Beam-type Structures Research Articles

Multiscale Damage Identification Method of Beam-Type Structures Based on Node Curvature

This paper proposes a multiscale damage identification method for beam-type structures based on node curvature. Firstly, based on the assumption that micro-damage has little effect on stress redistribution and the basic relationship between structural bending moment and curvature, combined with the denoising function of wavelet analysis, the linear matrix equation before and after node curvature damage is solved using the singular value decomposition (SVD) method. Then, the theoretical feasibility of this method is verified with laboratory tests of a simply supported beam. Finally, the damage sensitivity and noise resistance of this method are verified using field measurements of a beam bridge. The results show that the nodal curvature serves as an indicator parameter for damage identification in beam-type structures, enabling the precise localization of damage within these structures. When utilizing a multiscale finite element model for analysis, the nodal curvature enhances the ability to identify both the location and severity of damage within small-scale elements. Furthermore, this method can provide a reference for the damage identification and health monitoring of other types of bridges.

A simplified analytical solution of pipeline response under normal faulting

Buried pipelines are one of the critical lifeline structures, and the evaluation of pipeline performance under seismic faulting is essential for protection of pipeline networks. This paper explores an analytical solution incorporating implementation of Winkler models around a beam-type structure using the finite difference method to evaluate the pipeline response under normal faulting. The effectiveness of the analytical solution is assessed by comparing the calculated pipe strains with centrifuge and full-scale laboratory testing measurements. Subsequently, the effect of pipe size, faulting condition, and burial condition on pipe response are investigated. It can be found that a pipeline with a smaller pipe wall thickness or larger pipe diameter is generally more prone to failure. Larger pipe wall thickness or lower D/t ratio should be used for pipe design crossing an active fault. In geotechnically problematic areas, shallow burial depth and less stiff soil with lower modulus are recommended to reduce the probability of exceedance of allowable limit states due to normal faulting. In the end, empirical functions relating to critical D/t ratio are proposed to evaluate the critical states of fault displacement, burial depth, and spread of fault rupture with different diameter-to-thickness ratio considering the controlled limit of failure modes.

Control of edgewise vibration of a pre-twisted rotating beam with shunted piezoelectric tuned mass damper

The edgewise vibration control of a pre-twisted beam, rotating in the vertical plane, is considered in this study. A piezoelectric tuned mass damper (PTMD) comprising a spring–mass–damper system and a piezoelectric transducer with its associated shunt circuit is considered the control device. A finite element formulation of the pre-twisted rotating beam with the attached PTMD is developed while considering the effect of centrifugal stiffening due to rotation and the effect of gravity force. The natural frequencies of the beam (without PTMD) obtained using the present formulation are corroborated by comparing them with the results derived from Ansys. A single PTMD attached at the tip end of the beam can effectively suppress the response of the beam subjected to a distributed load in the edgewise direction. The best values of resistance and inductance of the shunt circuit are obtained through a parametric study on the peak and root mean square value of the beam tip response. A qualitative difference in the uncontrolled as well as in the controlled responses can be noticed while considering the effect of the gravity load component in the edgewise direction. Further, it has been observed that the conventional Tuned Mass Damper (TMD) provides better control than the PTMD system for ideally tuned conditions, however, the control performance of TMD degrades rapidly as compared to the PTMD in the presence of detuning. This demonstrates the effectiveness of PTMD in a practical implementation where achieving the perfectly tuned condition is seldom realized. The control performance of PTMD marginally degrades when the beam is subjected to multi-directional excitation. Hence, the proposed control system has the potential for application in rotating beam-type structures, such as wind turbine blades.

A Novel Semi-Active Control Approach for Flexible Structures: Vibration Control through Boundary Conditioning Using Magnetorheological Elastomers

This research study explores an alternative method of vibration control of flexible beam type structures via boundary conditioning using magnetorheological elastomer at the support location. The Rayleigh–Ritz method has been used to formulate dynamic equations of motions of the beam with MRE support and to extract its natural frequencies and mode shapes. The MRE-based adaptive continuous beam is then converted into an equivalent single-degree-of-freedom system for the purpose of control implementation, assuming that the system’s response is dominated by its fundamental mode. Two different types of control strategies are formulated including proportional–integral–derivative control and on–off control. The performance of controllers is evaluated for three different loading conditions including shock, harmonic, and random vibration excitations.

Homogenization of 3D laminated micro-structures including bending effects

In this paper, a homogenization method which captures intrinsic size effect associated with fiber diameter is revisited and adapted for three-dimensional laminated micro-structures. Based on a unit-cell composed of matrix and reinforcement layers, enhanced deformation gradients varying through the thickness, are introduced with the aid of an additional kinematic variable reflecting the difference between the homogenized and constituent level deformation gradients. In the current work, as opposed to the original formulation, higher order terms are preserved for both phases and therefore bending stiffness of the matrix phase can be taken into account as well. The formulation is implemented within the commercial finite element solver Abaqus through user element (UEL) subroutine considering a finite strain hyperelastic response for the reinforcement layers and a von Mises type hyper-elastoplastic one for the matrix phase. Explicitly discretized unit-cells with varying reinforcement phase fraction, layer inclination angle and layer thicknesses are used as references to assess the predictive capabilities of the homogenized model and the significance of bending stiffness of the phases. Similarly, explicitly discretized model of a beam type structure with a crossed lamellar micro-structure is used to evaluate the performance of the homogenized model under more general, non-periodic boundary conditions. The findings of both cases support the effectiveness of the homogenized model.

Quasi-static testing based structural modal parameter estimation

ABSTRACT Structural modal identification is generally implemented within a dynamic framework, requiring multidisciplinary knowledge and adequate operational experience. This preliminary study attempts to explore an easy-to-handle quasi-static alternative method for dynamics-based modal identification of beam-type structures. Acceleration time-history data are replaced by quasi-static deflections induced by slow moving loads. A concept of quasi-static deflection influence surface is proposed based on the theory of influence lines and the principle of virtual work. Its analytical expression is simplified into a deflection matrix by choosing specific points on the surface according to deflection measurement coordinates. The matrix form is divided by external loads to obtain a generalised quasi-static flexibility matrix, which is used to replace the inversion of the global stiffness matrix in the modal eigenvalue equation. The lumped-mass method is also employed to establish the mass matrix. Subsequently, the eigenvalue equation is analytically solved seeking for modal frequencies and mode shapeswithout performing modal tests. The feasibility of the proposed method has been successfully verified against three experimental examples including a continuous box girder with variable cross sections. It was observed that the modal frequencies and mode shapes estimated by the proposed method were very close to those given by the dynamically modal tests.

Damage quantification in beam-type structures using modal curvature ratio

Damage quantification in beam-type structures using modal curvature ratio

Vibration-based structural damage detection strategy using FRFs and machine learning classifiers

In this paper, a damage detection strategy for beam-type structures based on frequency response functions (FRFs) is presented. Five aluminum beams of equal nominal dimensions are used in an experimental program under laboratory conditions to obtain experimental FRF data from both undamaged and damaged conditions. Damages are induced by creating rectangular notches on the beams using saw-cutting. A stochastic finite element model of the beam is developed in MATLAB to construct several training datasets. The damages are modeled by reducing the cross-sectional area at the corresponding damaged elements. Simple damage indexes are proposed as damage-sensitive features. Decision Tree, Support Vector Machines, and Artificial Neural Networks classifiers are trained in the first stage to perform damage detection and localization. Single and multiple damages located in a single zone and more than one zone simultaneously are considered. In the second stage, experimental data not used for training are used for validation. The results from the first stage suggest that the proposed damage indexes can effectively detect and locate structural damage in beams. Among all classifiers, Artificial Neural Networks is the classifier that best performed. High accuracy is achieved to identify the presence of damage (99.3%) and detecting its location on the beam for some of the training datasets (from 80.0% to 97.1%). In the second stage of validation, accuracy, as expected, decreased. However, misclassifications occur mainly for FRF samples in the impact zone, which indicates that the proposed strategy can be efficient to detect damages at locations other than the excitation zone.

Thermally and mechanically induced strain gradient fields in architected 2D materials and beam structures

The current contribution investigates the strain-gradient thermomechanical performance of architected materials and structures with uniform and graded inner designs. To that scope, an integral representation of strain-gradients in thermoelasticity, along with its Galerkin Boundary Element Method (GBEM) implementation are elaborated. The formulation accounts for both mechanical and thermal strain-gradients for the first time. Thereupon, the complete strain-gradient response upon uniaxial tensile (UT) and thermal loading (Th) is analyzed, performing direct comparisons among the strain-gradient fields induced in each case and providing summarizing statistics that associate higher-order thermal and mechanical effects. The numerical framework is used as a basis for the quantification of the impact of the underlying structural patterns on the equivalent internal length parameters of architected beam-type structures under thermomechanical loads in the context of simple gradient theory. It is found that thermal loads relate to comparable, yet lower, internal length parameters with respect to the ones obtained for uniaxially tensioned structures with uniform inner cellular designs. Both internal length and temperature variation contributions determine the strain-gradient thermomechanical response of beam-type architected structures, for which, exact, higher-order equivalent 1D displacement field solutions are first derived. Thermally-induced, higher-gradient displacements are found to be comparable with the ones obtained in UT-loaded structures with uniform inner cellular topologies. Moreover, inner material gradings are found to be able to considerably mitigate higher-order effects, a sensitivity that is not reproduced in the UT loading case. The results provided, along with the numerical and analytical methodologies elaborated, set the basis for the thermomechanical strain-gradient analysis of advanced architected media well-beyond the designs here investigated.

A novel surrogate-based crack identification method for cantilever beam based on the change of natural frequencies

A novel crack identification method is presented in this paper for cantilever beam-type structures within the scope of vibration-based damage identification. Natural frequencies are more easily to be measured yet are weakly sensitive to damage in comparison to other dynamic parameters such as mode shape and damping ratio. Therefore, this paper develops a surrogate-based crack identification method in order to overcome the low sensitivity of frequency to damage. The surrogate model was constructed using radial point interpolation method (RPIM) and subsequently trained with the frequency shift database established from parametric finite element analysis (FEA) modeling of cracked/ non-cracked cantilever beams. On this basis, the crack identification problem had been converted to a standard optimization model with crack length and location as design variables. Subsequently, genetic algorithm (GA) was employed for solving the optimization model to achieve crack parameters. In the end, numerical examples and experimental test have been conducted to validate the developed method, revealing maximum relative errors within 0.5% and 2.5%, respectively.

Crack localisation in composite cantilever beams using natural frequency measurements

ABSTRACT Crack localisation is a fundamental step of damage identification. Most of the published research on crack localisation based on natural frequency consists in model updating which requires a great deal of calculation. This paper presents a simple method of crack localisation in composite cantilever beam-type structures. The proposed method consists of classifying the reduction of the first four measured natural frequencies and deducing the damage position from a table. For these purposes, a finite element model is first used to study the direct problem: the vibration behaviour of an intact beam and the changes caused in the damaged state. Then it is shown that the classification of the frequency reduction ratio is different for each damaged zone. Consequently, the beam is discretized into several areas according to the classifications of the first four frequency ratios. Therefore, this discretization is represented in a table to be used in damage localisation. The robustness of the suggested technique is first tested numerically by using the Abaqus/CAE finite element software environment. Then, the applicability of the localisation method is validated experimentally on a cracked glass fibre-reinforced epoxy beam. The results show that the proposed method can successfully localise damage in composite beams.

A wavelet based data coupling method for spatial damage detection in beam-type structures.

Spatial damage identification is of great significance in mechanical, aerospace, and civil engineering. In this study, a data coupling method based on continuous wavelet transform (CWT) is proposed to identify the spatial damage location of beam-type structures. The singularity of the wavelet coefficient can be used to identify the signal singularity, and data coupling method calculates the spatial location of the damage. Numerical simulations and experimental analyses of different type of beams with transfixion damage are carried out to evaluate the accuracy of the method. The results show that the wavelet based data coupling method (W-DCM) can identify the minimum 4.9% damage severity of fixed beam and continuous beam, and can also identify the damage of non-free end of cantilever beam. However, the 9.7% damage severity of the free end of the cantilever beam cannot be identified. It is also found that the W-DCM can effectively circumvent the problem of wavelet coefficients edge effect. This method and wavelet singularity are used to provide a solution to the problem of structural edge damage identification.

Vibration control of a pre-twisted rotating beam with nonlinear bi-stable attachments

The influence of the nonlinear bi-stable attachment on the vibration suppression of a pre-twisted rotating cantilever beam is investigated in this study. The kinetic and potential energies of the system, comprising a pre-twisted rotating Euler–Bernoulli beam and the nonlinear bi-stable attachments, are obtained, and the equations of motion are derived using the Rayleigh–Ritz method. The natural frequencies and mode shapes of the beam (without the attachments) obtained using the present formulation are validated with the results obtained from Ansys. Subsequently, the flapwise vibration control of the pre-twisted rotating beam subjected to a base excitation is studied. A parametric study is performed for various amplitudes of base excitation, rotational speeds, and the number and position of the bi-stable attachments. Results show significant vibration suppression capabilities of the nonlinear attachments, and hence the proposed system could potentially be used for rotating beam-type structures such as wind turbine blades.

Continuous bridge displacement estimation using millimeter-wave radar, strain gauge and accelerometer

Monitoring of bridge displacement is essential for providing critical information regarding the health of bridge structures. However, continuous and accurate monitoring of structural displacement remains challenging. This study proposes a bridge displacement estimation technique that combines an accelerometer, a strain gauge, and a millimeter-wave radar considering intermittent radar target occlusion common in long-term displacement monitoring. The technique primarily estimates displacement using radar and accelerometer measurements but switches to using strain and acceleration measurements when radar targets are occluded. A radar target occlusion detection algorithm is developed to automatically achieve this switching. Automated initial calibration is performed to select suitable targets from all radar-detected targets and estimate the conversion factor for converting radar-based displacement from the line-of-sight direction to the actual movement direction. An artificial neural network model is automatically trained for strain–displacement transformation without the need for any pre-knowledge of a target structure. The proposed technique was validated via a laboratory test on a 10-m-long beam-type structure and a field test on a pedestrian steel box-girder bridge. The proposed technique correctly detected the intermittent radar target occlusion, and continuously estimated displacements for up to 75 min. The intermittent radar target occlusion leads to errors of a few millimeters in the displacements estimated using radar and accelerometers. However, the proposed method accurately estimates displacements with errors of less than 0.1 mm.

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.

Perturbation approach for damage localization in beam-type structures: analytical, experimental and numerical exposition

ABSTRACT Structures are usually designed to undergo some yielding, cracking and damage during any catastrophic events like earthquakes. It is necessary to identify these damage locations to avoid the failure of the structure. In this study, a novel method of damage localization for a linear one-dimensional mathematical model of Euler-Bernoulli beam is developed. The damage is modeled as a normalized box-car function. The first-order perturbation in the form of a small change in the stiffness is introduced to the structure. This study employed an effective boxcar filtration technique in damage localization. The proposed formulation shows a distinct peak at the damage location. Further, a two-point roving technique is employed on the experimental model of an overhanging beam under impact loading to check the effectiveness of the proposed localization procedure under real measurement conditions. For its entirety, the finite element model for different end conditions through numerical simulations is also briefly addressed. It is observed that the results obtained from the experimental investigation and the simulation studies are in agreement with the proposed formulation. The proposed methodology does not consider the effect of noise, which can be addressed as the future scope of the present study.

Shape control of moderately thick piezoelectric beams

The present contribution focuses on shape control of thick beam-type structures. First the governing equations of a multi-layered beam are derived by taking advantage of the Timoshenko assumptions and the constitutive relations of piezoelectric materials. The deflection curves are explicitly given for a piezoelectric cantilever subjected to a polynomial distribution of the vertical load and the applied electric voltage. In order to find a solution for the optimal shape control voltage an objective function, which depends on the quadratic deflection curve over the beam length, is minimized. Finally several benchmark examples are given for thick beams and the outcome is compared to finite element results and previously derived shape control results from the scientific literature that hold for thin piezoelectric beams. The presented shape control method shows a better agreement with the numerical outcome than the analytical shape control results within the Bernoulli-Euler theory, but the desired voltage distribution only slightly differs from the outcome for thin beams. Furthermore it is found that for a given total thickness-to-length ratio piezoelectric bimorph structures may be more difficult to be perfectly controlled than three-layer beams with thin piezoelectric layers. This is due to higher order piezoelectric effects which are not considered by the present theory (e.g. the thickness deformation caused by the thickness piezoelectric coupling constant).

Metaheuristic-based crack detection in beam-type structures using peridynamics theory: A comparative study

This study is a first attempt to provide an effective tool for crack prediction in beam-type structures using the peridynamics (PD) theory and metaheuristic-based optimization. The norm of the difference between the response of the tested beam and that of the trial model (analyzed using PD), is minimized to find the position and depth of crack. Model calibration is discussed thoroughly. Five well-known metaheuristics as well as an upgraded charged system search algorithm are considered. Results reveal that the proposed procedure can effectively localize and detect the crack severity, even in noise contaminated cases.

Large displacement analysis of laminated beam-type structures

The paper presents a finite element formulation for analysis of 3D framed structures with thin-walled laminated composite cross-sections, using a co-rotational approach. The formulation considers the effects of large displacements on the response of space frames subjected to conservative and static external loads. Classical lamination theory for thin fiber-reinforced laminates has been employed. Stability analysis is performed in load deflection manner using co-rotational formulation. The shear strain of the middle surface is assumed to be zero, and the cross-section is not distorted in its own plane. In order to illustrate the application of the proposed formulation, several numerical examples are presented.

Predictive analysis toward the identification of cracks in functional gradient beam structures using an optimization algorithm based on the transit search technique

Machine learning techniques can be used for the prediction of cracks in beam type structures. Indeed, these techniques present an important management aspect which consists in developing a maintenance decision model, which can anticipate future failure trends in order to improve the maintenance decision process. The prediction of open cracks on the edges of beams is a problem often encountered in industry and can be detected by considering that the crack is simulated by means of a rotating spring, whose stiffness can be identified by the size of the crack. This article proposes two different techniques for crack detection in Euler-Bernoulli model functional gradient beams. The first technique generates frequency contours from a three-dimensional plot of the crack position and size, and the intersection of distinct mode contours predicts the crack location and size. The second technique uses a meta-heuristic optimization, which is inspired by astrophysics and based on well-known exoplanet discovery methods, to determine crack size and position concurrently. The weighted sum of the squared errors between the measured and computed natural frequencies is utilized to design the objective function in this second strategy. The results reveal that the two crack size and location prediction techniques agree quite well.