Values Of Natural Frequencies Research Articles

Analysis of vibration monitoring data of an onshore wind turbine under different operational conditions

A wind turbine structure works under the complicated environment and its operational state is complex. In this study, the operational state of a 1.5 MW wind turbine and the vibration response of the tower have been monitored for a long time. The vibration characteristic of the wind turbine under different operational conditions is discussed in detail, and it was observed that the rated rotation speed condition has the highest vibration level. The Campbell diagrams of wind turbine both in the FA direction and SS direction are drawn based on the natural frequencies results, which are identified by data-driven stochastic subspace identification method. It was observed from the Campbell diagrams that when the rotation speed is close to the grid-connected rotation speed, the blade-passing frequency 3f (0.43 Hz) is equal to the fundamental frequency of wind turbine which will easily lead to the resonance. This phenomenon is confirmed by the time history diagrams of the operational condition and vibration speed of a certain startup process. Lastly, the relationship between first-order, second-order modal parameters and operational conditions of the wind turbine are discussed in detail respectively. The mean value of first-order natural frequency is affected slightly by the different operational conditions while the value of second-order natural frequency increases significantly with the increase of rotation speed. The work in this paper can help us to better understand the response of the wind turbine under different operational conditions, which can also lay the foundation for the structure design, modal validation and damage diagnosis of wind turbine.

Особенности мониторинга собственных частот плотин гидроэлектростанций (на примере Чиркейской ГЭС)

A method is proposed for monitoring the natural frequencies of hydro power plant dams using continuous seismic observation data. The object of the research is the largest in Russia arched Chirkey dam located in the Caucasus. At the initial stage, a detailed study of the natural oscillations of the dam was performed using the method of coherent restoration of the standing wave fields with the definition of both the natural frequencies of the structure and their modes. The features of seasonal changes in the total field of standing waves are studied and factors affecting changes in natural frequencies are established. At the next stage, the values of natural frequencies were determined from the spectra of microseismic oscillations recorded by seismic equipment installed on the object. Observation points located in the antinodes of standing waves were used. The values of the natural frequencies of the Chirkey dam, as a whole, decrease with increasing upstream level. It was determined that there are additional factors leading to the hysteresis effect in the relationship between the values of the upstream level and natural frequencies, presumably associated with relaxation processes in the dam body and/or in the dam-base system after the change of level. A method for monitoring the state of the dam is proposed, based on a comparison of the observed values of natural frequencies with the predicted ones. The latter are determined by linear dependencies on the upstream level, taking into account the time shifts associated with relaxation processes

Optimal shells of revolution and main optimizations

Introduction. Optimization is a criterion, on the ground of which, comparative estimation of possible alternatives and selection of the best decisions is carried out. Cost of a shell, its minimum weight, absence of bending moments and tensile normal stresses, given stress state for acting external load, given bearing capacity when optimal shallowness, maximum external load, minimum weight under limitation on the value of natural frequencies of vibration and maximum displacements, absence of bending moments with taking into account internal pressure, dead weight, and centrifugal forces; maximum of critical force and something else can be criterion of selection of optimal shape of shell of revolution. Methods. The main criteria of optimality for shells of revolution and information sources for the 1970-2019 periods are presented in a paper. It will help to study previous results devoted to using optimizations and to set about further investigation. But there is no single approach to the definition of optimal shell of revolution and obviously will not be, because own optimizations are necessary for every concrete case of loading, or distribution of stresses along the thickness, or under the demands to the ratio of the volume and area of considered shell, or with due regard for different kind of expenses, and other demands. Results. For the first time, 24 criteria of optimality only for shells of revolution were discovered. The names of scientists offered presented criteria of optimality and the 45 references dealing with this question are pointed out. It is shown that principles put in the basis of optimal design and criteria of optimality must be given with the help of language quite naturally for computer. Having used optimi- For citation Krivoshapko S.N. (2019). Optimal shells of revolution and main optimizations. Structural Mechanics of Engineering Constructions and Buildings, 15 (3), 201-209. http://dx.doi.org/ 10.22363/1815-5235-2019-15-3-201-209 zations presented in the paper, designers can choose the criterion for their own design of optimal shell shape. Study of the prerequisites of the structural solutions in building and machine-building, the history of the development and perfecting of technologies of erection of shells of revolution will permit to generalize the experience accumulated by designers and to develop new fundamental solutions. Otherwise, architects, structural engineers, and designers will be repeating the achieved solutions in building, architecture, and machine-building.

Calculation of foundation vertical stiffness with the piles mutual influence effect

Aims of research. Studies to determine the effect of the distance between the piles in group with vertical oscillations of pile foundations on the value of dynamic stiffness are carried out and the results obtained in full-scale tests, within the wave model and according to SP 26.13330.2012 are compared. Methods. The eigenfrequency changes of the foundation of nine piles with a diameter ( d ) with a high pile cap are calculated depending on the distances between the piles - 2 d , 3 d and 5 d . The obtained results are compared with the data obtained after a series of pulse dynamic loads performed under semi-natural conditions on foundation models. The values of the transverse wave velocities were determined directly at the test site. Results. It is found that the reduction of the distance between the piles in the bush leads to a decrease in the natural vibration frequencies of pile foundations. Reducing the distance between piles from 5 to 2 diameters of piles leads to reduce the frequency of vertical vibrations of pile foundations by 1. times. It is shown the advantage of the results of calculations in the frame-work of the wave model in comparison with the method of SP 26.13330.2012. Also shown their high coincidence with the values obtained in the course of experiments, which allows to accurately determine the amplitude-frequency characteristics of the foundations. The results determined according to SP 26.13330.2012 have significantly lower values of natural frequencies and do not fully reflect the change in the distance between the piles. The maximum discrepancy with the experimental data is 2.7 times for the vertical oscillations of the pile foundation.

Experimental Free Vibration of Damaged RC Beam Models

Reinforced Concrete (RC) Beam undamaged and damaged were investigated by free vibration to obtain a variation of frequency values at different degree of damage. Experimental tests were carried out on RC beams in scale and in real scale. The damage of RC beams in real scale was obtained by cracking under static bending tests, while in the case of beam in scale is obtained by notches on the concrete cover with different width. In general, the effects on the dynamic response of diffused damages and of concentrated damages on a section of beam have been experimentally analyzed. The envelope of frequency response functions (FRFs) obtained by dynamic experimental tests was elaborated and the changes of natural frequency values were then correlated to the damage degree of RC beams. The experimental data have been discussed and analyzed by comparison with theoretical results.

Calculated-Experimental Determination of Values Natural Frequencies Oscillations of the Case and Parameters of the Case Determining these Values

The task of studying the behavior of various structures under the influence of intense pulsed (shock) loads that arise during the operation of many modern structures, machines and devices remains relevant for many years. One of the stages of this study is to find the values of the natural frequencies of vibrations and design parameters that determine these values. To find the natural frequencies of oscillations of the body, which are four flanges connected by cylindrical shells, the finite element method and analytical solutions were used. An analysis of experimental studies. Determination of natural frequencies values and design parameters determining these values will allow evaluating the response of the structure to the loads acting during its operation, and making corrections to the structure that change the response of the structure, as well as will help to more accurately select the installation sites of piezoelectric accelerometers for recording drums accelerations.

Rayleigh Damping Coefficients of Laminated Rubber Bearing

In isolating the ground structure and the above ground structure from seismic loads, a significant device called laminated rubber bearing is usually found in structure. The complexity of the material which is made up from a combination of rubber and steel shim plates in alternate layer, has made it difficult to measure damping value. Damping is a dissipation of energy or energy losses in the vibration of the structure. Measuring the accurate amount of damping is fundamental as damping plays a crucial role in fixing the borderline between stability and instability in structural systems. Therefore, to determine the damping value including dynamic properties in any materials, modal analysis can be used. Hence, the main objective of this research is to determine the Rayleigh’s damping coefficients α and β and to evaluate the performance of the laminated rubber bearing using finite element and experimental modal analysis. Finding shows that, the finite element modal analysis with the addition of Rayleigh’s damping coefficients α and β, shows a good agreement with the experimental modal analysis in term of natural frequencies and mode shapes. Findings show that, the values of natural frequencies reduced when precise Rayleigh’s damping coefficient added in the finite element modal analysis. It can be concluded that both finite element and experimental modal analysis method can be used to estimate the accurate values of damping ratio and to determine the Rayleigh’s damping coefficients α and β as well.

Comparative study for modal analysis of circular plates with various cutouts and end conditions

The applicational use of structural members in engineering and technology may take the form of a circular plate, for such members it becomes important to predict the vibrational characteristics when operated closer to resonance phenomena. In addition to, the effect of the cutout in the circular plate has a significant effect on modal characteristics. The part of the research work entitled in this paper emphasizes on the modal analysis of a circular plate with clamped boundary condition determined by the characteristics equation and mode shapes of the plate using FEM. The effects of inclusion of cut-out on the vibrational characteristics are discussed. The subject of the analysis was a circular plate considered with certain modifications i.e. free circular plate without cutout clamped on the outer periphery, circular plate with cut-out clamped on the outer periphery, circular plate with cutout clamped on the outer and inner periphery. The methodology applied to conventional material based circular plate is extended to Glass epoxy circular plate with the same set of modifications. The values of natural frequencies for various cases are tabulated and corresponding mode shapes are illustrated.

Experimental, Numerical and Finite Element Vibration Analysis of Delaminated Composite Plate

The vibration of the delaminated composites concerns the structure safety and dynamic behavior of the composite structures as it can be vital in the presence of delamination. In this research paper, the finite element simulations, numerical simulations and the experimental work are combined to analyze the vibration behavior at different delamination size, different stacking sequences and different boundary conditions. The finite element analysis software packages like Ansy and Abqus are used to fetch the vibration response of carbon fiber reinforced polymer composite plate for different boundary conditions, stacking sequences and delamination sizes. Experiments are carried out to study the vibration behavior. Numerical results were obtained using the first order shear deformation theory. Rayleigh-Ritz method was used to derive the governing equations to find the natural frequencies and the results were computed using Matlab tool. The results from finite element, numerical and experimental analysis were then compared and verified that the maximum percentage of error is ignorable. It is seen that the natural frequencies of carbon fiber reinforced polymer decreased with an increase in delamination size subjected to all boundary conditions. The higher values of natural frequencies found for all sides clamped boundary conditions.

Linearization of embedded patterns for optimization of structural natural frequencies

The dynamic characteristics of structures (beams and plates) can be significantly changed by embossing small out-of-plane patterns in these structures. Recent results in literature show, both numerically and experimentally, that shaping a beam in the geometry of its first mode shape significantly increases the value of the first natural frequency of the beam. This phenomenon also occurs when the beam is shaped in the geometry of other mode shapes, and in the case of plates. This work presents new results (numerical and experimental) regarding the linearization of the forms to be imposed to the structure, focusing on shapes composed of straight regions, which would ease the design of stamping tools for example. The results show that the use of straight regions in the geometry of the beams (linear embossed pattern) has a similar effect to that obtained with curved shapes but requiring bigger distances to the baseline (higher shaping deformations). It is also shown that the linearized shapes can be used to optimize the shape of a beam for desired natural frequencies.

Гармонический анализ упругого колосниково-карточного элемента динамически активной просеивающей поверхности вибрационного грохота

Поверхностные вибрирующие сита должны обеспечивать довольно сложное движение просеивания частиц сыпучего материала. Для обеспечения необходимых условий для работы просеивающих поверхностей предлагается использовать новую конструкцию динамической упругой поверхностно-активной просеивающей решетки самоочищающейся решетки - карты. Композитные упругие элементы решетки-карты без предварительной деформации, установленные в коробке вибрационного грохота. Консольные горизонтальные полки решетки элементов карты под воздействием виброустойчивых данных совершают сложные вибрационно-пространственные движения. Поскольку пласт URCC апертуры «активен» консольными горизонтальными полками, возникает необходимость в изучении их траекторий движения с учетом конструктивных параметров сита и вибрационной камеры вынужденных колебаний. Цель исследования: метод определения собственных частот и форм мод упругого (резинового) элемента, образующего тканевый ситовый вибратор, который достигнет наибольшей амплитуды колебаний при работе вибрационного грохота. Задача исследования: разработать модель решетчатого элемента карточного сита URCC для гармонического анализа методом конечных элементов. Поскольку элемент решетки имеет сложную форму, предлагается решение с использованием метода конечных элементов. Рассматривается решение задачи гармонического анализа движения составного элемента колосниково-карточного сита вибрационного грохота с помощью метода конечных элементов грохота. Для существующего элемента определено, что при диапазоне варьирования модуля упругости собственная частота горизонтальных колебаний изменилась в пределах 17…34 Гц, а вертикальных – 37…72 Гц.

Natural Frequency Sensitivity Analysis of Fire-Fighting Jet System with Adaptive Gun Head

The gun head is the end effector of the fire-fighting jet system. Compared with a traditional fixed gun head, an adaptive gun head has the advantages of having an adjustable nozzle opening, a wide applicable flow range, and a high fire-extinguishing efficiency. Thus, the adaptive gun head can extinguish large fires quickly and efficiently. The fire-fighting jet system with an adaptive gun head has fluid-structure interaction and discrete-continuous coupling characteristics, and the influence of key design parameters on its natural frequencies needs to be determined by a sensitivity analysis. In this paper, the dynamic model and equations of the jet system were established based on the lumped parameter method, and the sensitivity calculation formulas of the natural frequency of the jet system to typical design parameters were derived. Natural frequencies and mode shapes of the jet system were determined based on a mode analysis. The variation law of the sensitivity of the natural frequency of the jet system to typical design parameters was revealed by the sensitivity analysis. The results show that the fluid mass inside the spray core within a certain initial gas content is the most important factor affecting the natural frequency of the jet system. There was only a 0.51% error between the value of the first-order natural frequency of the jet system determined by the modal experiment and the theoretical one, showing that good agreement with the first-order natural frequency of the jet system was found. This paper provides a theoretical basis for the dynamic optimization design of the adaptive gun head of the fire water monitor.

Effect of Main Cable Pre-Tensioning on Stress – Strain Behaviour and Dynamic Response of Hybrid Cross-Tie System

The authors have addressed the change of main cable tensioning force as the means of suspension bridge stiffness control. An ANSYS 3D model of a suspension bridge was developed. The dead load stress-strain behaviour and dynamic response of the model were analyzed. The study has shown that 7.5 fold increase of the main cable pre-tensioning force reduced the displacement in the middle of the central span of the stiffening girder by 40%, while in the middle of the end span, a 9% increase in displacement was observed; and displacement of the tower apex reduced by 28%. Modal analysis has shown that the main cable pre-tensioning force in the 3D model had effect neither on the natural vibration frequency spectrum of the structure, nor on the distribution of the principal modes in the spectrum. With a 7.5 fold increase of the main cable pre-tensioning force, the values of natural fundamental frequencies have changed within 2% range. The results obtained by the authors allow for the conclusion that varying the pre-tensioning force of the main cable has little effect on a suspension bridge dynamic response control. At the same time, pre-tensioning of the main cable allows control over the stiffness of the hybrid cross-tie system.

Preliminary site characteristics for urban seismic hazard in pasuruan fault from microtremor measurements

The Pasuruan fault is one of active faults in East-Java with the minimum estimated earthquake magnitude to be 6.6 Mw. Although the Pasuruan fault is relatively small in term of estimated earthquake magnitude, because the area is highly populated, earthquake along the fault could pose a significant hazard to the densely populated region and infrastructure. This study mainly focuses on site characteristics of along the Pasuruan fault based on microtremor Horizontal-to-Vertical spectral ratios (HVSR) as a part of the seismic hazard assessment. Through this measurement, the output the site natural frequency, the amplification and the soil vulnerability maps which will be used to make an urban seismic hazard map for along Pasuruan fault. The microtremor measurements were carried out at 48 locations to investigate the natural frequencies and the amplifications at sites. The results showed that the natural frequency (f0) values range from 1 Hz to 10 Hz and the amplification factor (A0) values range from 2 to 8. Correlations between the natural frequency with the geological formation and topographic were established. Variations of both parameters are also indicated as a result of variations in surface soil parameters. The vulnerability index (Kg) is indicated the soil damage level due to ground motions. The weak zone failed during an earthquake on the Southwest site was identified by the highest Kg value.

Unbalanced pump detection using modified transfer path analysis

Unbalance is the term in a rotating machine that used for a mass distribution which is not rotationally symmetric. Vibration from unbalancing pump affects to other pumps located on the same single base frame due to transmissibility. However, the unbalanced vibration can disturb and give a negative impact to other pumps on the same base frame. Therefore it is important to detect unbalance pump early which transmitted through the base frame because it can save large amounts of money. The aim of this research is evaluating the modification of transfer path analysis method that applied as a detecting pump damage method compare to International Standard. In this research, Modified Transfer Path Analysis (MTPA) is equal to the operational force that found by convolution of the natural frequencies with operational acceleration. The value of natural frequencies are determined using experimental modal analysis and the value of operational acceleration is determined by measuring the acceleration when the vibration source (pump machine) is running on steady condition. ISO 13373-1 was used as the reference for damage detection on the pump system. The results show that MTPA has the same characteristics and in agreement with ISO 13373-1 in detecting unbalance pump condition for machinery condition monitoring. Unbalance is the term in a rotating machine that used for a mass distribution which is not rotationally symmetric. Vibration from unbalancing pump affects to other pumps located on the same single base frame due to transmissibility. However, the unbalanced vibration can disturb and give a negative impact to other pumps on the same base frame. Therefore it is important to detect unbalance pump early which transmitted through the base frame because it can save large amounts of money. The aim of this research is evaluating the modification of transfer path analysis method that applied as a detecting pump damage method compare to International Standard. In this research, Modified Transfer Path Analysis (MTPA) is equal to the operational force that found by convolution of the natural frequencies with operational acceleration. The value of natural frequencies are determined using experimental modal analysis and the value of operational acceleration is determined by measuring the acceleration when the vibratio...

Modal identification of localised damage in beams and trusses: experimental and numerical results

The paper discusses the possibility of detecting local damages in complex structures typical of civil engineering, as multispan beams and trusses. Namely, it describes a procedure to identify localised cracks in structures in the elastic range of behaviour using only the values of natural frequencies in the intact configuration and in the damaged one evaluated by means of dynamic tests. The error minimisation procedure described in the paper selects the solution within a set of finite element models that simulate a range of positions and levels of damage, by identifying the damaged configuration as the one whose modal frequencies minimise the least-square difference with the measured data. The accuracy of the method is first investigated by applying it to the damage detection of a two-span steel beam, whose modal frequencies were obtained by means of experimental tests. To explore the accuracy of the proposed procedure, numerically simulated data with random noise were also generated for several positions and levels of damage and for different values of the random noise. The procedure was then extended, by means of numerical simulations, to the case of a beam with two localised damages. Finally, the procedure proposed for multispan beams is adapted to the damage identification of plane truss structures.

Vibration Analysis of Kenyir Dam Power Station Structure Using a Real Scale 3D Model

In this paper, the vibration analysis in terms of modal and harmonic responses are investigated for the power station structure of Kenyir Dam in Terengganu, Malaysia. Modal analysis is carried out to provide the dynamic characteristics of the power station which includes the natural frequencies and mode shapes. Meanwhile, the harmonic response analysis is performed by applying the force to the structure to obtain the Frequency Response Function (FRF) in certain range of frequencies. A real scale three-dimensional (3D) model of the Kenyir Dam power station is constructed using SolidWorks software and imported to ANSYS software for the Finite Element (FE) analysis. A proper boundary condition is taken into consideration to demonstrate the real behaviour of the power station structure. From the results, six most significant natural frequencies and mode shapes including the FRF in all three axes are selected. The highest natural frequency value occurred at 5.4 Hz with the maximum deflection of 0.90361 m in the <i>z</i> axis direction. This value is important in order to verify whether the structure can overcome the resonance phenomenon from the external disturbance forces in the future.

Numerical analyses on seismic behavior of helical concrete columns

This paper presents the behavior of the helical reinforced concrete columns (HCC) subjected to horizontal 2D seismic motion excitation combined with the static axial load. Helical concrete columns are new types of elements which arose in the new twisted buildings, providing a special geometry by twisting the top section by an angle (ϕ), furthermore, offsetting the top section by a considerable distance respecting to the bottom section. In order to study seismic behavior of the HCC under a seismic load of the short period using finite element software, numerical simulation is carried out in this paper using ANSYS V 18.1 software. A brief comparison of the HCC behavior was made between different cases of conventional reinforcement in the longitudinal and transverse directions, as well as the different twisting angles (ϕ) of column sections. The comparison illustrated that all columns response with giving the same mode shapes of vibration in the modal analysis with different values of natural frequencies and relative amplitude deformations. However, the difference be very noticeable when changing the section size of the columns comparably with changing the twisting angles of the section, where increasing the section size of HCC from 250 mm to 400 mm cause increase the natural frequency by 55.4% for second mode shape, while it cause decreasing the relative amplitude response of HCC by 52.5% for sixth mode shape. The transient analysis of the six types of HCC excited by horizontal 2D seismic motion indicates the tendency of HCC to increase its responses, like twisting and buckling deformations. The deform shape-time history of 6 HCC demonstrated that with increasing (shear stress path section distance) S of HCC column which depends up on (ϕ value), the top section would have less stresses.

Finite Element Model Updating of Dissimilar Plate with Rivet Joint

This study focusses on experimental modal analysis (EMA), finite element analysis (FEA) and model updating. The result of FEA and EMA will be validated and analysed. Then, the study extended to the early stage of model updating by assuming that the riveted dissimilar plates is a rigid body instead of two dissimilar plates. These modal parameters are crucial in providing various periods at which it will naturally resonate to avoid the structure continue to resonate and experience structural damage. Modal parameters of the dissimilar plate with rivet joint which include natural frequency and mode shapes were determined through EMA and FEA. Comparison of experimental data and the simulation data reveals a good correlation between the values of natural frequency. Minor discrepancies of the percentage of error between EMA and FEA are acceptable with the percentage of error is within the range of 0.4% to 13%. Furthermore, the conducted model updating able to reduce to an error range of 0.03% to 0.1%. Through this study, the best way of conducting finite element analysis and model updating for dissimilar plate material with rivet joint is also determined.

Effect of increasing floors number on the natural frequency compared with further masses added to steel building models

This paper investigates the change in the natural frequency of whole building due to the increase or decrease of the number of floors of a steel building model. Five steel building models were adopted in the present study to investigate the natural frequency required to be identified in each model. The first model represents a one floor building model, the second building model contains two floors and so on. The first four models were subjected to further masses distributed upon four points within the last floor. Each model consists of the same structural details that are proposed in the other models such as details of the beams, columns and slabs. The herein parameters are the number of floors and the further added masses upon the models up to four floors. All models were analyzed using ANSYS software to identify the natural frequencies for the extracted modes of vibration about X, Y, and Z building axes. The study is aimed to produce a relationship between the change of floors number and the further mass addition in the field of structural frequency attenuation based on the indication of the first identified mode. Results show that higher masses required to be added to attenuate value of natural frequency for the one floor building model than the further masses required for building with two floors to achieve the same purpose. This relationship continues for the other models with higher number of floors but with less further required masses.