Stationary Vibration Research Articles

Continuous convolution and nonlinear transformation for multi-shaker non-Gaussian random vibration control

This study proposes a continuous convolution method combined with memoryless nonlinear transformation for multi-input multi-output stationary non-Gaussian random vibration tests. The challenge of the multi-shaker non-Gaussian random vibration test lies in the coupling problems that are manifested in the inherent physical system and in the existence of cross-spectral densities. In the presented method, the independent stationary Gaussian random signals pass through a designed finite impulse response filter with a convolution manipulation first, and then the resulting signals are transformed to the non-Gaussian random signals by the memoryless nonlinear transformation method. The desired drive signals are obtained by the input–output relationship in the frequency domain. The finite impulse response filter is constructed by the frequency sampling technique in which the amplitude characteristics of the filter are determined by the predefined reference power spectral densities. A new monotonic nonlinear transformation function with an approximate kurtosis solution is provided. It only contains one parameter for kurtosis control both in sub-Gaussian and super-Gaussian cases. The memoryless nonlinear transformation is used to maintain the cross-spectral densities, although some distortions are introduced to the power spectra during the transformation process. The inverse system method is used to overcome the coupling problem caused by the inherent physical system. A simulation example and a triaxial vibration test are carried out, and the results indicate the validity and feasibility of the proposed method.

Vision-Based Moving Mass Detection by Time-Varying Structure Vibration Monitoring

In recent years, vision-based vibration measurement methods have been widely used in the field of mechanical engineering for structural health monitoring and fault diagnosis. However, these current methods mainly focus on monitoring the stationary vibrations of time-invariant systems or structures, which cannot deal with the time-varying conditions. In this paper, a video camera is used to monitor the non-stationary vibrations of a time-varying structure for an unexplored usage of moving mass detection. In the study, the laboratory time-varying structure is a clamped beam with one or more masses sliding on. The general parameterized time-frequency transform is first introduced to extract the time-dependent instantaneous frequencies (IFs) from the video motions. Then a parameterized mathematical model is proposed to estimate the weight of the moving mass based on the extracted IFs. By optimizing the parameters in this model, the moving mass can be estimated with high precision. Besides, multi-moving masses can be also detected for abnormal mass classification and identification. Both the finite element method (FEM) and experiments are performed to demonstrate the performance of the proposed vision-based moving mass detection (VMMD) technique. The VMMD technique has valuable potential for online detection, localization and classification of inferior products with abnormal mass in industrial automation.

Variability of the fatigue damage due to the randomness of a stationary vibration load

This paper investigates the variability of the fatigue damage caused by the randomness of a stationary Gaussian random loading. After reviewing some methods from the literature (e.g. Madsen et al., Low), the paper presents a Monte Carlo simulation study to compare such methods with results from time- and frequency-domain analyses. Best-fitting expressions are derived to relate the variability of the damage directly to bandwidth parameters of a PSD. Finally, the paper analyses the variability of the damage when computed from one or few time-histories. For both cases, confidence intervals are constructed to bound the expected damage; simulations confirm their correctness.

Transverse Vibration of an Orthotropic Plate with Holes and Inclusions

Within the framework of the refined theory taking into account the transverse shear strains and inertial components, we consider the problem of stationary vibration of an orthotropic plate with holes and absolutely rigid inclusions. The inclusions may have different types of bonds with the plate. We analyze the case of translational motion of the inclusions along the direction of normal to the median surface of the plate. We study various harmonic (in time) boundary conditions on the outer boundary of the plate and on the contours of the holes. On the basis of the indirect method of boundary elements and a sequential approach to the representation of Green’s functions, the boundary-value problem is reduced to a system of integral equations and relations, which is solved by the collocation method. The numerical results are presented for a rectangular plate containing a circular hole and a circular inclusion.

Dynamics of a single mass vibrating system impacting into a deformable support

The investigated system comprises a mass attached by a deformable link to a fixed foundation, and an elastic-dissipative limiter of motion of that mass. Such types of systems are widely used in different technological devices and machines. This paper is devoted for the improvement of dynamical qualities of such systems. Free and forced stationary harmonic vibrations as well as the qualitative parameters of motions of the system are analyzed in this paper. Characteristics of vibrations are determined using analytical and numerical techniques. It is determined that for the case of zero fastening the values of eigenfrequencies of the system do not depend on the amplitude of excitation. Then the system has an infinite number of multiple eigenfrequencies. In the case of forced harmonic excitation single valued stable motions exist in the vicinity of the resonance. This gives rise to some qualities of the system which are useful in practical applications.

Transient vibro-acoustic analysis of squeal events based on the experimental bench FIVE@ECL

The proposed study investigates the transient and stationary non-linear vibrations and acoustic phenomena occurring during the squeal phenomenon. Experiments are performed on the test bench Friction-Induced Vibration and noisE at Ecole Centrale de Lyon (FIVE@ECL).The first major contribution of the study is to demonstrate the ability of this test bench to reproduce transient squeal events for a given operational condition, allowing to conduct a thorough and robust study on the physical understanding of transient vibration and acoustic squeal events. The second main contribution is to discuss the potential links between the emergence of vibrations on the two pads, the disc and the caliper, and the squeal noise in near-field and far-field.

Effects of material parameters on the transient dynamics of an impacted plate with partial constrained layer damping treatment.

Due to their dynamic properties, viscoelastic materials are largely used in different sectors of industry to reduce noise and vibration in mechanical structures. In particular, partial constrained layer damping (PCLD) treatments have been used and studied in order to lessen stationary vibration and ringing noise. In the present work, simulations are performed to predict the effect of PCLD on the initial transient dynamic response of a planar impacted structure. The structure is a simply supported, rectangular aluminum plate impacted at its center with a small steel sphere. A parametric study is carried out based on a finite element model using ABAQUS 6.5 [Dassault Systèmes (ABAQUS Inc., Silicon Valley, CA)], whose results are well correlated with previous experiments. The model reflects the effects of several PCLD parameters on the initial transient response of the padded plate. The results from the parametric study show that the stiffness of the viscoelastic layer is a crucial parameter in the initial transient dynamic response of the impacted plate. It is also shown that the pads locally modify the dynamic properties of the plate thus causing changes in the time evolution of the deformation field. The combined use of PCLD to reduce both the initial transient response of the impacted structure and the ensuing flexural vibration could open the way for a better reduction of impact noise.

A time-domain procedure for non-Gaussian stationary environmental testing using zero-memory nonlinear transformation

This article proposes a time-domain procedure for a non-Gaussian stationary random vibration test with prescribed power spectral densities. Previous procedures for generating non-Gaussianity suffered from certain defects. For example, zero-memory nonlinear transformation, an algorithm frequently applied to transform Gaussian signals into non-Gaussian signals, often produces changes in both auto-power spectral densities and cross-power spectral densities, which might result in control instability under certain circumstances. In this article, the authors propose a different approach for the zero-memory nonlinear function. First, a time-domain procedure for a non-Gaussian random test is introduced. Second, a rescaling method is applied to correct the magnitude amplification on the auto-power spectral density because of zero-memory nonlinear transformation. We offer experience formulas in this method to adjust the auto-power spectral density of both super-Gaussian and sub-Gaussian responses. Third, a control strategy using a finite impulse response filter is proposed to further improve the auto-power spectral density if the shape of the auto-power spectral density is distorted. The kurtosis loss induced by the filtering process is also analysed and a corresponding solution is put forward to ease the reduction. Numerical test and a biaxial shaker table test are conducted to validate the availability and superiority of the proposed procedure.

Analysis of low damping ratios in multi-exciter stationary non-Gaussian random vibration control

This article investigates the influence of low damping ratios on the performance of the multi-exciter stationary non-Gaussian random vibration control system. The basic theory of the multi-exciter stationary non-Gaussian random vibration method is reviewed first, and then the influences of low damping ratios on multi-output spectra and kurtoses are analyzed. The low damping ratios cause an ill-conditioned problem which will make the drive spectral matrix solution inaccurate; thus, some spectral lines located at resonance peaks in the response spectra cannot be modified within the preset tolerances by the control algorithms. The regularization method is used to alleviate the calculation error. The output kurtoses are dependent not only on the characteristics of the system but also on the input signals. It is found that the kurtosis control will be intractable if the damping ratios are very low. A two-input two-output cantilever beam simulation example is described to illustrate the analysis results.

Energy-based damage localization under ambient vibration and non-stationary signals by ensemble empirical mode decomposition and Mahalanobis-squared distance

Damage localization of damaged structures is an important issue in structural health monitoring. In data-based methods based on statistical pattern recognition, it is necessary to extract meaningful features from measured vibration signals and utilize a reliable statistical technique for locating damage. One of the challenging issues is to extract reliable features from non-stationary vibration signals caused by ambient excitation sources. This article proposes a new energy-based method by using ensemble empirical mode decomposition and Mahalanobis-squared distance to obtain energy-based multivariate features and locate structural damage under ambient vibration and non-stationary signals. The main components of the proposed method include extracting intrinsic mode functions of vibration signals by ensemble empirical mode decomposition, choosing adequate and optimal intrinsic mode functions, partitioning the selected intrinsic mode functions at each sensor into segments with the same dimensions, calculating the intrinsic mode function energy at each segment, preparing energy-based multivariate features at each sensor, computing Mahalanobis-squared distance values, and obtaining a vector of average Mahalanobis-squared distance quantities of all sensors. The major contributions of the proposed method consist of proposing an innovative non-parametric strategy for feature extraction, presenting generalized Pearson correlation function for the selection of optimal intrinsic mode functions, using a simple and effective segmentation algorithm, and applying energy-based features to the process of damage localization. The main advantage of the proposed method is its great applicability to locating single and multiple damage cases. The measured vibration responses of the well-known IASC-ASCE structure are applied to verify the effectiveness and reliability of the proposed energy-based method along with several comparative studies. Results will demonstrate that this approach is highly capable of locating damage under stationary and non-stationary vibration signals attributable to ambient excitations.

A spectrum-driven damage identification by minimum constitutive relation error and sparse regularization

Abstract This paper proposes a novel model-based damage identification strategy based on minimum constitutive relation error and sparse regularization using the power spectrum density data. Firstly, the stationary random vibration problem is transformed into a series of harmonic vibrations by the pseudo excitation method and the error in constitutive relation is established by the admissible stress field and admissible displacement field. A much more general and simpler strategy so as to build the admissible stress field is addressed by requiring only an extra decomposition of the stiffness matrix. Then, the sparse regularization is added to the original constitutive relation error objective function to circumvent the ill-posedness of the inverse problem. Finally, the solution of this nonlinear optimization problem is solved by the alternating minimization method. The proposed method has the advantage that only measurement power spectrum density data from few limited sensors are needed in the inverse analysis. Numerical and experimental results show the effectiveness and robustness of this approach.

Dynamic behaviour of a 13-story reinforced concrete building under ambient vibration, forced vibration, and earthquake excitation

This paper presents a unique study of dynamic behaviour of a full-scale 13-story reinforced concrete building under forced vibration, ambient vibration, and distal earthquake-induced excitation. Initially, an eccentric mass shaker located on the upper floor of the building was used to excite the building while instrumented with eight accelerometers. Then, ambient vibrations induced by traffic and wind were recorded over a period of two weeks, utilizing over 40 tri-axial accelerometers. During the sampling period, the building was excited by a M6.5 earthquake and high-quality vibration data sets were recorded. Modal parameters of the building were identified with a range of frequency and time domain system identification (SI) methods, and the influence of excitation force characteristics on performance of various techniques was also investigated. A finite element model of the building was developed using SAP2000 to compare modal properties to the identified counterparts from experiments. Results showed a strong correlation between modal parameters identified by different SI methods, and all techniques provided accurate estimation of modal parameters when used with output-only data. Modal parameters determined from ambient vibrations were comparable to their forced vibration counterparts, providing evidence that ambient vibration testing can be as effective as forced vibration testing in determining modal parameters for similar size structures. The near stationary vibration data can produce accurate estimation of modal parameters. However, further study is required to facilitate application of output-only SI techniques with non-stationary data. There was a good match between peak displacement amplitudes obtained by the numerical model and those experimentally measured at different excitation frequencies. This match demonstrated the accuracy of the finite element model to predict realistic dynamic behaviour of the building under various harmonic excitation forces.

Stationary random vibration of a viscoelastic Timoshenko cantilever beam under diverse random processes

In this paper, the stochastic properties of a uniform Timoshenko cantilever beam are investigated systematically. Based on the external viscous damping and Kelvin–Voigt viscoelastic damping, the partial differential equations of the Timoshenko beam subjected to random excitation are derived. The applied load is the concentrated force, and the excitation related to includes the ideal white noise, the band-limited white noise, and the exponential noise. Expressions are obtained for the space–time correlation functions and the space–frequency power spectral density functions of the transverse displacement response. The evident improvement is that the infinite integral and the definite integration in the mean square responses are worked out by means of the residue integral method and the integration by partial fraction, and the exact solutions of the mean square response are obtained in the form of an infinite series finally. This improvement provides a basis for both the mode truncation and the modal cross-spectral densities whether which can be ignored. Providing the numerical example, the numerical results obtained show the effectiveness of the theoretical analysis.

Formation of mathematical models of stationary dynamics of structures which include thin elastic plates with distributed inertial parameters

This paper is devoted to the problems of modeling stationary oscillatory processes in elastic systems that contain thin-walled plates. The described method allows us to include the mathematical formalization of thin-walled plates in oscillatory models of elastic structures with irregular boundaries of computational areas and heterogeneous boundary conditions. The formation of dynamic models of this kind is based on the use of discretization methods, in particular, finite element methods that allows approximating the initial models with distributed inertial and rigid parameters — discrete ones with concentration of parameters at certain points — nodes of a dynamic system. Obviously, such approximations are accompanied by errors, the estimation of which is extremely difficult to perform under the conditions of the mentioned heterogeneities and irregularities even in the interval variants. In the present work, the construction of elements of bending stationary vibrations of thin-walled plates under monoharmonic effects is proposed. Possessing all the properties of a finite element, the proposed element contains the values of the distributed masses as parameters. In contrast to the use of discretized parameters obtained by using the classical finite element, the proposed method eliminates discretization procedures and thus, eliminates the process of forming mathematical models from additional errors associated with discretization procedures. This element of mathematical modeling of the dynamics of bending is called a harmonic element (HaE). The proposed method is based on the development of dynamic compliance methods, previously used to simulate oscillations of beam systems with distributed parameters. The developed mathematical models of stationary oscillations of thin elastic plates with distributed inertial parameters make it possible to include them in discrete-continuous models containing infinite-dimensional flexural elements (plates and beams), material points, solids and concentrated elasticities. Thus, dynamic models of structures subjected to harmonic effects are represented by a set of harmonic elements (HaE), which allow harmonic matching of heterogeneous elements under different boundary conditions.

Stationary and flow-induced vibration of two elliptic cylinders in tandem by immersed boundary-MRT lattice Boltzmann flux solver

Numerical method, combining immersed boundary method and multi-relaxation-time lattice Boltzmann flux solver, is used to carry out flow-structure interaction problems in this paper. Without dynamic mesh technique and body fitted grid re-generation, the flow-structure interaction problems can be solved by Cartesian mesh in order to simplify calculation process and save computation time. The accuracy and rationality of this method are verified by comparison of force coefficients, vibration amplitudes and flow characteristics with previous numerical results. Numerical simulations of two stationary and flow-induced vibration elliptical cylinders in tandem are carried out in laminar flow. For two stationary elliptical cylinders, the existing of downstream elliptical cylinder effectively prevents the unsteady characteristic of upstream wake at small gap spacing. With the increase of aspect ratio, the critical gap augments. After reaching the critical gap, the upstream force coefficients decrease and the downstream ones increase as aspect ratio increasing. Flow characteristic presents three regimes, including steady flow, shear layer attachment and 2S shedding vortex and 2S or C(2S) shedding vortex. For two flow-induced vibration elliptical cylinders, in comparison with stationary simulations, upstream transverse vibration responses are strengthened and downstream ones are strengthened at larger gap spacing and aspect ratio. The in-line vibration responses are both weaken, especially for downstream bluff body. Flow characteristic show different flow-regimes: (a) shear layer attachment for upstream and 2S shedding vortex for downstream; (b) 2S shedding vortex for upstream and C(2S) shedding vortex for downstream; (c) 2S shedding vortex for upstream and vortex pair presenting in the downstream wake. Greater L/D and AR, the effects of upstream wakes on downstream elliptical cylinder are more intense.

Time-Varying Motion Filtering for Vision-Based Nonstationary Vibration Measurement

In the field of vibration measurement, the vision-based approach can achieve high spatial resolution compared to traditional accelerometers and lasers and thus has attracted much attention during the past decades. A recently developed phase-based video motion magnification (PVMM) technique to estimate subtle motions from videos is only suitable for stationary vibration measurement, because it is limited to analyze the well-separated vibration modes. In this article, a time-varying motion filtering (TVMF) method is presented to endow the PVMM technique with the ability to decompose nonstationary vibrations and visualize the time-dependent mode shapes of nonstationary systems. Specifically, we first build a parameterized mathematical model for the video motions and then extract each vibration mode by optimizing a set of parameters. After modulating each mode with an amplification factor, the time-varying characteristics of the vibration mode shapes can be visualized to naked eyes. Compared to the traditional PVMM technique, the merit of the proposed TVMF is verified to be able to produce less noise and fewer artifacts in nonstationary vibration measurement. The performance of TVMF is demonstrated on both a simulated experiment and a real nonstationary moving mass system.

Propagation and Attenuation of Statistically Stationary Ground Vibrations due to Human Activities

AbstractGround vibrations induced by human activities that can be considered a statistically stationary process can be represented by analytical solutions to Lamb’s problem. For a viscously damped ...

Transverse Vibrations of an Orthotropic Plate with a Collection of Inclusions of Any Configuration with Different Types of Connections with the Matrix

Within the framework of an improved theory that takes into account transverse shear strains and inertial components, we construct the solution of the problem of stationary flexural vibration of an orthotropic plate containing a collection of arbitrarily located curvilinear inclusions. We analyze various types of connections of these inclusions with the plate. The outer boundary of the plate has an arbitrary geometric configuration. In this boundary, we impose mixed boundary conditions harmonic in time. The solution is constructed by using the indirect method of boundary element. We used the sequential approach to the representation of Green functions.

Russian stationary vibration control and mechanical displacement systems for electric power pumps of thermal power plants

The article discusses the possibility of using Russian stationary vibration and mechanical quantities control systems for electric power boilers of thermal power plants, in particular, the implementation of automated control of absolute vibration bearing, axial shear and speed with the requirements of regulatory documents. A review and analysis of the market of stationary systems for monitoring vibration and mechanical quantities, their technical and metrological characteristics was carried out. The possibility of integrating Russian stationary systems for monitoring vibration and mechanical quantities into automated process control systems of thermal power plants, their application in various subsystems, including the subsystem of technological protection and safety locks, is considered. An assessment was made of compliance with regulatory documents governing the construction of such systems, taking into account the requirements of supervisory authorities.

Spectrotemporal shaping of itinerant photons via distributed nanomechanics

Efficient phase manipulation of light is the cornerstone of many advanced photonic applications1–4. However, the pursuit of compact, broadband and deep phase control of light has been hindered by the finite nonlinearity of the optical materials available for integrated photonics5,6. Here, we propose a dynamically driven photonic structure for deep phase manipulation and coherent spectrotemporal control of light based on distributed nanomechanics. We experimentally demonstrate the quasi-phase-matched interaction between stationary mechanical vibration and itinerant optical fields, which is used to generate an on-chip modulated frequency comb over 1.15 THz (160 lines), corresponding to a phase modulation depth of over 21.6π. In addition, an optical time-lens effect induced by mechanical vibration is realized, leading to optical pulse compression of over 70-fold to obtain a minimum pulse duration of 1.02 ps. The high efficiency and versatility make such mechanically driven dynamic photonic structures ideal for realizing complex optical control schemes, such as lossless non-reciprocity7, frequency division optical communication1 and optical frequency comb division8. Optomechanical coupling enables an on-chip frequency comb and optical time-lens for 70-fold optical pulse compression.