Stationary Vibration Research Articles

Vibrocreep of concrete

We study the creed of statically loaded concrete under stationary vibrations. Our considerations are closely connected with nonlinear rheological equation of mechanical state for concrete. The proposed approach for considered problem used so called energy of entirety. Note that this value can be successively utilized also instead of known Reiner’s invariant. In this paper in contrast to the traditional model a material concrete is considered as a union of its links with statistical disturbed strengths. This conception allows to modify Boltzmann’s principle superposition of fractions creep deformations. It is notable that the influence of vibrocreep on bearing capacity of the concrete structure is considerable.

Multi-exciter stationary non-Gaussian random vibration test with time domain randomization

Abstract This paper presents a new control method for multi-input multi-output stationary non-Gaussian random vibration test using time domain randomization. The control objectives are composed of response skewnesses, kurtoses and power spectral densities. The generation process of stationary and coupled reference non-Gaussian signals by specified reference skewnesses, kurtoses and spectra is analyzed. The reference non-Gaussian signals combined with system frequency response functions are then utilized to obtain the desired drive signals for dynamic inputs, in which the inverse system method in the frequency domain is employed. The primary advantages of the proposed methods are the high computational efficiency and simultaneous control of the time-frequency characteristics of response signals. In consideration of system cross coupling characteristics manifested in coherence and phase coefficients, the skewness and kurtosis tuning steps for each control channel are formulated by using a sequential phase modification method. The relationships between reference skewnesses, kurtoses and spectra are discussed and they reveal that the reference spectra have an influence on the settings of reference skewnesses and kurtoses, which implies that proper settings of reference skewnesses, kurtoses and spectra are necessary. A numerical example and a triaxial vibration test are provided and the results show the validity and feasibility of the proposed method.

ОБЕСПЕЧЕНИЕ КАЧЕСТВА ДЕТАЛЕЙ ПРИ КРУГЛОМ ШЛИФОВАНИИ В УСЛОВИЯХ ПЛАВУЧИХ МАСТЕРСКИХ

The paper considers the results of laboratory studies of the grinding process taking into account the quality assessment of the shaft neck surfaces under disturbing vibration effects of external forces on equipment. The external forces result from sea waves and neighboring operating equipment in the conditions of a floating workshop. The purpose of the study is development of practical recommendations for improving the quality of part grinding in the conditions of floating workshops based on the test results of new vibration insulating devices. The studies are based on tool and workpiece interaction simulation in the conditions of floating workshops as a dynamic system with complex stationary and non-stationary vibration effects, as well as shock effects from external equipment and lasting sea confusion through the floating platform and deck surface. Variations of the shape error of the processed parts, roughness of the machined surface, waviness of the shaft neck surfaces are determined according to the basic and achieved variants taking into account the use of new designs of effective vibration insulating mounts and devices. The obtained dependences ∆ = f (h3%) show that the difference in the deviation value of the shaft neck surface shape (∆max-∆min ) processed by the basic variant is larger than when processed by the achieved variant with vibration insulating mounts, respectively, by an average of 2.3 times. The dependences Ra = f (h3%) of roughness deviations for Ra max confirm the improvement in quality when using new antivibration mounts by an average of 1.25 times. The waviness indices W = f (h3%) for Wmax and Wz of shaft neck surfaces dependent on external influences and states of a cylinder grinding machine decrease by an average of 1.39 times. The study has proved the feasibility of using a new machine-tool vibroprotection system for solving the problems of ensuring dynamic stabilization of the grinding process based on the creation of designs of effective vibration insulating supports and devices that simplify the possibility of mounting and dismounting of technological equipment and improving the machining quality of parts by reducing their shape errors through decrease of external vibrational influences.

Transverse Vibration of an Orthotropic Plate with a Collection of Holes of Arbitrary Configuration and Mixed Boundary Conditions

Within the framework of a refined theory that takes into account the transverse shear strains and the inertial components, we consider the problem of stationary vibration of an orthotropic bounded plate containing an arbitrary number of curvilinear holes. Mixed boundary conditions harmonic in time are analyzed both on the outer boundary of the plate and on the contours of the holes. The solution is constructed on the basis of the indirect boundary-element method. We use a sequential approach to the representation of Green functions. Integral equations are solved by the collocation method. We also present numerical results obtained for a rectangular plate with two circular holes.

Symplectic analysis of stationary random vibration of vehicle–track coupled system with rail-borne electromagnetic generator

In this article, the authors establish the vehicle-track coupled model of smart railway track with rail-borne electromagnetic generator and conduct a symplectic analysis in frequency domain. A vehicle-track model considering vehicle traveling load is constructed, and the pseudo-excitation method is used. The frequency-dependent stiffness of rail pad is involved in the calculation model to get accurate results of rail natural frequency. The calculated results indicate that the smart railway track with electromagnetic generator will not affect the random vibration response of vehicle and bogie, but it could have certain influences on the wheelset and under-rail structure, especially the vibration response of rail, whose acceleration Power Spectrum Density difference reaches 18.6% with frequency shift of 54 Hz at basic frequency of 730.2 Hz, whereas the low frequency (below 200 Hz) rail vibration is not affected. The methods and results could serve as a guideline for the safety checking and dynamics calculation of smart railway track with rail-borne electromagnetic generator.

Transient amplitude amplification of mistuned structures: An experimental validation

Until now, only few works have dealt with the transient vibration response of bladed disks of turbomachinery. However, transient vibration of turbines has become more and more important due to the changes on the energy production sector. Recently, it has been theoretically demonstrated that the maximum amplitude of the resonance passage of mistuned blisks may even exceed the maximum amplitude of the steady-state response. This effect is called transient amplitude amplification of mistuned structures (TAMS). The phenomenon is investigated within this article. By using a lumped mass model, it is shown how the maximum amplitude of the steady-state solution may be exceeded by the maximum amplitude of the resonance passage. Further, the occurrence of transient amplitude amplification of mistuned structures is experimentally validated.A new experimental set-up is designed to perform a resonance passage. Hence, an accelerated traveling wave type excitation is created. Loudspeakers are used to perform a contactless excitation. With the designed test rig, the occurrence of TAMS can be demonstrated. The results are the first experimental proof that the maximum of a transient vibration response can exceed the maximum of the stationary vibration response of the same dynamic system.

Random Oscillations of the Vertical Continual and Discrete Rod under Seismic Influences

Stationary longitudinal vibrations of the vertical rod, kinematically excited by deterministic and random processes, are considered. In a joint examination, these tasks have many similarities. An additional reason for considering both problems was that the results obtained in the deterministic problem can be used to study the problem in stochastic formulation. In solving specific examples, analytical and numerical methods of solution are used. The amplitudes and variances of the oscillations are found. Numerical examples show the effect of broadband input random processes on the dispersion of oscillations. It is pointed out that it is necessary to expand the subject of studying random oscillations taking into account the results obtained.

Analogy of a Linear Chain and Seismic Vibrations of Segmental and Viscoelastic Pipelines

In the problem of seismic vibrations of a segmental pipeline with damping joints, deformed by the law of linear viscoelasticity, an original analogy with a linear chain of concentrated masses was put forward. The constructed discrete system generalizes the monatomic lattice model in the sense that the viscoelastic interaction between the masses of the chain is considered and, moreover, the forced (and not own) oscillations of such a system are investigated. By the transition from a discrete system to a continuous one, the integro-differential oscillation equation of a segmented pipeline with viscoelastic joints in an elastically resisting medium is obtained. This equation is a generalization of the well-known Klein–Gordon differential equation describing the “constrained” vibrations of an elastic rod or string in a medium with elastic resistance. In addition, the equation gives the problem of seismic vibrations of a continuous pipeline from a polymer (viscoelastic) material. Joint stationary seismic vibrations of a viscoelastic pipeline and soil were studied in an exact formulation and maximum stresses in the pipeline were found by solving the resulting integro-differential equation. The same stresses were found using the “hard pinch” engineering approach, according to which displacements and deformations in the seismic wave and pipeline are the same. By analyzing the stresses found under the viscoelasticity law in the form of the Kelvin–Voigt model relationship, it is established that the generally accepted position that the engineering approach gives an upper estimate for the stresses in the pipeline is valid only in the subsonic case (when the seismic wave velocity is lower than the wave velocity in the pipeline) and is not valid in the supersonic mode, when the exact theory can lead to stresses exceeding those calculated on the basis of the engineering approach.

Evaluation of Compacting of Fresh Concrete through Vibration Based on the Newton Viscous Model

The paper is based on dynamic modeling research and experimental results obtained for freshly compacted concrete under stationary vibration. Thus, computational relationships and laws for vibration parameters and dissipated energy will be presented. In correlation with the dissipated energy, it will be evidenced by the evolution of the compaction degree and the resistance of the concrete depending on the vibration duration. It is noted that significant correlations have been established between the displacement curve of the dissipated energy and the loop hysteresis area for several vibration frequencies specific to the dynamic compaction regime

Fragments of History and Science

Fragments of History and Science

Чисельно-аналітичний розв’язок задачі про демпфірування ізотермічних коливань прямокутної в’язкопружної пластини

The damping of vibrations of rectangular plates by means of both viscoelastic layers and using piezoelectric inclusions is considered. For modeling viscoelastic properties of passive and piezoelectric materials, linear models of integral type viscoelasticity are used, which are most effective for simulating the dissipative properties of materials in the linear region. In the case of taking into account the influence of the piezoelectric inclusions on the rigid characteristics of the passive plate and in other types of boundary conditions (for example, with rigid fixing of the ends), the finite element method was used to solve the problem of damping. The solutions of concrete problems of damping of stationary and non-stationary vibrations of plates using analytical and finite element methods are given. On the basis of the aforementioned approach, algorithms for solving dynamical problems with both fully and partially electrodes are implemented.

Probability distributions control for multi-input multi-output stationary non-Gaussian random vibration test

An inverse system method for multi-input multi-output stationary non-Gaussian random vibration test is proposed in the paper to control the response characteristics both in time-domain and frequency-domain simultaneously. Hence, the control objectives are not only the traditional response power spectral densities but also probability distributions. The control of the probability distributions is more comprehensive and reasonable than the control of kurtoses in order to duplicate the time-domain characteristics of the measured data because kurtoses provide only partial behaviors of the probability distributions. The nonlinear transformation process is introduced to generate non-Gaussian random signals with specified probability distributions. To obtain the desired vibration environments for the test, the reference response signals are synthesized first by the reference spectra and probability distributions, and then the coupled drive signals are generated via the inverse system in the time domain. The close loop correction algorithms are implemented to update the drive signals, actually to update the reference response signals according to the deviations between the references and the measured responses. Finally, a numerical example by a cantilever beam and a biaxial vibration test are carried out and the results demonstrate the effectiveness and feasibility of the proposed method.

Direct and inverse problems for prestressed functionally graded plates in the framework of the Timoshenko model

In this study, modelling and identification of prestress state in functionally graded plate within the framework of the Timoshenko theory are discussed. With the help of variational principles, statements of boundary problems for stationary vibration of inhomogeneous prestressed plates have been derived taking into account various factors of prestress state. The comparative analysis of classical and nonclassical models has been conducted. The effect of the prestress state factors on the solution characteristics has been estimated. New approaches to solving the inverse problems on a reconstruction of inhomogeneous prestress functions in a functionally graded plate have been proposed on the basis of derivation of reciprocity relations and iterative regularization. The results of numerical reconstruction experiments are presented; practical recommendations on a selection of frequency range for the purpose of getting the highest reconstruction accuracy are given.

Exact Solutions of Fully Nonstationary Random Vibration for Rectangular Kirchhoff Plates Using Discrete Analytical Method

This paper proposes the discrete analytical method (DAM) to determine exactly and efficiently the fully nonstationary random responses of rectangular Kirchhoff plates under temporally and spectrally nonstationary acceleration excitation of earthquake ground motions. First, the fully nonstationary power spectral density (PSD) model is suggested by replacing the filtered frequency and damping of Gaussian filtered white-noise model with the time-variant ones. The exact solutions of free vibration of thin plates with two opposite edges simply supported boundary conditions are introduced. Then, the full analytical procedure for random vibration analysis of the plate is established by using a pseudo excitation method (PEM) that can consider all modal auto-correlation and cross-correlation terms. Owing to involving a series of Duhamel time integrals of single degree of freedom systems, it is difficult to fully analytically evaluate the PSD of time-variant responses such as the transverse deflection, velocity, acceleration and stress components. Thus, DAM that combines the PEM with precise integration technique is developed to enhance the computational efficiency. Finally, comparison of the results by the DAM with Monte Carlo simulations and the analytical stationary random vibration analysis demonstrates the high efficiency and accuracy of DAM. Moreover, the fully nonstationary excitation imposes a remarkable effect on the response PSD of rectangular Kirchhoff plates.

Synthesis of Sine-on-Random vibration profiles for accelerated life tests based on fatigue damage spectrum equivalence

Abstract In many real life environments, mechanical and electronic systems are subjected to vibrations that may induce dynamic loads and potentially lead to an early failure due to fatigue damage. Thus, qualification tests by means of shakers are advisable for the most critical components in order to verify their durability throughout the entire life cycle. Nowadays the trend is to tailor the qualification tests according to the specific application of the tested component, considering the measured field data as reference to set up the experimental campaign, for example through the so called “Mission Synthesis” methodology. One of the main issues is to define the excitation profiles for the tests, that must have, besides the (potentially scaled) frequency content, also the same damage potential of the field data despite being applied for a limited duration. With this target, the current procedures generally provide the test profile as a stationary random vibration specified by a Power Spectral Density (PSD). In certain applications this output may prove inadequate to represent the nature of the reference signal, and the procedure could result in an unrealistic qualification test. For instance when a rotating part is present in the system the component under analysis may be subjected to Sine-on-Random (SoR) vibrations, namely excitations composed of sinusoidal contributions superimposed to random vibrations. In this case, the synthesized test profile should preserve not only the induced fatigue damage but also the deterministic components of the environmental vibration. In this work, the potential advantages of a novel procedure to synthesize SoR profiles instead of PSDs for qualification tests are presented and supported by the results of an experimental campaign.

Benchmark solutions of stationary random vibration for rectangular thin plate based on discrete analytical method

This paper aims to accurately and efficiently achieve the benchmark solutions of stationary stochastic responses for rectangular thin plate. Firstly, the exact solutions of free vibration for thin plate with SSSS, SSSC, SCSC, SFSF, SSSF and SCSF boundary conditions are introduced to random vibration analysis. Based on pseudo excitation method (PEM), the analytical power spectral density (PSD) functions of the transverse deflection, velocity, acceleration and stress responses for thin plate under random base acceleration excitation are derived. Subsequently, to enhance computational efficiency, the discrete analytical method (DAM) that realizes the discretization for the modal coordinates and frequency domain is proposed. Finally, the efficiency of DAM and the accuracy of benchmark solutions are scrutinized by comparison with the analytical solutions and finite element solutions.

Fault detection enhancement in wind turbine planetary gearbox via stationary vibration waveform data

Planetary gearbox fault diagnosis is very important for reducing the downtime, maintenance cost, and for improving the safety, reliability, and lifespan of wind turbines. The present work reports the results concluded by long-term experiments to a defected planetary gearbox system, with a transverse cut with a depth of 1.0 mm and thickness of 0.2 mm to simulate the planetary gearbox component crack. For each defect, recordings every 60.0 min were acquired and a total of 7 recordings (∼ 6.0 h of test duration) were resulted until the termination of the test. Fault is assured by increasing the test period to the point of where the remaining metal in the tooth area has enough stress to be in the plastic deformation region. An experimental procedure is developed to assess the severity of the gearbox component fault. Gearbox components faults of cracked planet gear tooth, cracked planet gears carrier, and cracked main bearing inner race were tested under accelerated fault conditions, where a comparative analysis of condition monitoring indicators for various crack detection has been done. The experimental localized fault signals (vibration acceleration signals) were subjected to the same diagnostic techniques such as spectrum comparisons, spectral kurtosis analysis, skewness analysis, and crest factor analysis. The method is validated on a set of seeded localized faults on all gears and components: sun gear, ring gear, etc. The results look promising, where the root mean square value analysis could be a good indicator when compared with the other indicators in terms of early detection and characterization of faults.

Adaptive operational modal identification for slow linear time-varying structures based on frozen-in coefficient method and limited memory recursive principal component analysis

Abstract To adaptively identify the transient modal parameters for linear weakly damped structures with slow time-varying characteristics under unmeasured stationary random ambient loads, this paper proposes a novel operational modal analysis (OMA) method based on the frozen-in coefficient method and limited memory recursive principal component analysis (LMRPCA). In the modal coordinate, the random vibration response signals of mechanical weakly damped structures can be decomposed into the inner product of modal shapes and modal responses, from which the natural frequencies and damping ratios can be well acquired by single-degree-of-freedom (SDOF) identification approach such as FFT. Hence, for the OMA method based on principal component analysis (PCA), it becomes very crucial to examine the relation between the transformational matrix and the modal shapes matrix, to find the association between the principal components (PCs) matrix and the modal responses matrix, and to turn the operational modal parameter identification problem into PCA of the stationary random vibration response signals of weakly damped mechanical structures. Based on the theory of “time-freezing”, the method of frozen-in coefficient, and the assumption of “short time invariant” and “quasistationary”, the non-stationary random response signals of the weakly damped and slow linear time-varying structures (LTV) can approximately be seen as the stationary random response time series of weakly damped and linear time invariant structures (LTI) in a short interval. Thus, the adaptive identification of time-varying operational modal parameters is turned into decompositing the PCs of stationary random vibration response signals subsection of weakly damped mechanical structures after choosing an appropriate limited memory window. Finally, a three-degree-of-freedom (DOF) structure with weakly damped and slow time-varying mass is presented to illustrate this method of identification. Results show that the LMRPCA algorithm, which is robustness to Gauss measurement noise disturbances, can well identify the transient modal parameters (transient natural frequencies & transient modal shapes) for weakly damped and slow LTV structures online only from non-stationary random response signals.

Vibration Control Design for a Plate Structure with Electrorheological ATVA Using Interval Type-2 Fuzzy System

This study presents vibration control using actively tunable vibration absorbers (ATVA) to suppress vibration of a thin plate. The ATVA is made of a sandwich hollow structure embedded with electrorheological fluid (ERF). ERF is considered to be one of the most important smart fluids and it is suitable to be embedded in a smart structure due to its controllable rheological property. ERF’s apparent viscosity can be controlled in response to the electric field and the change is reversible in 10 microseconds. Therefore, the physical properties of the ERF-embedded smart structure, such as the stiffness and damping coefficient, can be changed in response to the applied electric field. A mathematical model is difficult to be obtained to describe the exact characteristics of the ERF embedded ATVA because of the nonlinearity of ERF’s viscosity. Therefore, a fuzzy modeling and experimental validations of ERF-based ATVA from stationary random vibrations of thin plates are presented in this study. Because Type-2 fuzzy sets generalize Type-1 fuzzy sets so that more modeling uncertainties can be handled, a semi-active vibration controller is proposed based on Type-2 fuzzy sets. To investigate the different performances by using different types of fuzzy controllers, the experimental measurements employing both type-1 fuzzy and interval type-2 fuzzy controllers are implemented by the Compact RIO embedded system. The fuzzy modeling framework and solution methods presented in this work can be used for design, performance analysis, and optimization of ATVA from varying harmonic vibration of thin plates.

Stationary random vibration analysis of vehicle-track coupled system with nonlinear stiffness of railpads

According to time-temperature superposition (TTS) and WLF formula, the temperature-dependent and frequency-dependent kinetic parameters of the railpads of WJ-7 fasteners were predicted based on the experimental results at a certain frequency and under the different temperatures. By combining the pseudo excitation method and symplectic mathematics scheme, the impact of railpads frequency-dependent and temperature-dependent stiffness on the random variation of the coupled vehicle-track system was investigated efficiently. The results suggest that, within the range of environment temperature and frequency-dependent extent of railpads in the railway, the PSD peak of the vertical random vibration acceleration of the wheelsets and rail gets the largest increase of 3.3 times at least, and the increment of their 1st dominant frequency also reaches up to 20.6 Hz or more. Therefore, in order to accurately analyze the random vibration responses of the vehicle-track coupled system, experiments must be conducted to obtain the accurate kinetic parameters of the polymer materials like railpads.