Estimation Of Natural Frequencies Research Articles

Experimental validation of a short-term damping estimation method for wind turbines in nonstationary operating conditions

Abstract. Modal properties and especially damping of operational wind turbines can vary over short time periods as a consequence of environmental and operational variability. This study seeks to experimentally test and validate a recently proposed method for short-term damping and natural frequency estimation of structures under the influence of varying environmental and operational conditions from measured vibration responses. The method is based on Gaussian process time-dependent auto-regressive moving average (GP-TARMA) modelling and is tested via two applications: a laboratory three-storey shear frame structure with controllable, time-varying damping and a flutter test of a full-scale 7 MW wind turbine prototype, in which two edgewise modes become unstable. Damping estimates for the shear frame compare well with estimates obtained with stochastic subspace identification (SSI) and standard impact hammer tests. The efficacy of the GP-TARMA approach for short-term damping estimation is illustrated through comparison to short-term SSI estimates. For the full-scale flutter test, GP-TARMA model residuals imply that the model cannot be expected to be entirely accurate. However, the damping estimates are physically meaningful and compare well with a previous study. The study shows that the GP-TARMA approach is an effective method for short-term damping estimation from vibration response measurements, given that there are enough training data and that there is a representative model structure.

Nonlinear roll damping coefficients and natural frequency estimation via augmented extended Kalman filtering for floating body

ABSTRACT The nonlinear roll damping coefficients and natural frequency of a floating body are discussed in this article using an augmented Extended Kalman Filtering (EKF) method. This paper presents a non-linear model-based observer for the combined estimation of free roll decay motion states and damping coefficients. The identification framework uses an improved extended Kalman filter (EKF) to deal with model parameter variability and noisy measurement input. The estimated error was compared to the theoretical results obtained from the covariance matrix for filtering correctness. It is found that the nonlinear damping coefficients and natural frequency obtained from the EKF approach are a more realistic representation of the roll dynamics from the general estimation procedure given by the literature. The proposed method also has the built-in capability to remove random noise from the measured roll. The influence of noise levels in the measurements on the identification accuracy was investigated and discussed.

Study on estimation of natural frequencies of pier foundations according to the progress of scouring

Study on estimation of natural frequencies of pier foundations according to the progress of scouring

Estimating Bridge Natural Frequencies Based on Modal Analysis of Vehicle-Bridge Synchronized Vibration Data.

This paper presents a method for accurately estimating the natural frequencies of bridges by simultaneously measuring the acceleration vibration data of vehicles and bridges and applying modal analysis theory. Vibration sensors synchronized with GPS timing were installed on both vehicles and bridges, achieving stable and high-precision time synchronization. This enabled the computation of the bridge's Frequency Response Functions (FRFs) for each mode, leading to a refined estimation of natural frequencies. The validity of the theory was confirmed through numerical simulations and experimental tests. The simulations confirmed its effectiveness, and similar trends were observed in actual bridge measurements. Consequently, this method significantly enhances the feasibility of bridge health monitoring systems. The proposed method is suitable for road bridges with spans ranging from short- to medium-span length, where the vehicle is capable of exciting the bridge.

A novel method for the natural frequency estimation of the jet engine turbine blades based on its dimensions

This study provides a novel methodology for the natural frequency estimation of the jet engine turbine blade by using the dimension check. This paper presents a summarization of the ongoing research devoted to the method for the turbine blade natural frequency estimation. The main target of the research presented in the paper is to develop a novel method that can calculate the natural frequency of a particular turbine blade by using the dimensions of investigated turbine blade from a dimension check. This goal is achieved by the combination and interaction of several methods as for instance computed aided design (CAD) finite element modelling (FEM), artificial neural network (ANN) and others. As it is mentioned in the following chapters of the article a unique novel method is developed that can predict natural frequency according to the dimensions. The results confirmed the correctness of the new methodology, which can predict natural frequency by the dimensions of a turbine blade immediately with a relatively high level of accuracy (maximal errors are under 1.5%). Every jet engine manufacturer (GE aviation, Rolls Royce, Prat and Whitney, etc.) has to test jet engine parts for the natural frequencies in order to avoid the resonance at early stage of the manufacturing process in order to mount the blades into the engine. The experimental tests of every single turbine blade are time-consuming, a novel method can predict natural frequency according to the dimensions by using data from dimension check in 0.0051 s. The presented method is under patent pending.

Research on estimation and control methods of natural frequency of irregular building structure vibration

With the continuous increase in the number of irregular buildings, ensuring the safety of building structures has become the primary concern. The study used finite element analysis to estimate the natural frequency of vibration of irregular building structures, and further designed a fuzzy control algorithm combined with magnetorheological dampers to improve their seismic performance. The research results showed that the longitudinal and transverse natural frequencies of Model 1 were 10.44 Hz and 10.51 Hz, respectively, while those of Model 2 were 10.31 Hz and 9.89 Hz, respectively. Using the fuzzy control method, the peak displacement of the building structure was reduced to 11.64 cm, and the peak acceleration was 7.9 m/s2. Comparing the open-plus-closed-loop control with open-loop control methods, it was found that although the fluctuation amplitude of the open-loop control method was relatively large, its control effect was poor, while the open-plus-closed-loop control methods had good overall control effect, with the peak acceleration of 8.26 m/s2 in the open-loop control. The study provides an accurate method for estimating the natural vibration frequency of irregular building structures and demonstrates the effectiveness of the designed fuzzy control algorithm in controlling building vibration.

Quantum computing for solid mechanics and structural engineering – A demonstration with Variational Quantum Eigensolver

Variational quantum algorithms exploit the features of superposition and entanglement to optimize a cost function efficiently by manipulating the quantum states. They are suitable for noisy intermediate-scale quantum (NISQ) computers that recently became accessible to the worldwide research community. Here, we implement and demonstrate the numerical processes on the 5-qubit and 7-qubit quantum processors on the IBM Qiskit Runtime platform. We combine the commercial finite-element-method (FEM) software ABAQUS with the implementation of Variational Quantum Eigensolver (VQE) to establish an integrated pipeline. Three examples are used to investigate the performance: a hexagonal truss, a Timoshenko beam, and a plane-strain continuum. We conduct parametric studies on the convergence of fundamental natural frequency estimation using this hybrid quantum-classical approach. Our findings can be extended to problems with many more degrees of freedom when quantum computers with hundreds of qubits become available in the near future.

Stochastic free vibration analysis of FG-CNTRC plates based on a new stochastic computational scheme

Stochastic analysis can provide more accurate results compared to deterministic analysis. In this study, the spatial variability of material parameters is introduced into the free vibration analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates to achieve a higher degree of accuracy, and a new stochastic computational scheme is proposed to handle the low-level uncertainties. First-order shear deformation theory (FSDT) is employed to establish the displacement field of the plates. The Young's moduli of carbon nanotube (CNT) and matrix are regarded as one-dimensional (1D) and two-dimensional (2D) random fields, respectively, which is discretized by Karhunen-Loève (K-L) expansion. The obtained random variables are substituted into modified perturbation stochastic method (MPSM) and radial point interpolation method (RPIM) to calculate the first two order estimates of the stochastic non-dimensional natural frequencies ω¯. The sensitivity of the first to fourth ω¯ to the random fields is analyzed, and the corresponding stochastic bands are plotted. The results indicate that the presented approach can accurately solve the generalized eigenvalue problem in stochastic free vibration; ω¯ is sensitive to random fields E11CNT and Em, and insensitive to random field E22CNT; the CNT distribution mode also affects the sensitivity.

The natural frequency estimation for a system composed of a beam and a spring-mass system

This study presents an approximate method for determining the natural frequency of a system composed of a beam and a two-degree-of-freedom spring-mass system. The expression for estimating the natural frequency is derived following the standard procedures of the forced vibration analysis of a beam. The results obtained using the current method are in good agreement with those obtained through the dynamic stiffness method, especially when the spring stiffness is large. The innovativeness of the current method is that it reveals the relevance between the natural frequency of the system, the natural frequency of the beam, and the mode shape data at the positions where the spring-mass system is attached to the beam. The method is potentially useful in the dynamic wheel-track interaction analysis because the train wheel is normally simplified as a spring-mass system with high spring stiffness. It may also be applied to natural frequency-based damage detection where an auxiliary spring-mass system is used. When the spring-mass system roves on the beam, the curve of natural frequency versus spring-mass system location would be relevant to the mode shape square which is sensitive to local damage.

Short-term damping estimation for time-varying vibrating structures in nonstationary operating conditions

Various structures exhibit time-varying modal properties driven by short-term variability of environmental and operational conditions, which can cause considerable short-term variations in the modal characteristics, and modal damping, in particular. This study focuses on short-term damping estimation based on operational response measurements, for which a Gaussian process time-dependent auto-regressive moving average time series model is proposed. The model coefficients are represented by basis functions which express dependence on influencing environmental and operational variables, to account for various phenomena driving the time-varying nature of the modal characteristics. The method is verified by estimating short-term damping from the response of a simulated two-mode model. The applicability of the method for more complex cases is demonstrated by estimating the short-term damping of a multi-megawatt wind turbine in operation (and during an extreme wind gust) by means of its simulated edgewise blade response. The results demonstrate that the proposed method offers an enabling approach towards short-term damping and natural frequency estimation based on response measurements.

Estimation of ship roll damping and natural frequency using an extended Kalman filter applied to URANS output

Estimation of ship roll damping and natural frequency using an extended Kalman filter applied to URANS output

A Low-Cost Wireless Multinode Vibration Monitoring System for Civil Structures

Structural health monitoring (SHM) has gained importance because many structures are approaching the end of their design life and demanding maintenance and monitoring. Low-cost solutions may push forward a widespread implementation of SHM on infrastructures but further investigation is still required to assess the performance of technically accessible, simple, and scalable low-cost systems. This work presents the development and validation of a low-cost vibration-based SHM multinode wireless system, based on the Arduino platform, for identification of modal parameters in civil infrastructures. Full details about the hardware and source code of the system are disclosed in an open repository, allowing its reproduction even by non-specialists in electronics. The sampling frequency stability of the system is experimentally characterized, and interpolation postprocessing algorithms are proposed to solve inherent limitations. The system is validated, and its performance is investigated in impulse and ambient vibration tests performed in a real-scale slab and a high-grade system. The data obtained from the proposed system in impulse tests allowed estimation of natural frequencies within 2%, and MAC values around 0.3 to 0.9, in relation to those estimated with the high-grade system. However, the low-cost system was unable to produce usable data in ambient vibration tests.

Nonlinear thermo-electro-mechanical free vibrations of sandwich nanocomposite beams bonded with sensor layers considering pyroelectricity

An examination on the linear as well as nonlinear thermo-electro-mechanical free vibrations of a sandwich piezoelectric beam is performed in this research. Core layer has been strengthened with graphene platelets. Two piezoelectric layers as sensors are bonded to the bottom and top surfaces of the core layer. The formulation is developed for beams with general immovable end supports. A nonlinear integro-partial differential equation along with its nonlinear boundary conditions is discharged presuming a second order approximation for the nonlinear normal strain. The direct technique of multiple scales treats the nonlinear governing integro-partial differential equation along with its associated nonlinear boundary conditions. Subsequently, an analytical closed form relation is released for the estimation of amplitude dependent nonlinear natural frequencies. It is shown that the strengthening of a beam that is experiencing a thermal environment during its work with the graphene platelets becomes dysfunctional since it promotes the chance of static instability occurrence. On the other hand, it is seen that the pyroelectricity can postpone the static instability possibility. Furthermore, the pyroelectricity alleviates the hardening nonlinearity. Moreover, at large amplitude of vibrations, the influences of the temperature developing, the pyroelectricity, and the graphene platelet weight fraction decline.

Estimation of Natural Frequencies of Pipe–Fluid–Mass System by Using Causal Discovery Algorithm

Estimation of Natural Frequencies of Pipe–Fluid–Mass System by Using Causal Discovery Algorithm

Investigation of long-term modal properties of a supertall building under environmental and operational variations

The information on long-term modal properties of civil structures under environmental and operational variations is generally required in structural health monitoring and vibration control. In operational modal analysis (OMA), damping estimates usually present larger fluctuations and uncertainties than natural frequency and mode shape estimates, which affects the precise determination of the long-term damping characteristics of civil structures. To this end, a combined OMA scheme is adopted in this paper based on the variational mode extraction technique and covariance-driven stochastic subspace identification algorithm to reduce errors in modal identification, especially for damping estimates. Through numerical simulation study of a three-story frame structure, the effectiveness and accuracy of the combined scheme for modal estimations are validated. Moreover, the combined approach is further utilized to evaluate the long-term modal properties of a 600 m high skyscraper under environmental and operational variations from the measured response records of 183 days. Based on the reliable modal estimates by the combined method, the effects of environmental factors (air temperature and relative humidity), wind conditions, and building response amplitudes on the long-term modal properties and their statistical characteristics are investigated in detail. This paper aims to provide an effective tool for analyzing the long-term modal properties of civil structures and further reveal the time evolution of the dynamical characteristics of supertall buildings under environmental and operation variations. • Present a combined scheme based on variational mode extraction technique and covariance-driven stochastic subspace identification algorithm to reduce errors in structural modal estimates. • Suggest an empirical formula for determining minimum length of responses required for accurate modal estimates. • Validate effectiveness and accuracy of the combined scheme via numerical simulation study. • Investigate long-term evolution of dynamical characteristics of a 600 m high skyscraper under environmental and operational variations.

Modeling Flexible Multi-Body Systems Within the Udwadia–Kalaba Framework, a Lumped Parameter Approach

Abstract It is common practice within multi-body dynamic (MBD) modeling to assume that individual bodies are rigid however this can be an oversimplification especially when slender bodies are present resulting in inaccurate estimations of the system's natural frequencies and overall behavior. To address this shortfall, we extend the Udwadia–Kalaba (U–K) MBD formulation in this paper to model flexible multibody systems for purposes of exploring system natural frequencies. To model the flexibility, a lumped parameter approach is proposed, which in this work idealizes a flexible beam as a series of discrete rigid elements connected by torsional springs. In the U–K formulation, a mechanical system can also be discretized into rigid elements and adapted. This is viewed as a benefit for incorporating a lumped parameter approach within the U–K formulation to model flexible multibody systems. A flexible crank-slider mechanism is introduced and modeled within the Udwadia–Kalaba formulation to capture the dynamics of flexibility through linkage compliance. The model is validated against an alternatively formulated MBD model and system natural frequencies and mode shapes numerically predicted. Results of the study show the effectiveness and potential of extending the application of the Udwadia–Kalaba formulation by using a lumped parameter approach to dynamically model flexible multibody systems.

Estimation of Natural Frequencies of Cantilever Beam with Open Inclined Edge Crack

This paper presents an estimation of natural frequencies for free vibration of a cantilever beam in the presence of an inclined edge crack using linear elastic fracture mechanics. The Strain Energy Release Rate (SERR) approach is employed to compute the compliance coefficients for the edge crack inclined to the longitudinal axis at an arbitrary angle. A full compliance matrix under the general loading is presented and corresponding definitions of the compliance coefficients are given. Calculations of natural frequencies are carried out for both Timoshenko and Euler-Bernoulli beams under the influence of load P1, P3, and P5. Contribution to strain energy coming from various modes of fracture is accounted for by using stress intensity factors obtained numerically using ABAQUS 6.14 software. The effect of the crack on transverse and longitudinal natural frequencies is studied for different crack locations, depths, and inclination angles. Experiments are performed on short and long beams for a set of parameters for comparison purposes. It is found that the natural frequencies estimated by the proposed method compare well with the frequencies obtained experimentally for both beams.

Vision-based modal analysis of built environment structures with multiple drones

Unmanned Aerial Vehicles are employed for vision-based modal analysis of civil infrastructure, as they overcome range limitations of fixed cameras and measure the oscillations of a structure up close. Nevertheless, their potential is not fully exploited: they are often piloted manually and one at a time, though one drone is unable to capture high resolution displacement of a whole structure. An approach is explored here, employing multiple drones simultaneously to estimate natural frequencies and modal shapes of a structure, by synchronizing their measurement. The ability of the method to detect modal parameter variations is assessed, such that it can identify anomalies in the structure. Procedures are applied to a test structure, yielding maximum natural frequency estimation errors of 0.2% with respect to accelerometers. The results suggest the accuracy of the approach is high enough to warrant further development and support autonomous, multi-drone applications to the inspection of the built environment.

Variable Natural Frequency Damper for Minimizing Response of Offshore Wind Turbine: Principle Verification through Analysis of Controllable Natural Frequencies

Resonance causes extreme stress, acceleration of fatigue, and reduction in lifespan of offshore wind structures. The main factors that cause resonance are environmental loads such as wind and waves, and dynamic loads caused by rotor movement. Estimation of the natural frequency at the design stage is highly uncertain, and natural frequency changes occur due to various factors during long-term operation. Therefore, it is important to ensure structural safety from resonance through a vibration-monitoring system or an additional damper. In this study, the effect of seawater existing inside the substructure on the natural frequency of the structure was dealt with. The natural frequency estimation equation for a fixed offshore wind structure was derived with the “inner fluid simplification assumption”. The finite element modal analysis was performed to verify the principle of Variable Natural Frequency Damper (VNFD), a system that controls the natural frequency of offshore wind structures through a pump, and to find the range of natural frequency control. As a result, interior fluid affects the natural frequency of the wind turbine support structure. Specifically, the variable natural frequency range was very low, at about 0.027% for the monopile model at a depth of 10 m, but increased rapidly to about 3.66% at a depth of 70 m. Furthermore, when estimating the natural frequency of a fixed offshore wind turbine in deep water without consideration of interior fluid, the estimates can be higher than with consideration of it.

Investigation of time-varying natural frequencies of high-rise buildings under harsh excitations using a high-resolution combined scheme

High-rise buildings subjected to harsh excitations like typhoons or earthquakes usually present nonlinear features and exhibit time-varying behavior of structural modal properties. Under such circumstances, variation in structural natural frequencies can serve as a critical indicator for structural condition assessment. However, limited by noises contained in measurement records and time-frequency resolution of signal analysis, most instantaneous frequency identification methods are difficult to provide accurate estimation of time-varying natural frequencies of high-rise buildings. To address this issue, a combined scheme based on the variational mode decomposition method and adaptive superlets transform (VMD-ASLT) for time-varying natural frequency identification is presented in this paper. Through numerical simulation studies and field measurements of dynamic responses of a 508 m high skyscraper, the noise robustness and accuracy of the combined scheme for time-varying structural natural frequency estimation are validated. Moreover, the combined scheme is further utilized to investigate the time-varying features of natural frequencies of the skyscraper under typhoon and earthquake excitations. This paper aims to provide an effective tool for time-varying structural natural frequency estimation and further reveal the variation of the dynamical behavior of high-rise buildings under harsh excitations.