Displacement Mode Research Articles

Effect of Cyclic Loading on Mode I Fracture Toughness of Granite under Real-Time High-Temperature Conditions

Under hot dry rock development, rock formations undergo the combined challenges of cyclic loading and high temperatures, stemming from various sources such as cyclic hydraulic fracturing and mechanical excavation. Therefore, a fundamental understanding of how rocks fracture under these demanding conditions is fundamental for cyclic hydraulic fracturing technology. To this end, a series of three-point bending tests were conducted on granite samples. These tests entailed exposing the samples to cyclic loading under varying real-time high-temperature environments, ranging from 25 °C to 400 °C. Furthermore, different upper load limits (75%, 80%, 85%, and 90% of the peak load) obtained in monotonic three-point bending tests were used to explore the behavior of granite under these conditions. The analysis encompassed the study of load–displacement curves, elastic stiffness, and mode I fracture toughness under cyclic loading conditions. In addition, the microscopic features of the fracture surface were examined using a scanning electron microscope (SEM). The findings revealed notable patterns in the behavior of granite. Cumulative vertical displacement in granite increased with the growing number of cycles, especially at 25 °C, 200 °C, and 300 °C. This displacement exhibited a unique trend, initially decreasing before subsequently rising as the cycle count increased. Additionally, the critical damage threshold of granite exhibited a gradual decline as the temperature rose. As the temperature ascended from 25 °C to 200 °C, the damage threshold typically ranged between 80% and 85% of the peak load. At 300 °C, this threshold declined to approximately 75–80% of the peak load, and at 400 °C, it fell below 75% of the peak load. Within the temperature ranging from 25 °C to 300 °C, we noted a significant increase in the incidence of cracks, crystal microfracture zones, and the dislodging of mineral particles within the granite as the number of cycles increased.

Finite element analysis of the cervical spine: dynamic characteristics and material property sensitivity study

The study aimed to investigate the dynamic characteristics of the cervical spine and determine the effect of the material properties of the cervical spinal components on it. A finite element model of the head-cervical spine was developed based on CT scan data, and the first six orders of modes (e.g. flexion-extension, lateral bending, and vertical, etc.) were verified by experimental and simulation studies. The material sensitivity study was conducted by varying elasticity modulus of cervical hard tissues (cortical bone, cancellous bone, endplates, and posterior elements) and soft tissues (intervertebral disc and ligaments). The results showed that increasing the elastic modulus of ligaments by 4 times increased the natural frequency by 77%, while increasing that of cancellous bone by 4 times only increased the natural frequency by 6%. In the axial mode, the cervical spine had not only axial deformation but also anterior-posterior deformation, with the largest deformation located at the intervertebral disc C6-C7. Decreasing the elastic modulus of a component in soft tissues by 80% increased modal displacement by up to 62%. The material properties of the intervertebral discs and ligaments had opposite effects on the modal displacement and deformation of the cervical spine. Low cervical discs were more susceptible to injury in a vertical vibration environment. Cervical spine dynamics were more sensitive to soft tissue material properties than to hard tissue material properties. Disc degeneration could reduce the range of vibratory motion of the cervical spine, thereby reducing the ability of the cervical spine to cushion head impacts.

Pore-scale imbibition patterns in layered porous media with fractures

The presence of fractures increases the difficulty of flow mechanisms analysis, and it remains unclear how fractures affect multiphase flow displacement in the layered rock matrix. Herein, a pore-scale imbibition model considering the layered matrix-fracture system is established using the phase-field method, where oil is displaced by a range of fluids with various properties. Two typical flow modes are carefully analyzed, depending on the locations of the fracture and the interfaces between different layers of the matrix: fracture is parallel to the interface (mode I), and it penetrates through the interface (mode II), which are dominated by the co-current imbibition and countercurrent imbibition mechanisms, respectively. Interestingly, the surface tension is found to be negatively correlated with the ultimate oil recovery rate for mode I and plays an opposite effect on that of mode II. For flow mode I, the conditions of lower injection rate, higher viscosity ratio, higher grain diameter ratio, and injection of the invading fluid from the larger pore throat size (positive direction flow) can improve oil recovery. For flow mode II, the fracture bifurcation angle has little effect on the positive direction flow, while it can significantly regulate the phase distribution in the negative direction flow. Based on scaling analysis of relating pore-filling events to displacement modes and the equilibrium relationship between capillary and viscous forces, two theoretical models are derived to predict the imbibition patterns, and the variation of the flow regime under various parameters in the typical layered matrix-fracture models is systematically concluded.

Experimental study of the effects of a multistage pore-throat structure on the seepage characteristics of sandstones in the Beibuwan Basin: Insights into the flooding mode

To investigate the relationship between grain sizes, seepage capacity, and oil-displacement efficiency in the Liushagang Formation of the Beibuwan Basin, this study identifies the multistage pore-throat structure as a crucial factor through a comparison of oil displacement in microscopic pore-throat experiments. The two-phase flow evaluation method based on the Li–Horne model is utilized to effectively characterize and quantify the seepage characteristics of different reservoirs, closely relating them to the distribution of microscopic pores and throats. It is observed that conglomerate sandstones at different stages exhibit significant heterogeneity and noticeable differences in seepage capacity, highlighting the crucial role played by certain large pore throats in determining seepage capacity and oil displacement efficiency. Furthermore, it was found that the displacement effects of conglomeratic sandstones with strong heterogeneity were inferior to those of conventional homogeneous sandstone, as evidenced by multiple displacement experiments conducted on core samples with varying granularities and flooding systems. Subsequently, core-based experiments on associated gas flooding after water flooding were conducted to address the challenge of achieving satisfactory results in a single displacement mode for reservoirs with significant heterogeneity. The results indicate that the oil recovery rates for associated gas flooding after water flooding increased by 7.3%–16.4% compared with water flooding alone at a gas–oil ratio of approximately 7000 m3/m3. Therefore, considering the advantages of gas flooding in terms of seepage capacity, oil exchange ratio, and the potential for two-phase production, gas flooding is recommended as an energy supplement mode for homogeneous reservoirs in the presence of sufficient gas source and appropriate tectonic angle. On the other hand, associated gas flooding after water flooding is suggested to achieve a more favorable development effect compared to a single mode of energy supplementation for strongly heterogeneous sandstone reservoirs.

Extended component mode synthesis method for dynamic analysis of mechanical systems with local nonlinearities

Engineering structures are generally designed based on linear elasticity assumptions. However, it is difficult to describe the connected structures using a simple linear system, due to factors such as sliding and friction at interfaces, and variations in contact areas during vibration processes. Therefore, it is necessary to develop an approach to tackle such systems with interface nonlinearities. In this paper, we proposed an extended free-interface component mode synthesis method. According to the proposed method, the substructures are separated at the nonlinear interfaces. Then the component mode synthesis procedure is carried out. By reasonably neglecting the contributions of higher order modes to the damping and inertia terms, it is demonstrated that the nonlinear interface forces and their time derivatives can be expressed as functions of themselves, as well as modal displacements and velocities. This characteristic facilitates the synthesis of the reduced order models for substructures in the state space. Also owing to this operation, the original properties of nonlinear interface forces can be preserved as much as possible, without any linearization. This method is suitable for non-proportionally damped structures with local nonlinearities such as mechanical structures with nonlinear spring and dashpot connections, rotor-bearing systems and so on. It also may be an alternative for the dynamic analysis of jointed structures with contact nonlinearities. Two numerical examples are presented to demonstrate the capability of the proposed method: (1) an eighteen degrees of freedom spring-dashpot-mass system with cubic spring and cubic dashpot interface connections is studied and (2) a more complex mechanical structure: a dual-rotor system with deep-groove ball bearing inter-shaft support. The numerical simulation results indicate that the dynamic responses of the reduced order model match very well with that of the full model, revealing the high accuracy of the proposed method with low computational costs.

Effects of displacement velocity on interfacial reconstruction events during immiscible two-phase displacement

During the two-phase fluid displacement in porous media, with the increase in capillary number Ca, different wettability effects are suppressed; however, its potential control mechanism has not been clarified. Therefore, in this study, we have analyzed the pore scale process related to interface reconfiguration events in detail and profoundly clarified the nature of a series of interface reconfiguration events being suppressed. Based on typical pore throat, we elaborated and confirmed that the development and evolution direction of fluid displacement mode always follow the principle of minimum operating power. That is to say, in order to avoid extra work, the system will compare all the potential moving meniscus at the displacement front and always choose the local path with the minimum operating power (Po=ΔpQ) of the system for displacement. Under this theory, a series of interface reconfiguration events are considered energy favorable self-regulation events derived by the system in order to avoid extra energy consumption. However, the appearance and disappearance of interface reconstruction events are considered to be the result of the mechanism of “self-regulation of surface energy change rate” and “self-regulation of viscosity dissipation rate” in order to approach the minimum operating power. This study provides us with a sufficient physical explanation to understand the nature of the wettability effect being suppressed.

A modal-based method for blast-induced damage assessment of reinforced concrete columns: Numerical and experimental validation

Reinforced concrete (RC) columns play a crucial role in the overall performance of modern RC frame buildings under blast loading. The RC columns under blast loads might experience various irreversible consequences such as concrete cracks, crushing and spalling, changing the status of both modal properties and load-carrying capacity. In this paper, the blast-induced damage assessment of the RC columns involving the measurement of modal parameters was introduced and validated. Firstly, a modal-based method for blast-induced damage assessment of RC columns was proposed, in which the damage is characterized as the reduction of axial bearing capacity and further expressed as the explicit function of the vibration frequencies and the mass-normalized displacement mode shapes. Then, the finite-element analysis program LS-DYNA was employed to establish the numerical model of RC columns under axial compression loads and lateral blast loads. The residual load-bearing capacities and modal properties of the RC columns were illustrated. By using the numerical results collected in the present study, the validity of the proposed damage assessment method was discussed and proved numerically. Further, field explosion tests and experimental modal tests were conducted, and the results showed that the modal-based damage assessment method exhibited remarkable agreement with the blast damage determined by residual bearing capacities. Based on the numerical and experimental results, the proposed modal-based damage assessment method is applicable for the non-destructive evaluation of blast-induced damage of RC columns.

A Spectral Method Algorithm for Modeling the Dispersion of Non-Axisymmetric Modes in Fluid-Filled Elastic Tubes

In order to design a low-noise water-filled pipeline system, it is necessary to obtain knowledge of the dispersion characteristics of axial propagation modes in different water-filled elastic tubes. In this work, an algorithm is developed based on the spectral method, which has previously been used to solve the dispersion of axisymmetric modes in cylindrical structures but has not yet been applied to non-axisymmetric modes. The algorithm can obtain the dispersion characteristics, modal displacement, and stress distribution of axial propagation modes in a fluid-filled elastic multi-layer tube. The algorithm behaves well both at low and ultrasonic frequencies, and it is suitable for any tube dimensions, wall thickness and layers. The results of a water-filled PMMA tube obtained using the spectral method algorithm were verified using a COMSOL simulation, while the dispersion curves of the same tube from the literature were found to be missing some low-order modes. In addition, the dispersion curves of a water-filled three-layer tube are given. The spectral method algorithm has the advantages of fast calculation speed, less computational resources consumed, accurate results, and no modal omission.

Optimal design of piezoelectric energy harvesters for bridge infrastructure: Effects of location and traffic intensity on energy production

Piezoelectric energy harvesters (PEHs) can be used as an additional power supply for a Structural Health Monitoring (SHM) system. Its design can be optimised for the best performance, however, the optimal design depends on the input vibration and locations. In this work, we extend an optimisation framework from our previous studies to include the effect of the PEH’s location, which uses the cantilevered PEH Kirchhoff–Love plate model discretised by IsoGeometric Analysis (IGA) and coupled with Particle Swarm Optimisation (PSO) algorithm to find the designs with maximum energy outputs for a large number of input acceleration histories, extracted from the recorded dynamic response data of a real cable-stayed bridge in Australia. Then, clustering and evaluation under 24-h excitation are performed to find several best PEHs for the entire bridge. By comparing the best PEH at all locations with a typical benchmark device, the substantial performance improvement brought by the optimisation framework of this work is verified. The comparison results show a significant energy harvesting enhancement of 1.6 times at the best locations, 2.4 times at A2 and A3, and 3.6 times at the edge girders, respectively. The results also reveal the variability of the best design at different locations of the same structure to maximise the energy harvesting of the entire bridge, and demonstrate the design rule that the fundamental frequency of the device can be tuned within a certain frequency range to improve the robustness of PEHs design. Additional studies are performed to explore the effect of location and traffic intensity on energy harvesting by analysing the optimal PEH design and location throughout the bridge structure. The results indicate that the key factors of maximising energy harvesting efficiency are related to the input excitation and the mode of vibration being excited. The position of maximum displacement in the vibration mode corresponds to the best location for energy harvesting. Also, the best device has a fundamental frequency close to the frequency of the corresponding vibration mode. In addition, the change of traffic intensity affects the amount of convertible mechanical energy and also directs the tuning of the fundamental frequency of the PEH to achieve the highest energy conversion.

Experimental Study and Numerical Analysis of the Seismic Performance of Glass-Fiber Reinforced Plastic Tube Ultra-High Performance Concrete Composite Columns.

To investigate the impact of the filament winding angle of glass-fiber reinforced plastic (GFRP) on the seismic behavior of GFRP tube ultra-high performance concrete (UHPC) composite columns, this study designs two types of GFRP tube UHPC composite columns. Quasi-static tests are conducted on the specimens subjected to horizontal reciprocating load and axial force, and the skeleton curve characteristics of the structure are analyzed. Furthermore, a finite element analysis model of the composite column is established to explore the effects of the diameter-thickness ratio, circumferential elastic modulus of confined tubes, and tensile strength of concrete on the seismic performance of the composite column. The analysis includes a review of the skeleton curve, energy dissipation capacity, and stiffness degradation of the structure under different designs. The results indicate that the use of GFRP tubes effectively enhances the seismic performance of UHPC columns. The failure mode, peak load, and peak displacement of the composite columns are improved. The finite element analysis results are in good agreement with the experimental results, validating the effectiveness of the analysis model. Extended analysis reveals that the bearing capacity of the specimen increases while the energy dissipation capacity decreases with a decrease in the diameter-thickness ratio and an increase in the circumferential elastic modulus. Although the tensile strength of concrete has some influence on the seismic performance of the specimen, its effect is relatively small. Through regression analysis, a formula for shear capacity suitable for GFRP tube UHPC composite columns is proposed. This formula provides a theoretical reference for the design and engineering practice of GFRP tube UHPC composite columns.

Theoretical analysis of immunochromatographic assay and consideration of its operating parameters for efficient designing of high-sensitivity cardiac troponin I (hs-cTnI) detection

Troponin is the American College of Cardiology and American Heart Association preferred biomarker for diagnosing acute myocardial infarction (MI). We provide a modeling framework for high sensitivity cardiac Troponin I (hs-cTnI) detection in chromatographic immunoassays (flow displacement mode) with an analytical limit of detection, i.e., LOD < 10 ng/L. We show that each of the various control parameters exert a significant influence over the design requirements to reach the desired LOD. Additionally, the design implications in a multiplexed fluidic network, as in the case of Simple Plex™ Ella instrument, are significantly affected by the choice of the number of channels or partitions in the network. We also provide an upgrade on the existing LOD equation to evaluate the necessary minimum volume to detect a particular concentration by considering the effects of stochastics and directly incorporating the target number of copies in each of the partitions in case of multiplexed networks. Even though a special case of cTnI has been considered in this study, the model and analysis are analyte agnostic and may be applied to a wide class of chromatographic immunoassays. We believe that this contribution will lead to more efficient designing of the immunochromatographic assays.

An Experimental Study on Innovative Concrete Block Solutions for Reconstruction

In this study, an experiment was conducted to innovate a new design of interlocking concrete blocks (ICBs) containing recycled aggregates (RAs) by reducing the consumed time and cost in construction using an environmental approach. Accordingly, the designed ICBs were produced manually using RAs, and wallettes were easily built with a mortarless mechanism by stacking the blocks without any mortar layers. In the experiments, besides the individual compression tests of the two types of ICB with natural and recycled aggregates, the wallette samples that were produced using ICBs, containing either 100% natural aggregates or 100% Ras, were tested under axial compressive loading. The experimental results were assessed considering the compressive strength, displacement, and failure mode. In the obtained results, we noticed that the average compressive strengths of the wallettes that were produced with natural or recycled aggregate ICBs were large enough to meet the standards of Syrian regulations, which are considered an example reference. The resulting displacement values were acceptable and could be negligible in some wallette specimens. It was concluded that the innovative ICBs with both normal or recycled aggregates could be a good alternative to traditional blocks, especially in post-disaster or post-war areas.

Attenuation of Rayleigh and pseudo surface waves in saturated soil by seismic metamaterials

Seismic metamaterials have received extensive research interest due to their bandgap properties, simplicity in design principles, and stability in response. They have been developed to protect buildings or architectures susceptible to damage from surface elastic waves. In practice, the ground soil is generally a multiphase medium, and the influence of its permeability and viscosity on seismic metamaterials is not yet clear. In this work, we developed a formulation that combines Biot’s theory and Bloch-Floquet theorem to investigate the complex band structures and transmission properties of Rayleigh and pseudo surface waves (PSWs) for pillared and inclusion-embedded seismic metamaterials in saturated soil. It is shown that the ratio of fluid viscosity and permeability η/κ have an impact on the surface wave attenuation and the performances of seismic metamaterials, where the smaller ratio benefits the surface wave broadband attenuation and metamaterials attenuating effects. The complex band structures reveal that inclusion-embedded metamaterials can support the propagation of PSWs having a phase velocity higher than that of the transverse bulk waves. The PSWs are significantly affected by the rubber viscosity due to the mode displacements concentrated in the rubber coatings. The higher viscosity of metamaterials also allows for broadband attenuation of Rayleigh surface waves. The results of this study will present an appropriate way to design viscoelastic seismic metamaterials in saturated soil for low-frequency surface wave attenuation.

Study on the production law and optimization parameters of CO2 huff ‘n’ puff for continental shale oil

AbstractIn this study, nuclear magnetic resonance and computed tomography scanning were used to analyze the production law and displacement mechanism of Jimusaer continental shale oil during CO2 huff ‘n’ puff, and the optimal parameters were determined. The results indicated that CO2 huff ‘n’ puff mainly produces crude oil in pore throats with 0.1–1 μm radii, while crude oil in pore throats with radii below 0.1 μm cannot be produced. Multiple CO2 huff ‘n’ puff cycles can connect fluids in fractures with fluids in large–medium pore throats, eliminate fracture effects on the oil recovery factor, and achieve coefficient development of both fractured and unfractured shales. In the CO2 huff ‘n’ puff process, core pressure change could be divided into three stages of injection–holding–depletion, and the oil displacement mode was the piston type. The study of huff ‘n’ puff parameters revealed that huff ‘n’ puff cycles and injection pressure have a great influence on the CO2 huff ‘n’ puff efficiency, while the injection timing and soaking time imposed relatively small effects. For continental shale in the Jimusaer Sag, the optimal CO2 huff ‘n’ puff parameters are five cycles, 4‐MPa injection timing, 25‐MPa injection pressure, and 12‐h soaking time.

Quasi-static tests and seismic fragility analysis of RC bridge piers with high-strength steel bars and high-strength/ultra-high performance concrete

The use of high-strength steel bars (HSSB), high-strength concrete (HSC) and ultra-high performance concrete (UHPC) in bridge piers can obviously improve bearing capacity and save material consumption. However, the use of high strength materials may detrimentally affect the seismic performance of reinforced concrete (RC) piers. This paper tries to study the seismic performance of RC piers with HSSB and HSC/UHPC by quasi-static tests and seismic fragility analysis. Three RC piers, solid pier with normal strength steel bars (NSB) and normal strength concrete (NSC), solid pier with HSSB and HSC, and hollow pier with HSSB and UHPC, were designed and tested under quasi-static loading. The failure mode, hysteretic performance, stiffness degradation and residual displacement of three specimens were compared and analyzed. A fiber-based beam-column finite element model (FEM) was developed to simulate the nonlinear response of RC piers with HSSB and HSC/UHPC. On this basis, the seismic fragility analysis was performed to study the effects of high-strength materials on the seismic performance of RC piers. Research results show that, compared with NSC piers, HSC piers reinforced with a small amount of HSSB still exhibited slightly larger lateral bearing capacity but lower deformability due to the higher brittleness of HSC. The UHPC hollow pier presented obviously larger deformation capacity, and more slow decline speed of lateral stiffness than NSC and HSC solid piers. Meanwhile, the matching use of UHPC and HSSB in hollow pier can improve the elastic deformation, and then reduce residual displacement of RC piers. The proposed fiber-based finite element model (FEM) can simulate the nonlinear response of RC piers with different high-strength materials with reasonable accuracy. Fragility results demonstrate that, HSC pier presents lower seismic fragility than NSC pier at different damage states except for collapse due to lower ductility of HSC pier. The UHPC hollow pier with HSSB has lower seismic fragility than NSC and HSC solid piers at the same seismic intensity. Overall, the hollow pier with HSSB and UHPC can maintain good seismic performance while greatly saving material consumption.

Dynamic modeling and analysis of fluid-delivering cracked pipeline considering breathing effect

Crack is the most common failure mode of the pipeline system, which may lead to high-speed and high-pressure hydraulic oil leakage. In this paper, the dynamic modeling and model order reduction methods for the fluid-delivering cracked pipeline (FDCP) considering the breathing effect are proposed, and the structural intensity method (SIM) is introduced to visualize the vibration transmission and breathing effect of FDCP. The fluid, solid, and coupling elements are constructed to establish the dynamic model of FDCP, the spring element is used to simulate the breathing effect, the dynamic substructure method is extended to perform the model order reduction of FDCP, and the rationality of the modeling method is verified by experiments. SIM and energy principles are used to visualize and analyze the vibration transmission of FDCP. The analysis results show that the natural frequencies are sensitive to the cracks in the maximum modal displacement and stress regions, and the fluid velocity and pressure (FVAP) will enhance the breathing effect of FDCP. In addition, the vibration transmission analysis can accurately detect the crack with different damage degrees, and FVAP do not influence the vibration transmission laws. The modeling and analysis method in this paper can provide a theoretical reference for fault diagnosis of FDCP.

A novel method for continuous chromatographic separation of monoclonal antibody charge variants by combining displacement mode chromatography and step elution.

Charge heterogeneity of monoclonal antibodies is considered a critical quality attribute and hence needs to be monitored and controlled by the manufacturer. Typically, this is accomplished via separation of charge variants on cation exchange chromatography (CEX) using a pH or conductivity based linear gradient elution. Although an effective approach, this is challenging particularly during continuous processing as creation of linear gradient during continuous processing adds to process complexity and can lead to deviations in product quality upon slightest changes in gradient formation. Moreover, the long length of elution gradient along with the required peak fractionation makes process integration difficult. In this study, we propose a novel approach for separation of charge variants during continuous CEX chromatography by utilizing a combination of displacement mode chromatography and salt-based step elution. It has been demonstrated that while the displacement mode of chromatography enables control of acidic variants ≤26% in the CEX eluate, salt-based step gradient elution manages basic charge variant ≤25% in the CEX eluate. The proposed approach has been successfully demonstrated using feed materials with varying compositions. On comparing the designed strategy with 2-column concurrent (CC) chromatography, the resin specific productivity increased by 95% and resin utilization increased by 183% with recovery of main species >99%. Further, in order to showcase the amenability of the designed CEX method in continuous operation, the method was examined in our in-house continuous mAb platform.

Analysis of beam web panels with full length transverse stiffener in compression

The web panels of metal sections subjected to compression have resistances that are often driven by local buckling. Transverse stiffeners are used to increase their resistance. These stiffeners can be arranged at different positions in relation to the edge of the metal section. The strength of the stiffened panel can be compared to that of a compressed element whose cross-section consists of the stiffener and a participating length of the web. To observe the behavior of these stiffened walls and to evaluate the existing analytical calculation methods, an experimental campaign was carried out on two metal sections of different heights, stiffened or not over their entire height of the web. Thus, 33 zones of stiffened or unstiffened panels are tested in double localized compression until failure. The stiffeners are placed near the edge or in the middle of the panel and welded on both sides of the web over its entire height and on the panel flanges. In parallel, a finite element model using shell elements and non-linear calculations considering the plasticity of the materials, the geometrical imperfections and the large displacements is set up. It is validated by comparing its force–displacement curves and modes of ruin with those obtained by tests. The model thus validated makes it possible to enrich the results of the experimental tests to better describe the behavior of stiffened walls subjected to compression. It also allows to discuss the observed failure modes and some analytical formulas which estimate the resistance capacities of the stiffened panels.

Propagation of material uncertainty in modal parameters and its influence in damage quantification of shear buildings

Structural health monitoring (SHM) plays a crucial role in post-disaster mitigation in investigating the serviceability of an existing structure. The physical properties, namely mass density, cross-sectional area, Poisson’s ratio, modulous of elasticity, etc., vary spatially throughout a real system. These uncertainties propagate in the modal parameters involved in SHM techniques. In this study, the elastic modulous has been considered the primary source of uncertainty. A detailed literature survey has been performed to identify the suitable probability distribution recommended for defining material uncertainty. Although the Gaussian distribution cannot replicate realistic material behaviour, its explicit implementation makes it prevalent. However, based on the principle of maximum entropy, the gamma distribution is the most appropriate recommendation among all non-Gaussian continuous distributions ranging [0, ∞). The Karhunen–Loève (KL) expansion has been adopted to discretize the stochastic field to determine the spectral mass and stiffness of a multi-damaged axially vibrating prismatic cantilever bar-type structure. Closed-form orthogonal pairs of eigensolutions of the KL expansion considering (Adhikari and Friswell, 2010) exponential covariance function have been derived. The expressions for spectral mass and stiffness for a multi-damaged cantilever bar considering material uncertainty have been developed. The uncertainty propagation in the modal properties has been estimated. The complete procedure has been followed to identify uncertainty propagation in damage severity of a common class of civil structures like shear buildings. The influence of material uncertainty in determining the damage severity of a structure with numerable degrees of freedom using a non-destructive approach has been explored. Extensive simulations have been performed to evaluate the effectiveness of the present study in a multi-damaged bar as well as shear building. Statistical parameters, namely mean and standard deviation of natural frequencies, modal displacement and damage severity have been determined. The uncertainty propagation has been reflected in the mean value for varying input stochasticity. However, the standard deviation remained consistent for undamaged as well as damaged structure irrespective of material uncertainty type. Considering gamma distribution in material stochasticity, the spread of uncertainty propagation has been more than the Gaussian distribution. However, experimental studies need to be performed further to investigate the stochastic behaviour in modal parameters of a real structure.

A modified mode shape data-based method for beams structural damage detection

Damage detection methods based on changing modal parameters have received considerable attention in engineering applications due to the satisfactory results and the low associated cost compared with other techniques. The Mode Shape Data Based Indicator (MSDBI) is a damage indicator available in the literature, being used to identify damage in beam structures from the mode shape, mode shape slope and mode shape curvature, in the undamaged and damaged configurations of the element under study. However, in some situations, the configuration of the displacement mode shape of the ith mode, of the undamaged structure compared to the damaged one, presents mirroring. The damage identification algorithm could be a better indicator when these situations occur. Them, this paper presents a proposal to modify this method, called MSDBIM. The proposed modified method (MSDBIM) and the traditional method (MSDBI) were applied in two numerical examples that were elaborated in commercial software of finite elements, namely a simply supported concrete beam and a fixed-end steel beam in different single and multiple damage scenarios with sensitivity studies. A new discretization for the fixed-end beam was performed to assess whether there is a direct influence on the damage identification method. The results show that the proposed method (MSDBIM) performs better than the traditional method (MSDBI).