Steel Cantilever Beam Research Articles

Large deformation theory of thin steel cantilever beams under free end load cases

Large deformation theory of thin steel cantilever beams under free end load cases

Epsilon-Greedy Thompson Sampling to Bayesian Optimization

Abstract Bayesian optimization (BO) has become a powerful tool for solving simulation-based engineering optimization problems thanks to its ability to integrate physical and mathematical understandings, consider uncertainty, and address the exploitation–exploration dilemma. Thompson sampling (TS) is a preferred solution for BO to handle the exploitation–exploration trade-off. While it prioritizes exploration by generating and minimizing random sample paths from probabilistic models—a fundamental ingredient of BO—TS weakly manages exploitation by gathering information about the true objective function after it obtains new observations. In this work, we improve the exploitation of TS by incorporating the e-greedy policy, a well-established selection strategy in reinforcement learning. We first delineate two extremes of TS, namely the generic TS and the sample-average TS. The former promotes exploration, while the latter favors exploitation. We then adopt the e-greedy policy to randomly switch between these two extremes. Small and large values of e govern exploitation and exploration, respectively. By minimizing two benchmark functions and solving an inverse problem of a steel cantilever beam, we empirically show that e-greedy TS equipped with an appropriate e is more robust than its two extremes, matching or outperforming the better of the generic TS and the sample-average TS.

Vibration-based damage detection of beams using Hybrid Genetic Algorithm with combined l0 and l1 regularization

Vibration-based damage detection is an effective way of identifying beam damages before they become severe and potentially catastrophic. This paper introduces a novel and robust method for detecting multiple cracks in beams using a Hybrid Genetic Algorithm (HGA). The objective function of the proposed method, based on dynamic properties, can be employed with partial modal information and is enhanced by including the initial residuals between numerical and experimental models along with combined l0 and l1 regularization. This enhancement mitigates the impact of limited modal data, experimental noise, and modeling inaccuracies. Additionally, a method of selecting an appropriate regularization parameter by analyzing residual and solution norm curves is presented. The performance of the proposed method is evaluated and verified using both numerical simulations and experimental studies on a steel cantilever beam under four damage scenarios. In the experimental study, natural frequencies and mode shapes were determined under ambient vibration conditions using Enhanced Frequency Domain Decomposition (EFDD) and the Stochastic Subspace Identification (SSI) method. Finite element models of the beam were developed in ABAQUS software for numerical analysis, and a comparative study of numerical and experimental data was conducted. The proposed approach successfully identifies, locates and quantifies single and multiple damages in the beam, demonstrating its reliability and effectiveness, particularly in scenarios with limited modal data and significant experimental noise.

A Hybrid Testing Framework for Wind Turbine Mechanical Components

As wind turbines continue to increase in size, hybrid testing is emerging as a key-enabling solution for experimental assessment of their large mechanical components. Hybrid testing is conducted using a hybrid model which combines physically tested and numerically simulated components. In this work, the Kane method is proposed to formulate the equation of motion for the hybrid model of a wind turbine rotor system where one single blade is physically tested. The Kane method allows for formulating the equation of motion of multi-body-dynamic models efficiently and, therefore, it is widely used in state-of-art simulation software. The hybrid model of the rotor is successfully implemented on a single-degree-of-freedom test bench with a cantilever steel beam serving as the physical substructure. The performance of the implemented hybrid model is assessed through a comparison with a pure numerical simulation of the same system. The main finding of the study emphasizes the efficiency of incorporating physically measured restoring force as model parameters while formulating the equation of motion of a hybrid model.

SVM-assisted damage identification in cantilever steel beam using vibration-based method

SVM-assisted damage identification in cantilever steel beam using vibration-based method

Effect of the Cross-Sectional Shape on the Dynamic Response of a Cantilever Steel Beam Using Three Modal Analysis Methods

Effect of the Cross-Sectional Shape on the Dynamic Response of a Cantilever Steel Beam Using Three Modal Analysis Methods

Numerical Study for Damage Identification in Beams Using Continuous Wavelet Transformation and Convolution Neural Network

The discovery and identification of damages in engineering structures is very important in the field of engineering maintenance, as it is a great challenge in presenting new methods in measuring vibrations and discovering damages with the development in the field of automation and high accuracy in discovering damages. In this study, natural frequencies and mode shapes of transverse vibration for damage detection in structures are investigated. The study is performed for various crack depth and crack location. And suggested a new technique based on Continuous Wavelet Transform (CWT) and Convolution Neural Network (CNN). The comparison will be done by simulating the oscillations of a cantilever steel beam with and without defect as a numerical case. The proposed new technique proved to outperform classical methods and has achieved a100% accuracy in the identification of defect position for the data studied.

Formulation of a similarity law for static and low-velocity collision experiments for beam in gravitational field

Scaled testing offers a financially viable and pragmatic methodology for ascertaining the performance attributes of full-scale civil engineering structures. While the necessity for a similarity law to guide scaled experiments is well-understood, few studies has been directed toward formulating a similarity law that comprehensively addresses both geometrical and mechanical equivalences in experiments where material properties and gravitational factors remain constant between the scaled and full-scale tests. Our prior work has introduced a similarity law tailored for scaled experiments conducted within gravitational fields, utilising materials that bear a resemblance to those used in full-scale structures; however, the scope of applicability was restricted to elastic responses. This study introduces a method for approximating the elasto-plastic displacement in full-scale beams based on data gathered from scaled tests, utilising an integrated approach that combines the principles of similarity and equal-energy laws as formulated by Veletsos et al. Validation of this innovative method was achieved through static three-point bending tests using circular cross-sectional steel beams, with tests conducted at six varying similarity ratios, ranging from 0.26 to 1.00. The empirical results demonstrated that the estimated displacement for the full-scale structure exhibited an error margin of approximately 10 %. When an impact analysis involving a steel ball was carried out on a steel cantilever beam, the residual displacement estimates were found to be significantly imprecise when plastic deformations occurred at multiple locations within the structure. In conclusion, this research contributes to foundational advancements in the field of structural modelling through the introduction of a new methodological approach.

Nonlinear instantaneous characteristics and asymmetry of the bilinear system with application to the structural damage estimation

Common structural damage usually exhibits bilinear behavior in the vibration. To identify such damage, the nonlinearity and asymmetry shown in the free vibration of the bilinear system are studied. The instantaneous characteristics of the free vibration are analyzed by employing the well-known HT method. The modulated instantaneous parameters and softening stiffness are used as damage indicators. Three new indices are proposed for ‘bilinear-type’ damage detection. For further damage severity estimation, two bilinear-stiffness estimation methods are developed based on the asymmetric restoring force and the asymmetric phase trace, respectively. Numerical study shows that the methods can accurately estimate the bilinear stiffness of the cracked beam with strong noise robustness and low sensitivity to initial weak nonlinearity. Experimental study was carried out on a steel cantilever beam with loose-connection. The damage can be effectively detected by the proposed indices and the stiffness coefficient ratios can be estimated by the two proposed methods.

A lightweight stochastic subspace identification-based modal parameters identification method of time-varying structural systems

The application of stochastic subspace identification (SSI) on identifying structural time-varying modal parameters suffers from the shortcomings of poor computational efficiency and susceptibility to spurious modes. This work overcomes the shortcomings by the following procedures based on existing covariance-driven SSI. First, the covariance-driven SSI is embedded with techniques of randomized singular value decomposition and subspace iteration for reducing computation cost and avoiding accuracy loss, forming the lightweight SSI (lwSSI). Then, the lwSSI is combined with the technique of sliding window for eliminating spurious modes and continuously identifying time-varying modal parameters. The proposed lwSSI-based identification method is applied on the simulation of a gravity dam, and the identified time-varying modal parameters show the same trend as the assumed time-varying elastic modules. Furthermore, the characteristics of the lwSSI-based identification method, including noise resistance, computational efficiency, and identification accuracy, are investigated. Finally, the identification of a steel cantilever beam with the time-varying modal parameters caused by the mass distribution experimentally validates the effectiveness of the proposed lwSSI-based identification method.

Detection of transverse cracks in steel beams using damage location coefficients and artificial neural networks

Structural health monitoring plays a crucial role in ensuring the integrity and safety of engineering structures such as steel beams. This research paper presents a comprehensive methodology for detecting transverse cracks in beams with a constant section and any boundary conditions. The proposed approach utilizes the normalized squared modal curvature of the beam, the damage severity, and the natural frequency of the undamaged beam. By analyzing the natural frequencies of both the undamaged and damaged states, Relative Frequency Shift (RFS) values are obtained. Subsequently, the Damage Location Coefficients (DLC) are calculated by normalizing the RFS values. These DLC values are then employed to establish a comprehensive database of known damage signatures, enabling the training of an artificial neural network (ANN) in MATLAB. The trained ANN can predict the locations of damages for new scenarios by utilizing DLC values obtained from measurements. To validate the effectiveness of the ANN, extensive simulations using Finite Element Method (FEM) and experimental measurements are conducted on a steel cantilever beam. The results demonstrate the ANN’s capability to accurately predict the locations of transverse cracks, showcasing its potential as a reliable tool for structural health monitoring of steel beams.

Dynamic parameters identification of 3D sandwich wall panels from phase-based video measurement via smartphones camera

This study, unlike prior studies, utilizes a smartphone camera as a high-speed camera for output-only operational modal analysis by using video measurement and advanced computer vision algorithms. Besides, the accelerometer sensors of the three smartphones collect the acceleration data. In contrast to recent research, this study has been conducted outdoors without any additional light setup and solid color background to contrast the motions. First, multi-scale image processing and blind source separation techniques are applied to each video frame to obtain the modal coordinates. The logarithm decrement technique and Fourier transform extract the damping ratios and frequencies of dominant modes of structures. To validate the smartphone camera measurements, two 3D sandwich walls were used and their results compare with accelerometer data. After that, the modal properties of a cantilever steel beam were identified by only smartphone camera measurements. The obtained modal parameters from smartphones camera and accelerometers are in excellent agreement, results indicated that. This study showed that smartphones camera has great potential to use as a non-contact modal analysis facility.

Dynamic analysis of a free vibrating cantilever beam

This paper has as subject a theoretical, numerical and experimental study of the behavior of a 1.5 meters long and cross section of 0.02 meters wide and high beam. The main objective was to analyze a structure, in this case it was a cantilever steel beam, to establish the possible solutions that best define the behavior of this structure, to obtain the results and to prove the veracity of the results obtained by means of an experimental analysis method. In this sense, essential theoretical foundations were used for the understanding and realization of the mathematical formulations of this project, in order to obtain the analytical results of the vibration modes of the beam and respective natural frequencies. To complement the analysis of the beam behavior, the finite element method procedure was applied using the ansys software to obtain more accurate results. The results obtained for the beam from these two methodologies include bending modes among the first 10 degrees of freedom. To validate the study done previously a physical model of the beam was used for the experimental test, for this it was defined that the equipment for measuring the resonance frequencies would be a digital stroboscope, enabling the measurement of only 8 vibration modes due to its small frequency range.

Lateral–Torsional Buckling of Cantilever Steel Beams under 2 Types of Complex Loads

Cantilever steel beams are an essential structural element in civil engineering fields such as bridges and buildings. However, there is very little research on the critical moment (Mcr) of cantilever beams subjected to a concentrated load (CL) or a combination of concentrated load and uniformly distributed load (CUDL) when the concentrated load is not limited to the free end. Therefore, the focus of the current paper is the calculation of Mcr for cantilever steel beams under CL and CUDL. This paper proposes a program and a simple closed-form solution for Mcr that are applicable to the elastic buckling analysis of cantilever I-beams under CL and CUDL. Based on the Rayleigh–Ritz method, a matrix equation and the corresponding procedure about Mcr under CL and CUDL are derived by using infinite trigonometric series for the buckling deformation functions. The value of Mcr and the corresponding mode of buckling can be obtained efficiently by considering the symmetry of the section, the ratio of two load values and the load action position. Experimental results and finite element calculations validate the numerical solutions of the procedure. A closed-form solution for Mcr is derived according to the assumption of a small torsion angle and the specific values of each coefficient in the closed-form solution of Mcr are calculated by the proposed procedure. The results show that the procedure and closed-form solution for Mcr presented in this paper have a high degree of accuracy in calculating the Mcr of the cantilever beam under CL and CUDL. The deviations between the results calculated by the proposed procedure and data from existing literature are less than 8%. These conclusions are capable of solving the calculation problem of Mcr for cantilever beams under CL or CUDL, which are both significant load cases in engineering. The study provides a reference for the design of cantilever steel beams.

Validation of an FE model updating procedure for damage assessment using a modular laboratory experiment with a reversible damage mechanism

In this work, the systematic validation of a deterministic finite element (FE) model updating procedure for damage assessment is presented using a self-developed modular laboratory experiment. A fundamental, systematic validation of damage assessment methods is rarely conducted and in many experimental investigations, only one type of defect is introduced at only one position. Often, the damage inserted is irreversible and inspections are only performed visually. Thus, the damage introduced and, with it, the results of the damage assessment method considered are often not entirely analyzed in terms of quantity and quality. To address this shortcoming, a modular steel cantilever beam is designed with nine reversible damage positions and the option to insert different damage scenarios in a controlled manner. The measurement data are made available in open-access form which enables a systematic experimental validation of damage assessment methods. To demonstrate such a systematic validation using the modular laboratory experiment, a deterministic FE model updating procedure previously introduced by the authors is applied and extended. The FE model updating approach uses different parameterized damage distribution functions to update the stiffness properties of the structure considered. The mathematical formulation allows for an updating procedure that is independent of the FE mesh resolution and free of assumptions about the defect location while only needing few design variables. In this work, the FE model updating procedure is based only on eigenfrequency deviations. The results show a precise localization within pm , {0.05}{textrm{m}} of the nine different damage positions and a correct relative quantification of the three different damage scenarios considered. With that, first, it is shown that the deterministic FE model updating procedure presented is suitable for precise damage assessment. Second, this work demonstrates that the opportunity to introduce several reversible damage positions and distinctly defined types and severities of damage into the laboratory experiment presented generally enables the systematic experimental validation of damage assessment methods.

Development and Validation of a LabVIEW Automated Software System for Displacement and Dynamic Modal Parameters Analysis Purposes

The structural health monitoring (SHM) technique is a highly competent operative process dedicated to improving the resilience of an infrastructure by evaluating its system state. SHM is performed to identify any modification in the dynamic properties of an infrastructure by evaluating the acceleration, natural frequencies, and damping ratios. Apart from the vibrational measurements, SHM is employed to assess the displacement. Consequently, sensors are mounted on the investigated framework aiming to collect frequent readings at regularly spaced time intervals during and after being induced. In this study, a LabVIEW program was developed for vibrational monitoring and system evaluation. In a case study reported herein, it calculates the natural frequencies as well as the damping and displacement parameters of a cantilever steel beam after being subjected to excitation at its free end. For that purpose, a Bridge Diagnostic Inc. (BDI) accelerometer and a displacement transducer were parallelly mounted on the free end of the beam. The developed program was capable of detecting the eigenfrequencies, the damping properties, and the displacements from the acceleration data. The evaluated parameters were estimated with the ARTeMIS modal analysis software for comparison purposes. The reported response confirmed that the proposed system strongly conducted the desired performance as it successfully identified the system state and modal parameters.

Performance assessment of steel cantilever beams based on connection behaviour using DIC technique and improved hybrid PSO algorithm

Cantilever beams can have various behaviour depending on the details of the connection. Partially-fixed connections have a different performance from conventionally-fixed connections, in which the exact information is not available. In this paper, using the finite element model updating (FEMU) of a steel cantilever beam, the support conditions of a partially-fixed connection and the behaviour of the beam are investigated. The FEMU is utilized as an appropriate technique for structural health monitoring, which requires the use of data acquisition methods from the structure. In this research, instead of using discrete sensors, displacement and strain information are continuously measured from the beam surface using the digital image correlation (DIC) method. The difference between the initial model and the data extracted from the DIC is determined by a cost function. A hybrid method called Powell particle swarm optimization is used to minimize the cost function. This method includes particle swarm optimization (PSO) as a global search technique and Powell optimization as a local search technique; the hybrid method achieves better performance by combining the two methods. A dynamic inertia weight is presented to improve the performance of the PSO algorithm. Abaqus software and Python programming have been used to carry out the FEMU process. Finally, the amount of rotation and displacement of support are calculated, and the dependency of beam behaviour on each of the variables is investigated. This method yields acceptable convergence of the results and can be extended to study other structural components.

Operating modal analysis from sub-sampled vibration response based on compressed sensing and FastICA

In order to identify more high order modal from a small amount of vibration response signal sampling, this paper proposes a method for identifying the OMA of sub-sampled vibration response signals based on compression sensing (CS) and fast independent component analysis (FastICA). Firstly, the method subsamples a large number of vibrational signals to retain the original key information of the signal; Secondly, the subsampled signal is restored by using the compressive sampling matching pursuit (CoSaMP) algorithm of the compression-aware reconstruction algorithm. Finally, the source signal is separated by FastICA to obtain the multi-order natural frequencies and modal mode shapes of the structure. According to Shannon’s theorem, if the analog signal is reproduced without distortion, the sampling frequency should be no less than 2 times the highest frequency in the analog signal spectrum. This method can reduce the amount of original signal acquisition and the requirements for the frequency of the sampled signal, and the recovery signal has a high similarity with the original signal and the natural frequency is not changed. It can effectively identify the higher-order modes of the structure on the basis of breaking through the Nyquist sampling frequency. Experimental results of the subsampled vibration response signal on the uniform steel cantilever beam show that the method can reconstruct the original signal from a small number of subsampled vibration response signals, and identify the high-order nature frequency and modal mode shape that break through the Nyquist sampling frequency.

Long Short-Term Memory Recurrent Neural Network Approach for Approximating Roots (Eigen Values) of Transcendental Equation of Cantilever Beam

In this study, the natural frequencies and roots (Eigenvalues) of the transcendental equation in a cantilever steel beam for transverse vibration with clamped free (CF) boundary conditions are estimated using a long short-term memory-recurrent neural network (LSTM-RNN) approach. The finite element method (FEM) package ANSYS is used for dynamic analysis and, with the aid of simulated results, the Euler–Bernoulli beam theory is adopted for the generation of sample datasets. Then, a deep neural network (DNN)-based LSTM-RNN technique is implemented to approximate the roots of the transcendental equation. Datasets are mainly based on the cantilever beam geometry characteristics used for training and testing the proposed LSTM-RNN network. Furthermore, an algorithm using MATLAB platform for numerical solutions is used to cross-validate the dataset results. The network performance is evaluated using the mean square error (MSE) and mean absolute error (MAE). Finally, the numerical and simulated results are compared using the LSTM-RNN methodology to demonstrate the network validity.

A probabilistic approach for quantitative evaluation of fatigue cracks using nonlinear vibration responses

Fatigue cracks can cause nonlinearities in the vibration responses of cracked structural components. Nevertheless, there is a noticeable barrier to quantitatively evaluating the fatigue cracks using vibration responses owing to the difficulty in extracting crack-induced weak dynamic nonlinearities and quantifying probabilities of crack statuses. To overcome this barrier, this study proposes a probabilistic approach for quantitatively evaluating fatigue cracks. Crack-induced nonlinearities in the vibration responses are extracted by the singular spectrum analysis (SSA) and embodied in status features (SFs). The dispersed distributions of the SF clusters in the status space can visually characterize different crack statuses. In particular, the mechanism of the SSA for extracting crack-induced dynamic nonlinearities is interpreted in this study. In addition, the 3D probability density functions of the SFs are formed, based on which a status probability index is established to quantify the relative probabilities of different known crack statuses. Hereby, the statuses of fatigue cracks can be quantified in a probabilistic manner. The approach is experimentally validated on a steel cantilever beam that bears a fatigue crack, attached to which an electromagnetic shaker is used to generate transverse harmonic excitations. The excitation amplitudes are increased to produce increasing open extents of the fatigue crack. Simultaneously, steady-state velocity responses are acquired from the free end of the beam through non-contact measurement using a Doppler laser vibrometer. The results reveal that the crack statuses corresponding to different open extents are visually characterized and their relative probabilities are quantified.