A comprehensive review on modal parameter-based damage identification methods for beam- or plate-type structures is presented, and the damage identification algorithms in terms of signal processing ...are particularly emphasized. Based on the vibration features, the damage identification methods are classified into four major categories: natural frequency-based methods, mode shape-based methods, curvature mode shape-based methods, and methods using both mode shapes and frequencies, and their merits and drawbacks are discussed. It is observed that most mode shape-based and curvature mode shape-based methods only focus on damage localization. In order to precisely locate the damage, the mode shape-based methods have to rely on optimization algorithms or signal processing techniques; while the curvature mode shape-based methods are in general a very effective type of damage localization algorithms. As an implementation, a comparative study of five extensively-used damage detection algorithms for beam-type structures is conducted to evaluate and demonstrate the validity and effectiveness of the signal processing algorithms. This brief review aims to help the readers in identifying starting points for research in vibration-based damage identification and structural health monitoring and guides researchers and practitioners in better implementing available damage identification algorithms and signal processing methods for beam- or plate-type structures.
•The operational dynamic strains of a steel bridge are monitored with FBGs for one year.•The modal characteristics of the bridge are systematically identified from the dynamic strains.•The mode ...selection process in automated with the use of hierarchical clustering.•The influence of temperature on modal strains and natural frequencies is investigated.•The influence of retrofitting on modal strains and natural frequencies is investigated.
Vibration monitoring from strain data is a promising alternative to the more conventional acceleration-based monitoring because a dense measurement grid can be achieved at a relatively low cost and because strain mode shapes are more sensitive to local stiffness changes than displacement mode shapes. However, the feasibility of monitoring strain mode shapes of full-scale civil structures, where the operational dynamic strain levels are of very low amplitude and temperature changes can influence the modal characteristics, has remained an open question. The present work provides a proof of concept in which the deck of a steel tied arch railway bridge is instrumented with eighty Fiber-optic Bragg Grating strain sensors, multiplexed in four fibers, that are interrogated with a technique that achieves high accuracy and precision. For more than a year, the natural frequencies and strain mode shapes of ten modes have been automatically identified from operational strain time histories, with typical root-mean-square values of 0.01 microstrain, on an hourly basis. Furthermore, using these modal data, the influence of temperature fluctuations and that of a retrofitting of the hangers connecting the bridge deck and the arches, which took place during the monitoring period, are extensively investigated. Both have an influence on the overall stiffness of the bridge and therefore they result in clear changes in the natural frequencies. They do not have an influence on the local stiffness and therefore they do not influence the strain mode shapes, except when the retrofitting induces an interaction between previously well-separated modes.
Thin plates are widely applied in engineering structures due to their excellent mechanical performance. This paper studies the stress modal analysis (SMA) of thin plates with holes/notches for the ...purpose of local structural dynamic modification (SDM). Identification of predominant components of stress state at critical locations is theoretically demonstrated. To pursue possible dynamic stress reduction, a fast modification strategy is proposed by using the SMA information, which involves a two-step procedure. First, modal participation factors (MPFs) are validated in SMA and then utilized to determine the predominant modes. Second, components of stress are evaluated for the predominant stress mode shapes (sSMSs11The superscript is to distinguish the stress from the strain in present paper.). Structural dynamic simulations of a representative L-shaped thin plate with hole/notches were implemented. The sSMSs in x-, y-, and xy- directions were compared in details. Together with MPFs, sSMSs can help to identify the dangerous stresses (both the location and the direction), and then to modify the local structure to suppress dynamic stress response. By taking full advantage of numerically-obtained sSMSs along different directions, local structural modification for dynamic stress reduction can be applied in a straightforward way with high efficiency prior to the full dynamic response analysis. This research is aimed to serve as a first step towards the development of SMA-based SDM strategy for real thin-walled structures with more complex geometric details and local changes.
Using analytical equations, the paper aims to solve the dynamic behaviour of beams where a clamped end of the beam does not respect the ideal boundary conditions by introducing a weakening ...coefficient. In the paper, the characteristic equation for determining the eigenvalues and the relationship of the modal function and strain energy are derived. The results show the first six vibration modes for different values of the weakening coefficient which is considered in the clamped end and the evolution of the strain energy.
In the second part of the paper, the dynamic behavior of a doubly clamped beam is presented, where the right clamped end of the beam is weakened by introducing a weakening coefficient. The analytical ...calculation is based on the determination of the bending moment from the weakened clamped end expressed as a function of slope, after which the modal function, strain energy and the characteristic equation are determined to obtain the eigenvalues of the first six vibration modes depending on the weakened coefficient of the clamped end. The obtained mode shapes and strain energies are determined for seven values of the weakened coefficient.
Reduced-order models (ROMs) are developed for obtaining the natural frequencies of offshore wind turbines (OWTs) considering the soil–structure interaction (SSI) by distributed springs along the ...monopile and employing three different modeling strategies. The ROM is derived considering a non-prismatic beam with mass at the tip. Once the mathematical model is obtained, the natural frequencies of the NREL 5 MW reference wind turbine are analytically obtained and the results are compared with those obtained by higher-order hierarchical models based on the Finite Element Method (FEM). The novelty here is the presentation of a mathematical model for this SSI representation that allows obtaining different natural frequencies and the vibration modes representation in an analytical scheme. The analyses developed raise a discussion about the choice of the shape function in the use of Galerkin’s method. The results show that, depending on the modeling strategy, the fundamental frequency of the OWT studied is obtained with great accuracy when compared to the FEM analysis (considered as a reference value), with difference below 3.5%. The ROMs obtained allow evaluating the natural frequencies and mode shapes with very low computational cost, a feature that can be useful especially in the early stages of design.
•Reduced-order models (ROMs) considering the soil-structure interaction are obtained.•The ROMs obtained allow evaluating the natural frequencies and mode shapes for offshore wind turbines.•A discussion about the choice of the shape function in the use of Galerkin’s method is carried out.
Sensor location optimization plays a key role in the application and development of structural integrity monitoring methodologies, especially in large mechanical structures. Given the existence of an ...effective damage detection and identification procedure, the question of how many and where to place the acquisition points (sensors) so that the monitoring system operates at peak efficiency arises. In this study, an innovative methodology is proposed in order to maximize the quality of modal information and minimize the number of sensors in the SHM system. To maximize the quality of modal information, it considered the reconstruction of mode shapes using Kriging interpolation. The study was carried out on plate-type composite material structures for initial validation and later applied and validated on a main rotor blade of the AS-350 helicopter. The initial modal information (modal deformation) was obtained through the finite element method, and the multi-objective Lichtenberg algorithm was used in the complex optimization process. The proposed method presented in this work allows for the best possible distribution of a minimum and sufficient number of acquisition points in a structure in order to obtain more modal information for a better modal reconstruction from kriging interpolation of these minimum points. Numerical examples and test results show that the proposed method is robust and effective for distributing a reduced number of sensors in a structure and at the same time guaranteeing the quality of the information obtained, even in noisy situations. Numerical results considering both the simple and complex geometric cases show that the proposed combined FS-kriging method is effective in distributing a finite number of sensors on the structures and at the same time guaranteeing the quality of the modal information obtained. The results also indicate that the layout of sensors obtained by multi-objective optimization does not become trivial and symmetrical when a set of modes is considered in the objective function formulation. The proposed strategy is an advantage in modal testing as it is only necessary to acquire signals at a limited number of points, saving time and operating costs in vibration-based processes.
•Kriging and thin-plate mode shape interpolation comparison.•Multi-objective sensor placement optimization considering number of sensors and position.•Feature selection based SPO.•SPO applied in a AS-350 main rotor blade.
•A transformation matrix T is used as a correlation technique.•Matrix T is used to know the source of discrepancies between two models.•Matrix T is factorized with the polar and QR ...decompositions.•Matrix T is a rotation matrix in the case of no mass discrepancies.•A novel version of the modal assurance criterion (ROTMAC) is proposed.
According to the structural dynamic modification theory, the perturbed mode shapes can be expressed as a linear combination of the unperturbed mode shapes through a transformation matrix T. This matrix is proposed in this paper as a powerful technique to determine whether the discrepancies between two models can be attributed to differences in stiffness, in mass, or both. It is demonstrated that matrix T becomes a rotation matrix when there are no mass discrepancies. In the case of mass discrepancies, or a combination of mass and stiffness differences, matrix T can be decomposed into a product of a rotation matrix and a matrix containing information about the changes in scaling and in shear. The angle of rotation depends on the closeness of the modes, and large rotations can be obtained when the system presents closely spaced or repeated modes. The polar and the QR decompositions are used in this paper to factorize matrix T as a product of two matrices, one of them being a rotation matrix. A new version of the modal assurance criterion (MAC), denoted in this paper as rotated MAC or ROTMAC, is proposed to detect mass discrepancies between two models. The equations and the conclusions derived in this paper have been validated through numerical simulations on a 2-degrees-of-freedom system and by correlating a numerical model and an experimental model of a square laminated glass plate.
•A model was developed for biodynamic responses of the human body to triaxial vibration.•The model included two thighs, pelvis, lumbar spine, middle torso, upper torso, head.•Experimental modal ...analysis of the human body in sagittal and coronal planes was conducted.•Two of the five modes mainly featured the body vibration in the coronal plane.•The other three mode shapes featured the body vibration in the sagittal plane.
While most of the previous studies on biodynamics of the seated human body focused on vertical vibration in the sagittal plane, this study was designed with combined tri-axial translational vibration excitation to investigate the biodynamics in both sagittal and coronal planes. In this study, an analytical model was developed to represent the biodynamic responses of the seated human body to tri-axial translational vibration. The model consisted of thighs, pelvis, lumbar spine (L3 and L4), middle torso (thoracic spine T5-T12 and lumbar spine L1-L2), upper torso (thoracic spine T1-T6), and head (including cervical spine C1-C7). The transmissibilities from the seat to various body locations of subjects sitting with an upright backrest under single-axis and tri-axial vibration were measured. The parameters of the seated human model were determined by fitting the modelled in-line transmissibilities to the chest, L3 and pelvis along the fore-aft, lateral and vertical directions to the measured values. Five vibration modes were identified from the measured transmissibilities below 20 Hz. The first mode at 1.3 Hz featured the lateral sway of the upper body in the coronal plane. The second mode at 2.5 Hz characterised the lateral motion of the whole body accompanied by the lateral bending motion of the torso. The third mode at 3.6 Hz contained the fore-aft and pitch movements of the upper body with pitch of the pelvis. The fourth mode at 6.4 Hz included the vertical motion of the entire body with pitch of the pelvis, and the fifth mode at 10.3 Hz involved the vertical motion of the thighs with pitch and vertical motion of the pelvis. The model was verified with the measured vibration modes. This study provided a method for the identification of model parameters using the body transmissibilities and modal properties.
When two vessels in a side-by-side configuration are under wave actions, fluid resonance occurs in a narrow gap between two vessels, termed ‘gap resonance’, leading to large free-surface responses. ...Large free-surface responses due to gap resonance can induce large relative motions and drift forces by both vessels, which influences operational safety. The present study aims at investigating the free-surface response near resonance in a narrow gap between two fixed, identical barges with square corners numerically and experimentally. Gap resonance is driven by three typical incident wave conditions including beam sea, quartering sea, and head sea. In light of the fact that the potential-flow theory overestimates the response in the gap, a potential-flow model with energy dissipation effects is developed based on the boundary element method. A dissipation surface is devised at the bottom opening as well as two end openings of the gap. Both linear and quadratic damping terms associated with laminar boundary layer wall friction and flow separation from sharp corners are accounted for. Physical experiments of gap resonance excited by irregular waves with different significant wave heights and peak periods are carried out and used for calibration and validation of the potential-flow model. Nonlinear correlation is observed between the incident wave amplitude and resonant gap response, which is predicted with satisfactory agreement by the developed potential-flow model. In-depth discussion on the mode shapes is made. It is found that the first mode is predominant in the beam sea, and the natural modes exhibit standing wave behaviors. Under quartering sea and head sea excitations, the second and third modes dominate over other modes. Waves propagate slowly along the gap in the head sea condition. Under the quartering sea excitation, the first and second modes propagate along the gap, but the third mode exhibits standing wave behavior, indicating the quartering sea response is a transition between head sea and beam sea. The significance of the present study is threefold. Firstly, the experimental measurements provide reference results for numerical simulation. Secondly, a simple but effective damping model to suppress unrealistic free-surface response near resonance is developed. Lastly, this work gives an insight into the spatial structure and dominance of natural modes under different wave conditions.
