Variation Of Natural Frequency Research Articles

Vibration Control of Metal Spatial Structures With Tuned Mass Dampers

additional-mass-type vibration-control devices, especially TMDs, and confirm their control performance under seismic loadings by both analytical and experimental methods. Firstly, to effectively control spatial structures that have different vibration properties than multi-story frame structures, we propose a spatially distributed MTMD method. This method is characterized by controlling plural modes with closely spaced natural frequencies based on the robust property of the MTMD against variation of natural frequencies. Next, we propose a TMD-with-initial-displacement method to improve transient response. Then, we describe a shaking table test using TMD models and compare test results and analytical results. Lastly, we describe a method of applying a Houde damper system through a real construction project; the Eye of the Yellow Sea Pedestrian Bridge.

Long-term investigations of dynamic behavior of a pre-stressed concrete ballasted railway bridge

Dynamic properties of civil structures such as natural frequencies, damping ratios, and mode shapes are essential parameters for evaluating the health condition of structures. However, dynamic properties are prone to be biased by environmental effects which may lead to fault structural health assessment. To investigate the environmental effect on the dynamic parameters of ballasted bridge, in this paper, a series of vibration experiments were performed on a multi-span pre-stressed concrete beam railway bridge. The dynamic properties of the bridge were identified and analyzed. In total, 9 experiments were conducted in 2 years. In the first 8 experiments, only sleepers and tracks had been removed. For the last experiment, the bridge was under destruction. The subsidiary components of the structure were destructed, and some holes were drilled on the slab for hoisting. The results show a clear seasonal variation in natural frequencies that in winters the natural frequencies reach local maximum values. Damping ratios show no clear variation regularity, indicating the complex correlation between the damping ratios and the environmental variation. Additionally, compression tests of concrete pieces of the slab were also conducted to investigate the degradation of material properties. The result of the compression tests indicates that there is approximately no degradation of compression strength of the concrete slab after the bridge was in service for several over 4 decades.

Research on the natural frequencies of an integrated offshore wind turbine model considering blades

The offshore wind turbine (OWT) is a high-rise structure that is extremely sensitive to dynamic loads such as wind, waves, and earthquakes. Therefore, in order to avoid resonance, it is extremely important to accurately calculate the natural frequencies of the OWT at the design stage. The integrated finite element model of DTU (Technical University of Denmark) 10 MW OWT is established based on OpenSees finite element software. The correctness of the superstructure simplification method is confirmed by comparing it to the frequencies calculated by the wind turbine dynamic analysis software HAWC2 for the single-blade model and the fixed constraint model at the bottom of the tower. The frequencies and mode shapes calculated by the overall model are compared with those calculated by the fixed model at the mudline and the concentrated mass model at the top of the tower. Then, the parameters of the soil shear modulus G0, void ratio e, pile embedded length L, pile diameter D, water depth, and blade stiffness are analyzed using the lumped mass model and the blade model at the top of the tower, and some regular conclusions about the variation of natural frequency with the parameters are obtained. Finally, based on the blade model, the influence of short-term cyclic loading on the natural frequency for OWT monopiles in dense sand is studied. The results indicate that the pile-soil interaction has a significant impact on the natural frequencies, the blade has a higher influence on the second bending frequency of the OWT, and the front-after direction is more significantly impacted than the side-side direction. The short-term cyclic loading are unlikely to significantly affect natural frequency for OWT monopiles in dense sand.

Development and robustness investigation of track-based asymmetric nonlinear energy sink for impulsive response mitigation

Nonlinear energy sinks (NESs) are known for their capacity of resonating with a wide range of frequencies. However, the occurrence of resonance in NESs strongly depends on the input energy level. To further enhance energy as well as frequency-related robustness and tailor the robust performance to the need of engineering structures, track asymmetric nonlinear energy sinks (TANESs) are proposed in this study. Integrating the merits of two existing mass dampers, TANESs are able to broaden the energy range for effective response mitigation toward both the upper and lower limits. First, the theoretical model of TANESs is developed and validated through experiments on a two-story frame structure. The validated model is then applied to analytically derive the fundamental dynamics of the standalone TANES under impulsive and harmonic excitation. Subsequently, the robust performance of the TANES predicted by the analytical results is numerically investigated when the structure, considering natural frequency variations, is subjected to impulsive excitation of different amplitudes. Finally, the control characteristics and applicable situations of the TANES and other comparable mass dampers are discussed. The results show that the TANES can act as a well-tuned linear mass damper when the input energy is below a certain level and perform more effectively on frequency-decreased structure as the energy level further increases. As decrease in structural frequency is often caused by damages under stronger excitation, TANESs are considered to be a suitable control strategy for engineering structures in practice.

Crack identification driven by the fusion of mechanism and data for the Variable-Cross-Section cantilever beam

Crack identification for variable-cross-section cantilever structures is a main means of avoiding sudden failure caused by cracking and realizing the prognostics and health management (PHM) of such structures. This paper proposes an inverse crack identification method driven by mechanism and data for variable-cross-section cantilever beams. First, the Rayleigh method is revised for the fast, accurate calculation of the natural frequencies of a healthy cantilever beam, which is regarded as a basic criterion. Subsequently, for the rapid, accurate expression of the relationship between crack information and natural-frequency variations, a data-driven method based on the radial basis function is proposed to calculate the response variations accurately according to the crack information. Then, the obtained acceleration of the cantilever beam is decomposed to determine its natural frequencies, and the variations in these natural frequencies are obtained and compared with the results of the mechanism model. Finally, crack positions, lengths, and widths are identified based on the forward model and decomposition results. Particle swarm optimization is employed to minimize the discrepancy in the changes between the monitored and calculated natural frequencies. The proposed forward model is compared with other methods, and the superiority of the crack identification method is verified experimentally. Results indicate that the proposed method accurately identifies cracks on variable-cross-section cantilever beams and provides an effective PHM approach for beam-type structures.

Damage Estimation of Full-Scale Infilled RC Frames under Pseudo-Dynamic Excitation by Means of Output-Only Modal Identification

To assess the health condition of structures and infrastructure during their service lives, continuous vibration-based monitoring represents a viable and cost-effective solution. Model updating and digital twins are increasingly adopted for damage detection. However, significant gaps and uncertainties in damage quantification still arise. This work presents original data from output-only modal identification tests on full-scale, two-storey reinforced concrete (RC) frames subjected to pseudo-dynamic loading to simulate seismic damage. The frames are tested with two masonry infill wall configurations with three-sided and four-sided boundary conditions, and the observed seismic damage is correlated to a damage scale. Output-only modal identification tests are performed before and after testing to catch variations in modal properties due to observed damage. Experimental data are used to build a refined finite element model able to reliably simulate the static and dynamic performance of the infilled RC frames before and after damage. The model allowed for the further assessment of the variation in natural frequencies of tested specimens at different earthquake intensities, the correlation of such variations to damage levels, and identification of the contribution of structural and non-structural components to the overall frequency variation.

Vibration analysis of thermally loaded isotropic and composite beam and plate structures

This work proposed the use of the Carrera Unified Formulation (CUF) for the vibration and buckling analysis of structures subjected to thermal loads. In detail, the variation of natural frequencies for progressively large thermal loads is investigated. Here, particular attention is focused on the study of buckling thermal loads as degenerate cases of the vibration analysis and on the mode aberration caused by thermal stresses. From this standpoint, the use of CUF for the development of high-order beam and plate models is fundamental. Indeed, Lagrange-like (LE) polynomials are considered for developing the kinematic expansion and Layerwise (LW) theories are employed to characterize the complex phenomena that may appear in composite structures. A linearized formulation to study the natural frequencies variation as a function of the progressive increasing thermal loadings is adopted. Different isotropic and laminated composite structures have been analyzed and compared with the Abaqus solution to validate the presented methodology and provide some benchmark solutions. In addition, a parametric study was conducted to evaluate the stacking sequence and thickness effect in the vibration modes and thermal buckling loads. The results document the excellent accuracy and reliability of the presented methodology and show the potentialities of this numerical tool able to analyze cases that are difficult to study experimentally.

Computational Modeling and Parametric Analysis of SMA Hybrid Composite Plates under Thermal Environment.

This paper presents a coupled thermoelastic finite element formulation for static and dynamic analysis of composite laminated plates with embedded active shape memory alloy (SMA) wires, which accounts for both the phase transformation and the nonlinearity effects of SMA wires. The equations of motion are obtained by using Hamilton's principle and first-order shear deformation theory (FSDT). Furthermore, based on Brinson's one-dimensional phase transformation constitutive law, a novel coupled thermoelastic finite element model that enables analysis of the SMA hybrid composite (SMAHC) plate is developed. The accuracy and efficiency of the developed computational model for analysis of SMAHC plates are reinforced by comparing theoretical predictions with data available from the literature. The results of the numerical examples also show the ability of the proposed model to predict the thermal-mechanical behavior of SMAHC plates in accordance with SMA's hysteresis behavior. In addition, based on the proposed model, the influence of temperature as well as SMA volume fraction, pre-strain value, boundary condition and layup sequence on the static bending and free vibration behavior of the SMAHC plates is investigated in detail. The results of parametric analysis show that the variations of both static deflection and natural frequency of the SMAHC plate over temperature exhibit a nonmonotonic behavior.

Structural health monitoring and finite-element modelling of Suramadu Bridge, Indonesia

Structural health monitoring (SHM) has received significant public attention due to its potential to optimise the maintenance, long-term reliability and life-cycle cost of infrastructure systems. The main goal of SHM is to identify, characterise and diagnose anomalous performance of structures. Usually, the most common approach to attain this goal is by investigation of variations in structural natural frequencies. However, both structural degradations and environmental conditions can affect structural performance and, therefore, decoupling natural frequency variations from operational conditions is essential. This paper reports on a monitoring system and measurement data of a long-span cable-stayed in Indonesia (Suramadu Bridge). The main objective of this work was to explore and report the environmental and operational conditions of the bridge for the first time. A detailed finite-element model was developed to investigate the operational performance of the bridge under different environmental conditions. The results showed that the vertical modal properties of the Suramadu Bridge are less affected by ambient excitations in comparison with lateral/torsional modes.

An experimental investigation on the effectiveness of damping changes for damage detection in a Fibre Reinforced Plastic Plate

Fibre reinforced plastics (FRP) are extensively used because of their high specific strength and stiffness. However, throughout their service life, such materials are susceptible to damages, which when accumulated may result in catastrophic failure. Studies on effects of stiffness loss due to damage has been exercised by quite a large number of researchers but very less investigators have involved the variations in dissipative behaviour in combination with such stiffness loss. However, damage in these structures not only causes local reduction of stiffness but is also observed with increased dissipation behaviour. One of the most convenient ways to carry out health monitoring exercise to detect damages is to conduct systematic vibration testing. The present study investigates the likely changes in natural frequencies and mode shapes of a rectangular FRP composite plate along with damping factors due to the induced damage. The FRP plate considered has been modal tested and dynamic responses i.e., natural frequencies, mode shapes and modal damping factors are derived through curve-fitting technique from the frequency response function measurements. In this study, changes in dynamic responses due to a locally induced damage in the FRP plate is studied. For this, in order to maximize the effects of local reduction in the stiffness on the modal parameters, a partial-cut is provided in a localised region of the plate in the first damage case. In the second damage scenario, the partially-cut area has been filled with epoxy resin matrix to create a region with localised change in material properties and with limited stiffness loss. Damping changes has been observed to be significant and more sensitive than variations in natural frequencies and mode shapes. The study suggests that damping parameters along with stiffness changes together can be put into practice to develop an effective vibration-based health monitoring scheme

Vibration-based approach for structural health monitoring of ultra-high-performance concrete bridge

Structural Health Monitoring (SHM) is a valuable tool for keeping track of the performance and health of engineering structures over extended periods. The purpose of SHM is to ensure structural safety by relying on information derived from real-time measured data and offer suitable recommendations for the structure's maintenance and management. The fundamental idea of SHM is that the structure's response to vibrations will change noticeably if its mass or stiffness is altered. It is a way to keep tabs on how well a building keeps itself safe and sound with as little human intervention as possible. Throughout this research, a Finite Element (FE) model was updated, and an ambient vibration test was performed on an Ultra-High-Performance Concrete (UHPC) bridge, given its slimmer as well as lighter properties to get modal parameters, including natural frequency and mode shape. Measured modal parameters were acquired and verified with the aid of several Operation Modal Analysis (OMA) techniques, and the FE model has then modified accordingly. The bridge's condition was evaluated and predicted using a mathematical method called simple linear regression, which considered the variations in natural frequency produced by the structure's mass and stiffness. The findings indicate that the stiffness index ratio is a practical and efficient tool for evaluating the bridge's effectiveness. The applied method demonstrated the Sungai Raia bridge's safe functioning in real-world situations.

Safety of a quarter-vehicle car through negative derivative feedback controller

The aim of this paper is presenting the acts of a resonant control technique called Negative Derivative Feedback (NDF) controller on a quarter-vehicle car subjected to principal parametric excitation. This control technique is useful and effective as it helps to avoid any dangerous vibrations caused during its operation. Therefore, we considered the NDF controller that plays an important role in it. Moreover, robustness to natural frequency variation has been investigated for the first time on a quarter-vehicle car system. The multiple scale homotopy (MSH) approach has been used for solving the equations of the controlled system mathematically. At the studied resonance case Ω=2,ω=1, the acts of actual various parameters and system conduct are calculated. Frequency-response equations (FREs) governing the controlled system vibration amplitude have been derived. The simulation outcomes were completed with the help of MATLAB 7.0 programs. A comparison between PPF and NDF controllers has been made in the vibration system to show the best controller. Numerical outcomes reveal that the best one in removing the oscillations and decreasing the value of amplitudes is the NDF controller. Furthermore, after adding this controller, its gains lessened the steady-state amplitudes of the model in a minor time. In addition, this controller made the structure more stable than those of other controllers. The impacts of the effective parameters on the controlled system have been discovered. The different response curves for the framework when the controller is off and on action have been plotted by the obtained frequency-response equation displaying the stable and unstable zones. Finally, the obtained numerical results have shown an outstanding agreement per the analytical ones.

Estimation and Adjustment of Interface Stiffnesses for Machine-Tool

This study adopts a practical approach to establish the estimation and adjustment methods of the interface stiffness for the machine-tool through the finite element analysis (FEA). First, numerical and experimental modal analysis (FMA and EMA) for each single subsystem of the machine-tool structure are performed. Then, the parameters obtained from EMA are used as the objective criterion function, and the FMA is conducted iteratively to solve the material Young’s modulus and Poisson’s ratio for each single subsystem structure, in which the geometrical model is simplified and FE mesh convergence is performed to ensure the quality and efficiency of the numerical analysis. Next, by considering that the machine-tool is assembled by subsystem stacking and that loading on each contact surface is deduced, the FE method is used to calculate the deformation of each contact interface after the single subsystem is stacked successively. The initial value of the interface stiffness estimated by the deformation formula in the mechanics of material is utilized as the initial condition for the iterative calculation in FMA. The changes of the modal parameters are observed in the analysis and the interface, which have a significant impact on the natural frequency variations of the whole machine-tool is selected as the main adjustment object. Then, the adjustment method proposed in this study is applied repeatedly to modify this interface stiffness. The results show that footing interface stiffnesses play the most important role that intensively affects the numerical analysis results of modal parameter. After the repeated adjustments of the interface stiffnesses of the footing, the error of the natural frequency of the whole machine-tool is less than 5%, which is calculated from the comparison between EMA and FMA results. It indicates that the proposed adjustment method in this study for footing interface stiffness determination has a valuable reference in practical use.

A New Ice Quality Prediction Method of Wind Turbine Impeller Based on the Deep Neural Network

More and more wind turbines are installed in cold regions because of better wind resources. In these regions, the high humidity and low temperatures in winter will lead to ice accumulation on the wind turbine impeller. A different icing location or mass will lead to different natural frequency variations of the impeller. In order to monitor the icing situation in time and in advance, a method based on depth neural network technology to predict the icing mass is explored and proposed. Natural-environment icing experiments and iced-impeller modal experiments are carried out, aiming at a 600 W wind turbine, respectively. The mapping relationship between the change rate of the natural frequency of the iced impeller at different icing positions and the icing mass is obtained, and the correlation coefficients are all above 0.93. A deep neural network (DNN) prediction model of ice-coating quality for the impeller was constructed with the change rate of the first six-order natural frequencies as the input factor. The results show that the MAE and MSE of the trained model are close to 0. The average prediction error of the DNN model is 4.79%, 9.35%, 3.62%, 1.63%, respectively, under different icing states of the impeller. It can be seen that the DNN shows the best prediction ability among other methods. The smaller the actual ice-covered mass of the impeller, the larger the relative error of the ice-covered mass predicted by the DNN model. In the same ice-covered state, the relative error will decrease gradually with the increase in ice-covered mass. In a word, using the natural frequency change rate to predict the icing quality is feasible and accurate. The research achievements shown here can provide a new idea for wind farms to realize efficient and intelligent icing monitoring and prediction, provide engineering guidance for the wind turbine blade anti-icing and deicing field, and further reduce the negative impact of icing on wind power generation.

Damage Detection in Cantilever Piping System-Transporting Fluid Using Finite Element Method

Fracture existence in a pipe is considered disruptive as well as detrimental to the pipe systems and equipments. Cracks are the most common mechanism of failure for pipelines of any kind. Therefore, early crack identification may help save the pipe system from catastrophic breakdown. This study focuses on fluid-transporting cantilevered tapered pipes. By using the Bernoulli beam theory, ANSYS is used to simulate the pipe's performance by the finite element method for an incompressible fluid flow through a tapered cantilevered pipe. The effect of a non-propagating open crack on the dynamic and modal behavior of a cantilevered pipe used to convey fluid is investigated. Flow velocity and crack relative location, as well as the crack's depth, will be explored as they relate to the fundamental natural frequency, second, and third natural frequency. Results have showed clearly that crack depth and relative position play a significant role in natural frequency variation. However, fluid inlet velocity is found to have less impact on the natural frequencies considered at a certain relative crack position.

On the natural frequency investigation of the thick hollow cylinder with 2D-FGM Mori-Tanaka scheme

ABSTRACT In this paper, we conduct the natural frequency analysis for a 2D-FGM (functionally graded material) finite-length, thick-walled cylinder by the graded finite element method. The material properties gradations are considered along with the thickness and the longitudinal axis of the cylinder according to the Mori-Tanaka scheme and power-law volume fraction distributions. Therefore, the graded properties are implemented by user subroutine UMAT in ABAQUS/Standard™. The eigenvalue problem is solved using three-dimensional elasticity equations, and the current technique has been confirmed by earlier research. The major purpose of this study is to see how FGM configurations affect the vibration behaviour of the cylinder. The variation of the cylinder's first natural frequencies for various thickness-to-outer-radius and length-to-outer-radius ratios is presented, taking into account varied material distributions. According to the findings, raising the power exponents, particularly the radial one, increases the natural frequencies.

Model tests of a 10 MW semi-submersible floating wind turbine under waves and wind using hybrid method to integrate the rotor thrust and moments

Abstract. This paper describes the results of a wave tank test campaign of a 1/49 scaled SATH 10 MW floating platform. The software-in-the-loop (SiL) hybrid method was used to include the wind turbine thrust and the in-plane rotor moments. Experimental results are compared with a numerical model developed in OpenFAST of the floating wind turbine. The tank test campaign was carried out in the scaled model tested at the deep ocean basin from the Lir National Ocean Test Facility at Cork, Ireland. This floating substructure design was adapted by Saitec to support the 10 MW wind turbine within the ARCWIND project (Adaptation and Implementation of Floating Wind Energy Conversion Technology for the Atlantic Region) with the aim of withstanding the environmental conditions of the European Atlantic Area region. CENER provided the wind turbine controller specially designed for the SATH 10 MW configuration. A description of the experimental setup, force actuator configuration and the numeric aerodynamic parameters is provided in this work. The most relevant experimental results under wind and wave loading are shown in time series and frequency domain. The influence of the submerged geometry variations in the pitch natural frequency is discussed. The paper shows the simulation of a case with rated wind speed, where the tilted geometry for the computation of the hydrostatic and hydrodynamic properties of the submerged substructure is considered. This case provides a better agreement of the pitch natural frequency with the experiments than an equivalent simulation using the undisplaced geometry mesh for the computation of the hydrodynamic and hydrostatic properties.

The analysis and validation of natural frequencies and mode shapes of 3D plates in the framework of the generalized thermoelastic theory

This article considers thermal effects that induce thermoelastic damping and, which, consequently, because of the absorbed thermal energy, cause thermal stresses. The problem is stated in the framework of the generalized thermoelastic theory. The natural frequency and mode shape analyzes of 3D plates are presented under uniform and nonuniform heating. From the modeling point of view, this results in the quadratic eigenvalue problem where complex frequencies and modes are obtained. Moreover, the quality factor related to the thermoelastic damping is also calculated in terms of the imaginary and the real parts of the frequencies for both the uniform and nonuniform thermal distributions. The variation of natural frequencies with temperature is investigated and compared with the experimental results for the plates with free boundary conditions. The first two mode shapes are also examined for all clamped edges for the uniform and nonuniform cases. Complex frequencies and complex modes are observed due to the thermal effects. For the uniform case, the real part of the modes decreases and the complex part increases, while the mode’s norm remains the same as in the classical modes as temperature increases. For the nonuniform case, the mode shape analysis is performed under the assumption that the elasticity modulus, thermal expansion, and specific heat parameters are functions of temperature. The peak point of the out-of-plane displacement is shown to be shifted toward the warm zone. The obtained outcomes may help design thermal structures and allow for future extensions.

A High-Precision Method of Stiffness Axes Identification for Axisymmetric Resonator Gyroscopes.

Axisymmetric resonators are key elements of Coriolis vibratory gyroscopes (CVGs). The performance of a CVG is closely related to the stiffness and damping symmetry of its resonator. The stiffness symmetry of a resonator can be effectively improved by electrostatic tuning or mechanical trimming, both of which need an accurate knowledge of the azimuth angles of the two stiffness axes of the resonator. Considering that the motion of a non-ideal axisymmetric resonator can be decomposed as two principal oscillations with two different natural frequencies along two orthogonal stiffness axes, this paper introduces a novel high-precision method of stiffness axes identification. The method is based on measurements of the phase difference between the signals detected at two orthogonal sensing electrodes when an axisymmetric resonator is released from all the control forces of the force-to-rebalance mode and from different initial pattern angles. Except for simplicity, our method works with the eight-electrodes configuration, in no need of additional electrodes or detectors. Furthermore, the method is insensitive to the variation of natural frequencies and operates properly in the cases of either large or small frequency splits. The introduced method is tested on a resonator gyroscope, and two stiffness axes azimuth angles are obtained with a resolution better than 0.1°. A comparison of the experimental results and theoretical model simulations confirmed the validity of our method.

Design and experiment of an adaptive dynamic vibration absorber with smart leaf springs

An adaptive dynamic vibration absorber (ADVA) is designed for low-frequency vibration suppression. The leaf springs are applied as the tuning stiffness elements. The principle of variable stiffness is analyzed to obtain the effective range of the first natural frequency variation. A classic simply supported manipulator is selected as the controlled system. The coupled dynamic model of the manipulator-ADVA system is built to obtain the maximum damping efficiency and the vibration absorption capacity of the designed ADVA. An experimental platform is set up to verify the theoretical results. It is revealed that the ADVA can adjust the first natural frequency on a large scale by changing the curvature of the leaf springs. The amplitude of the manipulator is reduced obviously with the installation of the designed ADVA. Finally, based on the short-time Fourier transformation (STFT), a stepwise optimization algorithm is proposed to achieve a quick tuning of the natural frequency of the ADVA so that it can always coincide with the frequency of the prime structure. Through the above steps, the intelligent frequency tuning of the ADVA is realized with high vibration absorption performance in a wide frequency range.