Local Stiffness Change Research Articles

Structural damage detection using auto correlation functions of vibration response under sinusoidal excitation

Structural damage detection using time domain vibration responses has attracted more and more researchers in recent years because of its simplicity in calculation and no requirement of a finite element model. This paper proposes a new approach to locate the damage using the auto correlation function of vibration response signals under sinusoidal excitation from different measurement points of the structure, based on which a vector named Auto Correlation Function at Maximum Point Value Vector (AMV) is formulated. A sensitivity analysis of the normalized AMV with respect to the local stiffness shows that under several specific frequency excitations, the normalized AMV has a sharp change around the local stiffness change location, which means that even when the damage is very small, the normalized AMV is a good indicator for the damage. In order to locate the damage, a damage index is defined as the relative change of the normalized AMV before and after damage. Several example cases in stiffness reduction detection of a frame structure valid the results of the sensitivity analysis, demonstrate the efficiency of the normalized AMV in damage localization and the effect of the excitation frequency on its detectability.

Stiffness evolution of granular layers and the origin of repetitive, slow, stick-slip frictional sliding

We demonstrate the frictional behaviors of steady state sliding, stick-slip, and repetitive, slow stick-slip sliding through a carefully-designed suite of laboratory experiments focused on exploring the role of loading system stiffness in controlling the frictional response to shear. We performed tests on sheared layers of baking flour, with three configurations of loading blocks made of steel and cast acrylic to achieve different stiffnesses. Slide-hold-slide and velocity step tests were conducted and analyzed in a rate-and-state friction framework. With compliant loading blocks, the material exhibits unstable stick-slip behavior with slow-slip events of duration up to 20 s. Slow-slip has been difficult to achieve in the lab and has only been observed for a narrow variety of boundary conditions and materials. Our results suggest that this behavior is strongly controlled by the stiffness of the system, the strain history of the sample, and shear fabric evolution. We describe a new suite of automated tools that greatly improve friction analysis and provide insight to the underlying mechanisms of slow stick-slip. We demonstrate that layer stiffness evolves with shear strain and modifies the mechanical behavior of stick-slip sliding. Our work suggests that slow earthquakes in tectonic fault zones may be linked to shear fabric development and associated changes in local stiffness, likely in combination with variations in frictional constitutive properties and effective stress.

Attenuation of lipopolysaccharide-induced lung vascular stiffening by lipoxin reduces lung inflammation.

Reversible changes in lung microstructure accompany lung inflammation, although alterations in tissue micromechanics and their impact on inflammation remain unknown. This study investigated changes in extracellular matrix (ECM) remodeling and tissue stiffness in a model of LPS-induced inflammation and examined the role of lipoxin analog 15-epi-lipoxin A4 (eLXA4) in the reduction of stiffness-dependent exacerbation of the inflammatory process. Atomic force microscopy measurements of live lung slices were used to directly measure local tissue stiffness changes induced by intratracheal injection of LPS. Effects of LPS on ECM properties and inflammatory response were evaluated in an animal model of LPS-induced lung injury, live lung tissue slices, and pulmonary endothelial cell (EC) culture. In vivo, LPS increased perivascular stiffness in lung slices monitored by atomic force microscopy and stimulated expression of ECM proteins fibronectin, collagen I, and ECM crosslinker enzyme, lysyl oxidase. Increased stiffness and ECM remodeling escalated LPS-induced VCAM1 and ICAM1 expression and IL-8 production by lung ECs. Stiffness-dependent exacerbation of inflammatory signaling was confirmed in pulmonary ECs grown on substrates with high and low stiffness. eLXA4 inhibited LPS-increased stiffness in lung cross sections, attenuated stiffness-dependent enhancement of EC inflammatory activation, and restored lung compliance in vivo. This study shows that increased local vascular stiffness exacerbates lung inflammation. Attenuation of local stiffening of lung vasculature represents a novel mechanism of lipoxin antiinflammatory action.

Role of Suspended Fiber Structural Stiffness and Curvature on Single-Cell Migration, Nucleus Shape, and Focal-Adhesion-Cluster Length

It has been shown that cellular migration, persistence, and associated cytoskeletal arrangement are highly dependent on substrate stiffness (modulus: N/m2 and independent of geometry), but little is known on how cells respond to subtle changes in local geometry and structural stiffness (N/m). Here, using fibers of varying diameter (400, 700, and 1200 nm) and length (1 and 2 mm) deposited over hollow substrates, we demonstrate that single mouse C2C12 cells attached to single suspended fibers form spindle morphologies that are sensitive to fiber mechanical properties. Over a wide range of increasing structural stiffness (2 to 100+ mN/m), cells exhibited decreases in migration speed and average nucleus shape index of ∼57% (from 58 to 25 μm/h) and ∼26% (from 0.78 to 0.58), respectively, whereas the average paxillin focal-adhesion-cluster (FAC, formed at poles) length increased by ∼38% (from 8 to 11 μm). Furthermore, the increase in structural stiffness directly correlates with cellular persistence, with 60% of cells moving in the direction of increasing structural stiffness. At similar average structural stiffness (25 ± 5 mN/m), cells put out longer FAC lengths on smaller diameters, suggesting a conservation of FAC area, and also exhibited higher nucleus shape index and migration speeds on larger-diameter fibers. Interestingly, cells were observed to deform fibers locally or globally through forces applied through the FAC sites and cells undergoing mitosis were found to be attached to the FAC sites by single filamentous tethers. These varied reactions have implications in developmental and disease biology models as they describe a strong dependence of cellular behavior on the cell’s immediate mechanistic environment arising from alignment and geometry of fibers.

Sensitivity analysis of an auto-correlation-function-based damage index and its application in structural damage detection

Structural damage detection using time domain vibration responses has advantages such as simplicity in calculation and no requirement of a finite element model, which attracts more and more researchers in recent years. In present paper, a new approach to detect the damage based on the auto correlation function is proposed. The maximum values of the auto correlation function of the vibration response signals from different measurement points are formulated as a vector called Auto Correlation Function at Maximum Point Value Vector, AMV for short. The relative change of the normalized AMV before and after damage is used as the damage index to locate the damage. Sensitivity analysis of the normalized AMV with respect to the local stiffness shows that the normalized AMV has a sharp change around the local stiffness change location, which means the normalized AMV is a good indicator to detect the damage even when the damage is very small. Stiffness reduction detection of a 12-story frame structure is provided to illustrate the validity, effectiveness and the anti-noise ability of the proposed method. Comparison of the normalized AMV and the other correlation-function-based damage detection method shows the normalized AMV has a better detectability.

Monitoring and Staging Abdominal Aortic Aneurysm Disease With Pulse Wave Imaging

The abdominal aortic aneurysm (AAA) is a silent and often deadly vascular disease caused by the localized weakening of the arterial wall. Previous work has indicated that local changes in wall stiffness can be detected with pulse wave imaging (PWI), which is a non-invasive technique for tracking the propagation of pulse waves along the aorta at high spatial and temporal resolutions. The aim of this study was to assess the capability of PWI to monitor and stage AAA progression in a murine model of the disease. ApoE/TIMP-1 knockout mice (N = 18) were given angiotensin II for 30 days via subcutaneously implanted osmotic pumps. The suprarenal sections of the abdominal aortas were imaged every 2–3 d after implantation using a 30-MHz VisualSonics Vevo 770 with 15-μm lateral resolution. Pulse wave propagation was monitored at an effective frame rate of 8 kHz by using retrospective electrocardiogram gating and by performing 1-D cross-correlation on the radiofrequency signals to obtain the displacements induced by the waves. In normal aortas, the pulse waves propagated at constant velocities (2.8 ± 0.9 m/s, r2 = 0.89 ± 0.11), indicating that the composition of these vessels was relatively homogeneous. In the mice that developed AAAs (N = 10), the wave speeds in the aneurysm sac were 45% lower (1.6 ± 0.6 m/s) and were more variable (r2 = 0.66 ± 0.23). Moreover, the wave-induced wall displacements were at least 80% lower within the sacs compared with the surrounding vessel. Finally, in mice that developed fissures (N = 5) or ruptures (N = 3) at the sites of their AAA, higher displacements directed out of the lumen and with no discernible wave pattern (r2 < 0.20) were observed throughout the cardiac cycle. These findings indicate that PWI can be used to distinguish normal murine aortas from aneurysmal, fissured and ruptured ones. Hence, PWI could potentially be used to monitor and stage human aneurysms by providing information complementary to standard B-mode ultrasound.

Pressure Wave Propagation in Full-body Arterial Models: A Gateway to Exploring Aging and Hypertension

It is now widely recognized that changes in arterial wall properties have a significant impact on hemodynamic indices such as pressure pulse amplification and pulse wave velocity. It is also becoming increasingly evident that changes in wall mechanics may progress both spatially and temporally (e.g., in age-related arterial stiffening and hypertension). Modeling studies can help delineate how local changes in stiffness affect global hemodynamics. Previously, several modeling studies have investigated blood and pressure in full-body scale arterial trees using one-dimensional formulations. In this paper, we work towards the goal of deepening our understanding of arterial pulse propagation phenomena while incorporating detailed information on localized hemodynamics. To this end, we present the first multi-scale simulation of unsteady blood flow and pressure within a three-dimensional deformable full-body arterial network. This simulation framework builds upon previous advances in fluid-structure interaction, multi-scale outflow boundary conditions, and perivascular tissue support modeling. We consider application examples featuring realistic distributions of spatially and temporally varying mechanical properties. Simulations successfully demonstrate realistic pressure and flow waveforms, regional blood flow distribution, pressure pulse amplification and pulse wave velocity.

Mapping Local Nanoscale Changes in Cell Tension and Stiffness by Combinatorial Microscopies

Cellular processes such as division, migration, and remodeling are clearly dependent in the cytoskeletal network, and its local mechanical properties, including stiffness and tension. We have applied a combinatorial microscopy platform that integrates atomic force microscopy with confocal and TIRF microscopy to examine three different scenarios wherein protein-protein interactions are thought to influence these characteristics. Cell migration is intimately tied to cortical actin organization and cell tension. Understanding how these characteristics are impacted by specific protein-protein interactions will be important for our understanding of metastasis in cancer. Cell integrity and stiffness may also be altered during infection with the parvovirus minute virus of mice, which has been shown to alter the local vimentin intermediate filament network. During cell division, changes in the cytoskeletal network are clearly evident. Quantitatively measuring these changes, in real-time, during the process of cell division will provide unique insights into local changes in membrane stiffness and tension that can be linked to specific developmental pathways.

Quantification of Magnetically Induced Changes in ECM Local Apparent Stiffness

The stiffness of the extracellular matrix (ECM) is known to influence cell behavior. The ability to manipulate the stiffness of ECM has important implications in understanding how cells interact mechanically with their microenvironment. This article describes an approach to manipulating the stiffness ECM, whereby magnetic beads are embedded in the ECM through bioconjugation between the streptavidin-coated beads and the collagen fibers and then manipulated by an external magnetic field. It also reports both analytical results (obtained by formal modeling and numerical simulation) and statistically meaningful experimental results (obtained by atomic force microscopy) that demonstrate the effectiveness of this approach. These results clearly suggest the possibility of creating desired stiffness gradients in ECM in vitro to influence cell behavior.

The Finite-Element Modeling of Dynamic Motions of a Constraint Wind Turbine and the System Diagnosis for the Safety Control

The aim of this paper is to present a finite element modeling of the dynamic motion of a turbine rotor and its controller design with the mass unbalance under a crack on a rotating shaft. This process is an advanced method to the mathematical description of a system including an influence of a mass unbalance and a crack on the rotor shaft. As the first step, the shaft is physically modeled with a finite element method and the dynamic mathematical model is derived by using the Hamilton principle; thus, the system is represented by various subsystems. The equation of motion of a shaft with a mass unbalance and a crack is established by adapting the local mass unbalance and stiffness change through breathing and gaping from the existence of a crack. This is a reference system for the given system. Based on a fictitious model for transient behavior induced from vibration phenomena measured at the bearings, an elementary estimator is designed for the safety control and detection of a mass unbalance on the shaft. Using the state estimator, a bank of an estimator is established to get the diagnosis and the system data for a controller.

Acoustic Radiation Force Impulse Imaging of Mechanical Stiffness Propagation in Myocardial Tissue

Acoustic radiation force impulse (ARFI) imaging has been shown to be capable of imaging local myocardial stiffness changes throughout the cardiac cycle. Expanding on these results, the authors present experiments using cardiac ARFI imaging to visualize and quantify the propagation of mechanical stiffness during ventricular systole. In vivo ARFI images of the left ventricular free wall of two exposed canine hearts were acquired. Images were formed while the heart was externally paced by one of two electrodes positioned on the epicardial surface and either side of the imaging plane. Two-line M-mode ARFI images were acquired at a sampling frequency of 120 Hz while the heart was paced from an external stimulating electrode. Two-dimensional ARFI images were also acquired, and an average propagation velocity across the lateral field of view was calculated. Directions and speeds of myocardial stiffness propagation were measured and compared with the propagations derived from the local electrocardiogram (ECG), strain, and tissue velocity measurements estimated during systole. In all ARFI images, the direction of myocardial stiffness propagation was seen to be away from the stimulating electrode and occurred with similar velocity magnitudes in either direction. When compared with the local epicardial ECG, the mechanical stiffness waves were observed to travel in the same direction as the propagating electrical wave and with similar propagation velocities. In a comparison between ARFI, strain, and tissue velocity imaging, the three methods also yielded similar propagation velocities.

Structural Condition Assessment from White Noise Excitation and Covariance of Covariance Matrix

The sensitivity of covariance of covariancematrix with respect to a local stiffness change in the structural system is derived analytically based on the auto/cross-correlation function of the acceleration response, and the original covariance of covariance formula is improved for use with any number of selected structure modes. This paper presents the approach using the improved covariance of covariance matrix of acceleration response for structural condition assessment under white noise support excitation. A simply supported 31 bar plane truss with and without 10% measurement noise is studied numerically. Results show that the sensitivity approach with the covariance of covariance matrix is accurate, and when including the finite impulse response forward and backward filtering technique, themethod would be suitable for industrial application. The covariance of covariancemethod is shown to be insensitive to measurement noise when the measurement time duration is sufficiently long.

Effect of drop in pipe wall stiffness on water-hammer speed and attenuation

The effect of local drop of wall stiffness in pressurized waterways on the pressure wave speed and the wave attenuation during transients is investigated experimentally. A new signal-processing procedure to identify the presence of a weak reach is introduced and validated by physical experimentation based on assessing the pressure and vibration records acquired at both ends of a multi-reach steel test pipe. Water-hammer was generated by closing a downstream valve, whereas the weak reaches were simulated by replacing the steel portions with aluminium and PVC material. The wave speed and wave attenuation factor during transients are considered as global indicators of local and large changes in stiffness of the pipe wall. The method is capable of locating the stiffness weakness along the test pipe if one PVC reach is used. The error in estimating the position of such a reach relative to the real position of its mean value varies up to 23%.

Damage Detection of Bridges by Using Displacement Data of Two Symmetrical Points

AbstractThis paper investigates new damage detection method for bridges to ensure their safety. The idea of using displacement data of two symmetrical points for multiple damage detection is presented for the first time. After introducing the concept of Equivalent Element, a novel index termed as “Symmetrical Displacement Difference Index (SDDI),” is proposed. The displacement under static load is used for constructing the new index. Then the relationship between the local flexural stiffness change caused by damage and SDDI value is generated. In application, SDDI values can be plotted after the measurement of displacement. The relative changes between the intact state and the damage state in the curve shapes can be used to indicate the position of damage. This new damage detection method based on SDDI is flexible enough to be applied to real-world bridges with inherent random uncertainty and actual support condition. Numerical and experimental examples have been conducted to examine the suitability of th...

A new approach to free vibration analysis of a beam with a breathing crack based on mechanical energy balance method

In this paper, a new approach to free vibration analysis of a cracked cantilever beam is proposed. By considering the effect of opening and closing the crack during the beam vibration, it is modeled as a fatigue crack. Also, local stiffness changes at the crack location are considered to be a nonlinear amplitude-dependent function and it is assumed that during one half a cycle, the frequencies and mode shapes of the beam vary continuously with time. In addition, by using the experimental tests, it is shown that the local stiffness at the crack location varies continuously between the two extreme values corresponding to the fully closed and the fully open cases of the crack. Then, by using the mechanical energy balance the dynamic response of the cracked beam is obtained at every time instant. The results show that for a specific crack depth, by approaching the crack location to the fixed end of the beam, more reduction in the fundamental frequency occurs. Furthermore, for a specific crack location, the fundamental frequency diminishes and the nonlinearity of the system increases by increasing the crack depth. In order to validate the results, the variations of the fundamental frequency ratio against the crack location are compared with experimental results.

Damage Detection for Simply Supported Beams Using Mid-Span Displacement Indicator

This paper investigates the detection of damage for simply supported beams to ensure their safety. Based on the analysis of possible kinds of damage may occur, this paper presents a new approach which relies on the fact that any change in local stiffness caused by damage can be reflected by the change of mid-span displacement between the intact and damaged beams. Direct relationship between the change in local stiffness and the measured mid-span displacement values is developed. This approach can identify the geometric locations of damage and then inspection means are used as a complement to find the real damage phenomena within the obtained small region. A numerical example is given to illustrate the feasibility and the effectiveness of the approach. The novel content offered by authors provides a simple, convenient, cost-effective, and nondestructive damage detection approach for simply supported beams.

Regulation of Dendrite Arborization by Substrate Stiffness is Mediated by Glutamate Receptors

Brain injury or disease can initiate changes in local or global stiffness of brain tissue. While stiffness of the extracellular environment is known to affect the morphology and function of many cell types, little is known about how the dendrites of neurons respond to changes in brain stiffness. To assess how extracellular stiffness affects dendrite morphology, we took biomaterial and biomedical engineering approaches. We cultured mixed and pure hippocampal neurons on hydrogels composed of polyacrylamide (PA) of varying stiffnesses to mimic the effects of extracellular matrix stiffness on dendrite morphology. The majority of investigations of cortical and spinal cord neurons on soft hydrogels examined branching at early time points (days in vitro (DIV) 2-7), an important distinction from our study, where we include later time points that encompass the peak of branching (DIV 10-12). At DIV 12, dendrite branching was altered by stiffness for both pure and mixed neuronal cultures. Furthermore, we treated hippocampal cultures with glutamate receptor antagonists and with astrocyte-conditioned media. Blocking AMPA and NMDA receptors affected the changes in dendrite branching seen at varying rigidities. Moreover, extracellular factors secreted by astrocytes also change dendrite branching seen at varying rigidities. Thus, astrocytes and ionotropic glutamate receptors contribute to mechanosensing.

Novel Acoustic Radiation Force Impulse Imaging Methods for Visualization of Rapidly Moving Tissue

Acoustic radiation force impulse (ARFI) imaging has been demonstrated to be capable of visualizing changes in local myocardial stiffness through a normal cardiac cycle. As a beating heart involves rapidly-moving tissue with cyclically-varying myocardial stiffness, it is desirable to form images with high frame rates and minimize susceptibility to motion artifacts. Three novel ARFI imaging methods, pre-excitation displacement estimation, parallel-transmit excitation and parallel-transmit tracking, were implemented. Along with parallel-receive, ECG-gating and multiplexed imaging, these new techniques were used to form high-quality, high-resolution epicardial ARFI images. Three-line M-mode, extended ECG-gated three-line M-mode and ECG-gated two-dimensional ARFI imaging sequences were developed to address specific challenges related to cardiac imaging. In vivo epicardial ARFI images of an ovine heart were formed using these sequences and the quality and utility of the resultant ARFI-induced displacement curves were evaluated. The ARFI-induced displacement curves demonstrate the potential for ARFI imaging to provide new and unique information into myocardial stiffness with high temporal and spatial resolution.

A local flexibility method for vibration-based damage localization and quantification

A method for vibration-based damage localization and quantification, based on quasi-static flexibility, is presented. The experimentally determined flexibility matrix is combined with a virtual load that causes nonzero stresses in a small part of the structure, where a possible local stiffness change is investigated. It is shown that, if the strain–stress relationship for the load is proportional, the ratio of some combination of deformations before and after a stiffness change has occurred, equals the inverse local stiffness ratio. The method is therefore called local flexibility (LF) method. Since the quasi-static flexibility matrix can be composed directly from modal parameters, the LF method allows to determine local stiffness variations directly from measured modal parameters, even if they are determined from output-only data. Although the LF method is in principle generally applicable, the emphasis in this paper is on beam structures. The method is validated with simulation examples of damaged isostatic and hyperstatic beams, and experiments involving a reinforced concrete free–free beam and a three-span prestressed concrete bridge, that are both subjected to a progressive damage test.

Differential wear and plastic deformation as causes of squat at track local stiffness change combined with other track short defects

Squats have become a major problem in the track of many railways. In the quest for the root causes of squats, it is observed that they are occasionally found at locations of track stiffness changes such as at fish-plated insulated joints and at switches and crossings. Obviously, there should be other factors in the track, which, together with the stiffness change, have played important roles otherwise there will be squats at all such locations. A validated hybrid multibody-finite element model of vehicle–track vertical interaction is extended to simulate the frictional dynamic rolling contact at a fish-plated insulated joint in order to identify such factors. Elastic–plastic rail material property is taken into account. It is found that it is track short defect in the preload condition of the bolts and the contact between the fishplates and the rail head, which together with the stiffness change, causes large normal and longitudinal contact force variation at the fishplate end so that differential wear and differential plastic deformation may accumulate at a fixed location. With proper wavelength, the accumulated rail top geometry deviation may grow into a squat. The significance of the present work lies in that other track short defects such as damaged and improper railpads and fastening, and ballast voids may also have such effects, which may be responsible for a large portion of the many squats in the tracks. This gives the direction for further work.