristics of steel-spring fulcrum force and natural vibration characteristics of integrated structures into comprehensive consideration. In this way the expensive steel-spring floating-slab track can be economically and efficiently utilized according to the site condition, and at the same time, the economic losses and bad social impact resulted from the resonance during usage of steel-spring floating-slab track can be avoided.

Vibration analysis of large bulb tubular pump house under pressure pulsations

A 3D finite element model of the Huaiyin third pumping station of the Eastern Route of the South-to-North Water Transfer is described in this paper. Two methods were used in the calculation and vibration analysis of the pumping station in both the time domain and the frequency domain. The pressure pulsation field of the whole flow passage was structured on the basis of pressure pulsations recorded at some locations of the physical model test. Dynamic time-history analysis of the pump house under pressure pulsations was carried out. At the same time, according to spectrum characteristics of the pressure pulsations at measuring points and results of free vibration characteristics analysis of the pump house, the spectrum analysis method of random vibration was used to calculate dynamic responses of the pump house. Results from both methods are consistent, which indicates that they are both reasonable. The results can be used for reference in anti-vibration safety evaluation of the Huaiyin third pumping station.

DIRECT SPECTURM ANALYSIS OF THE STATE SPACE FOR RANDOM VIBRATION OF MDOF LINEAR DAMPED SYSTEM

This paper proceeds from the general case of the unsymmetric linearized multi-degrees of free- dom(MDOF)systems.By adopting the general complex modal theory of the state space,the response analysis for a sys- tem subjected to random excitation of the same source is carried out using as a kind of direct spectrum analysis method in frequency domain.With the input of power spectral density function given,the explicit expression of the power spectral density function matrix of the output response can be obtained.By taking Fourier inverse transform,the integrated expres- sions of the correlation function matrix and of the spectrum moment matrix are obtained.Comparing with the time domain method,this method enjoys the merit of visualization and avoids the procedure of transformation from the obtained re- sponse correlation function to be solved for the output spectrum utilizing Fourier transform.This paper has extended the application range of the traditional frequency domain analysis method.The mean square values and variety of statistical val- ues can be obtained conveniently.This method and the time domain method are different in approach but equally satisfac- tory in their results.

Random Vibration Analysis of the Electronic Equipment Cabinet

In order to understand the vibration characteristic of system structure of electronic equipment cabinet within the particular vibration frequency,the finite element analysis software-ANSYS is used to simulate the tests of random vibrations of the cabinet system and obtain the isopleths graph of deformation and stress of the cabinet.It can confirm maximum of deformation and stress of the cabinet and position happened.Through more analysis of the frequency response curve,which can confirm harm- ful consequences random vibrations caused and weak link of the cabinet structure.The numerical simulation results are in good a- greement with the experimental results.It shows that this research provides an efficient method for the anti-seismic design and the dynamic optimization design.

Investigation of active vibration drilling using acoustic emission and cutting size analysis

This paper describes an investigation of active bit vibration on the penetration mechanisms and bit-rock interaction for drilling with a diamond impregnated coring bit. A series of drill-off tests(DOTs) were conducted where the drilling rate-of-penetration(ROP) was measured at a series of step-wise increasing static bit thrusts or weight-on-bits(WOBs). Two active DOTs were conducted by applying 60 Hz axial vibration at the bit-rock interface using an electromagnetic vibrating table mounted underneath the drilling samples, and a passive DOT was conducted where the bit was allowed to vibrate naturally with lower amplitude due to the compliance of the drilling sample mountings. During drilling, an acoustic emission(AE) system was used to record the AE signals generated by the diamond cutter penetration and the cuttings were collected for grain size analysis. The instrumented drilling system recorded the dynamic motions of the bit-rock interface using a laser displacement sensor, a load cell, and an LVDT(linear variable differential transformer) recorded the dynamic WOB and the ROP, respectively. Calibration with the drilling system showed that rotary speed was approximately the same at any given WOB, facilitating comparison of the results at the same WOB. Analysis of the experimental results shows that the ROP of the bit at any given WOB increased with higher amplitude of axial bit-rock vibration, and the drill cuttings increased in size with a higher ROP. Spectral analysis of the AEs indicated that the higher ROP and larger cutting size were correlated with a higher AE energy and a lower AE frequency. This indicated that larger fractures were being created to generate larger cutting size. Overall, these results indicate that a greater magnitude of axial bit-rock vibration produces larger fractures and generates larger cuttings which, at the same rotary speed, results in a higher ROP.

Suppression of Vortex-Induced Vibration by Fairings on Marine Risers

Vortex-induced vibration is quite common during the operation of offshore risers or umbilical cables,commonly leading to serious damage to risers and reduced service life.Vortex-induced vibration of the offshore risers could be effectively suppressed by fairing devices.In this paper,a newly developed vortex-induced vibration fairing and large eddy simulation model of the FLUENT software were used for numerical analysis,experimental research and stimulating vortex-induced vibration at 0.1–2 ms^-1.The data of the numerical model with fairing was compared and analyzed to study the vortex shedding frequency at different Reynolds numbers and changes in drag and lift coefficients.The displacement state of 12 in risers with and without fairing was experimentally tested using a five degree-of-freedom balance.The vortex-induced vibration effect of the fairing was tested at different velocities.The result shows the drag reduction effect of the fairing is more obvious when the flow velocity is 0.4–1.2 ms^-1 and the maximum drag reduction reaches 55.6%when the flow velocity is 0.6 ms^-1.Additionally,the drag reduction effect was obvious when the flow velocity was greater than 1.3 ms^-1 and less than 0.3.The result indicates that the developed 12 in fairing,with good potential in engineering applications,has good vortex-induced vibration-suppression effects.

A case study of blasting vibration attenuation based on wave component characteristics

A typical blasting vibration wave is a composite wave,and its attenuation law is affected by the type of dominant wave component.The purpose of the present study is to establish an attenuation equation of the peak particle velocity(PPV),taking into account the attenuation characteristics of P-,S-and R-waves in the blasting vibration wave.Field blasting tests were carried out as a case to specifically apply the proposed equation.In view of the fact that the discrete properties of rock mass will inevitably cause the uncertainty of blasting vibration,we also carried out a probability analysis of PPV uncertainty,and introduced the concept of reliability to evaluate blasting vibration.The results showed that the established attenuation equation had a higher prediction accuracy,and can be considered as a promising equation implemented on more complex sites.The adopted uncertainty analysis method can comprehensively take account of the attenuation law of blasting vibration measured on site and discrete properties of rock masses.The obtained distribution of the PPV uncertainty factor can quantitatively evaluate the reliability of blasting vibration,which is a powerful and necessary supplement to the PPV attenuation equation.

Virtual vibration test rig for fatigue analysis of dozer push arms

To obtain accurate fatigue life results for construction machinery components,acquiring load spectra is crucial,as their authenticity and validity directly determine the precision of the analysis.In working conditions,component attitudes change continuously,but they remain static on the vibration test rig(VTR),so the acquired target signals should match with the actual component attitudes in the driving signal generation.This paper proposes an efficient and economical simulation-based virtual VTR for fatigue analysis of dozers.First,the relationship between the push arm rotation angle and the cylinder stroke is established,since the cylinder strokes can be measured easily in data acquisition experiments.Second,load decomposition is used to determine the attitude relationship between virtual VTR conditions and actual conditions,and target signals are calculated based on this attitude relationship and measured data.According to the system's frequency response function,the driving signals are iterated until the system's response signals converge with the target signals.Finally,the iteratively obtained load spectra are utilized for fatigue life analysis.The results show that the virtual VTR can effectively and accurately obtain the results of fatigue analysis and has engineering application significance.

Analysis of the track system in bumpy unstructured hard road environment by vibration test

The complex terrain environment in the hilly land directly affects the operational reliability of agricultural robots.In order to study the impact of road irregularity on walking chassis vibration,the 3CYLZ-750 remote-controlled weeding machine which is applied to orchards was taken as the object of study,and the rear roller was selected as the object of observation to reveal the rules under which the vibration of the track chassis changes as there is a sudden change in road surface elevation.A column-type test-to-pass method based on unit excitation was proposed in this study.The excitation behavior and action process were analyzed by category.A critical acceleration prediction model was built and verified by virtual simulation and hard road surface excitation testing.The results showed that at the forward velocity of 0-2.5 km/h and exciter height of 20-100 mm,the vertical vibration acceleration of the target roller was significantly affected by Track Contact Point Centrifugal Acceleration(TCPCA).As TCPCA increased,the change rate of vertical vibration acceleration decreased,reaching a minimum of[−13.8,28.8];as TCPCA decreased,the vertical vibration acceleration tended to increase positively at a maximum variation range of[−13.3,42.2].The measured and simulated macroscopic change rules were consistent with the theoretical analysis,further verifying the correctness of variable extraction,and providing a research basis for the accurate modification and improvement of the model.The research conclusions can lay a theoretical foundation for analyzing the walking reliability of the track chassis,and provide a design basis and technical support for the development of a tracked agricultural robot chassis for the hilly land in the future.

Stochastic Response Analysis of Piled Offshore Platforms to Earthquake Load

In this paper, using the theory of stochastic analysis of the response to earthquake load, a stochastic analysis method of the response of piled platforms to earthquake load has been established. In the method, the strong ground motion is considered as three dimensional stationary white noise process and the pile-soil interaction and water-structure interaction are considered. The stochastic response of a typical platform to earthquake load has been computed with this method and the results compared with those obtained with the response spectrum analysis method. The comparison shows that the stochastic analysis method of the response of piled platforms to earthquake load is suitable for this kind of analysis.

Vibration test and analysis of mini-tiller

Intense vibration happens at the handle of the mini-tillers that abundantly used in mountainous and hilly areas of southwest China.It is absolutely essential to probe into the vibration characteristics and factors why handle of the tiller vibrates violently.Therefore,the vibration acceleration signals of a mini-tiller’s handle and engine cover were tested under the following four conditions:the engine being idle,racing at medium and high speeds,and the tiller working in the field with high engine speed.The signals were processed by means of the time domain eigenvalue analysis and the frequency spectrum analysis.The results showed that when the tiller was under static condition,with increase of the engine speed,the handle vibration decreased in the vertical direction,increased in the fore-and-aft direction and had marginal changes in the left-to-right direction.When the tiller worked at high engine speed,the handle vibrated most violently in the fore-and-aft direction,while the vibrations at the engine cover and handle decreased substantially in each direction,compared with the static conditions.Rotary blades cutting soil increased the damping of the whole machine so as to reduce the vibration at the handle and the engine cover,but the handle vibration was still violent.When the tiller worked,that soil absorbing energies of some frequencies led to the first order unbalanced inertia force of the engine becoming the main reason why handle vibrated intensely.

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage, This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform （WPT）. The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum （WPES） has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.

A More Precise Computation of Along Wind Dynamic Response Analysis for Tall Buildings Built in Urban Areas

Modern tall buildings are generally built in urban areas, where value of the terrain roughness length is much greater than that of the general terrain areas, therefore wind-induced vibrations become more pronounced. The present formulas of numerical analysis of wind-induced response become less accurate. A more accurate expression of along-wind load spectrum matrix is proposed. On the basis of the expression, structural analysis formula of along-wind displacement and acceleration response are developed and programmed. The rationality of these formulas are illustrated in examples.

A machine learning vibrational spectroscopy protocol for spectrum prediction and spectrum-based structure recognition

Vibrational spectroscopy is one of the most commonly applied techniques for determining molecular structures.Conventional applications often involve extensive expertise or expensive first-principles computational effort in order to establish one-to-one spectrum-structure relationships.Here we developed a machine-learning protocol to correlate spectral fingerprints with local molecular structures.Our protocol enables not only quick and accurate prediction of infrared(IR)absorption and Raman vibrational spectra based on molecular structures,but more importantly,also enables structure recognition of chemical groups from vibrational spectral features.IR and Raman spectral features arising from different selection rules were recurrently fed to the model to achieve a nearly zero error rate in structure recognition.Both the spectrum prediction and structure recognition models have good transferability,implying a high possibility of being extended to various spectral or non-spectral characteristics.This machine learning protocol may provide impovements to real-time field applications in many areas of spectroscopy.

Matrix Power Control Algorithm for Multi-input Multi-output Random Vibration Test

Both auto-power spectrum and cross-power spectrum need to be controlled in multi-input multi-output （MIMO） random vibration test. During the control process with the difference control algorithm （DCA）, a lower triangular matrix is derived from Cholesky decomposition of a reference spectrum matrix. The diagonal elements of the lower triangular matrix （DELTM） may become negative. These negative values have no meaning in physical significance and can cause divergence of auto-power spectrum control. A proportional root mean square control algorithm （PRMSCA） provides another method to avoid the divergence caused by negative values of DELTM, but PRMSCA cannot control the cross-power spectrum. A new control algorithm named matrix power control algorithm （MPCA） is proposed in the paper. MPCA can guarantee that DELTM is always positive in the auto-power spectrum control. MPCA can also control the cross-power spectrum. After these three control algorithms are analyzed, three-input three-output random vibration control tests are implemented on a three-axis vibration shaker. The results show the validity of the proposed MPCA.

虚拟仪器平台下旋转机械振动应用研究

利用LabVIEW软件图形化程序和可视化前面板,基于旋转机械结构和运动特点构建虚拟仪器仿真平台基本框架,设计了与真实仪器功能相当的旋转机械齿轮振动虚拟仿真研究平台。通过仿真验证,齿轮振动虚拟仿真平台能够有效采集振动信号,并对振动信号特征进行提取和分析,测试结果与旋转机械齿轮实际振动情况一致。开发的虚拟仿真平台达到了预期功能目标,为旋转机械关键部件振动检测和故障诊断提供了可视化技术支持,降低了旋转机械故障检测成本。

Ambient vibration testing and updating of the finite element model of a simply supported beam bridge

An ambient vibration test on a concrete bridge constructed in 1971 and calibration of its finite element model are presented.The bridge is characterized by a system of post-tensioned and simply supported beams.The dynamic characteristics of the bridge,i.e.natural frequencies,mode shapes and damping ratios were computed from the ambient vibration tests by using the Eigensystem Realization Algorithm(ERA).Then,these characteristics were used to update the finite element model of the bridge by formulating an optimization problem and then using Genetic Algorithms(GA)to solve it.From the results of the ambient vibration test of this type of bridge,it is concluded that two-dimensional mode shapes exist:in the longitudinal and transverse;and these experimentally obtained dynamic characteristics were also achieved in the analytical model through updating.The application of GAs as optimization techniques showed great versatility to optimize any number and type of variables in the model.

Relative vibration identification of cutter and workpiece based on improved bidimensional empirical mode decomposition

In the process of cutting,the relative vibration between the cutter and the workpiece has an important effect on the surface topography.In this study,the bidimensional empirical mode decomposition(BEMD)method is used to identify such effect.According to Riesz transform theory,a type of isotropic monogenic signal is proposed.The boundary data is extended on the basis of a similarity principle that deals with serious boundary effect problem.The decomposition examples show that the improved BEMD can effectively solve the problem of boundary effect and decompose the original machined surface topography at multiple scales.The characteristic surface topography representing the relative vibration between the cutter and the workpiece through feature identification is selected.In addition,the spatial spectrum analysis of the extracted profile is carried out.The decimal part of the frequency ratio that has an important effect on the shape of the contour can be accurately identified through contour extraction and spatial spectrum analysis.The decomposition results of simulation and experimental surface morphology demonstrate the validity of the improved BEMD algorithm in realizing the relative vibration identification between the cutter and the workpiece.

基于LMS Test.lab的电机振动测试与分析

应用比利时LMS公司的test lab振动噪声测试系统,对某空调内部电机的异常抖动进行测试和分析。首先利用有限元软件ANSYS进行模态分析获取电机的固有特性,然后通过试验,得到电机在不同转速下的各个方向的振动速度,分析电机产生异常抖动的原因,并且提出了改进措施,使电机振动速度在标准范围以内,从而消除电机异常抖动的现象,为改善电机、减少振动噪声提供参考。