Stiffness Identification Research Articles

Bending Stiffness Identification of Continuous Girder Bridges Using Multiple Rotation Influence Lines

Bending Stiffness Identification of Continuous Girder Bridges Using Multiple Rotation Influence Lines

Contact Stiffness Identification Method for Joint Surface and the Effect of Contact Stiffness on the Dynamic Response of the Cable Bracket

The cable bracket is one of the crucial components of high-speed Electric Multiple Units (EMUs), which is fixed to the axle box by bolts to support the cable. As an important parameter of the joint surface, contact stiffness significantly affects the dynamic response and service life of the cable bracket. However, it is difficult to directly measure the contact stiffness of the joint surface. As a result, an identification method is proposed in this investigation to identify the contact stiffness. A finite element model incorporating both normal and tangential stiffness parameters is developed. According to the finite element model and modal testing results, an improved particle swarm optimization algorithm is employed to identify the contact stiffness of the joint surface. The effect of the contact stiffness on the vibrations of the cable bracket is investigated. The findings indicate that pre-tightening torque significantly influences the contact stiffness of the cable bracket. The contact stiffness has a great effect on the vibrations of the cable bracket. Optimal contact stiffness notably reduces vibrations of the cable bracket, thereby extending its service life.

Identification of stiffness and damping characteristics of magnetorheological elastomers due to immersion in seawater

ABSTRACT Magnetorheological elastomer (MRE) materials are commonly used as vibration dampers in offshore structures. Therefore, it is urgent to investigate the degradation of this smart material because of seawater interaction. This work focuses on the immersion of MRE material in seawater, which alters its rheological and mechanical characteristics. Hence, it is important to investigate the impact of seawater immersion on the rheological characteristics of substances. This study contributes to the assessment of the stiffness and damping characteristics of MRE materials after exposure to seawater for one year. The MRE samples comprise MRE with a silicone matrix devoid of any Carbonyl Iron Particle (CIP) and MRE with 70% CIP, exhibiting both isotropic and anisotropic properties. Immersing the subject in seawater was carried out for one year. The study involved doing multiple tests, such as scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA), and rheological testing. The findings indicated that the samples underwent harm, erosion, and deterioration of their rheological characteristics during immersion. The stiffness values for isotropic MRE and anisotropic MRE decreased by 97% and 11%, respectively. Meanwhile, the deterioration of the damping characteristics values of isotropic MRE and anisotropic MRE was 96% and 14%, respectively.

Investigation on the Seismic Damage and Identification of Lateral Stiffness for Ancient Timber Structures

ABSTRACTThis paper investigates the seismic damage and identification of lateral stiffness for ancient timber structures. Based on the shaking table test of a palace‐style timber structure, the lateral displacement responses, interstory equivalent lateral stiffness (IELS), and sensitivity of lateral displacement to degradation of IELS were analyzed to investigate the degradation and identification of IELS. The state and observation equations of a simplified mechanical model of the timber frame considering the friction slipping of the column base were predicted. Considering the noise disturbance in the test, the IELS of the model was identified by the partial least squares–singular value decomposition (PLS‐SVD) and extended Kalman filter (EKF) method. Results shown that the ratio of the IELS of the column frame layer to Ru‐Fu layer decreased as the seismic damage increased, and the peak lateral displacement was more sensitive to the damage of the column frame layer than the Ru‐Fu layer. Under nondamage conditions, the identification error of the IELS was about 10%, while the error ranged from 15% to 20% under damage conditions. Through the identification of the equivalent lateral stiffness of the Xi'an bell tower, it was validated that the hybrid method is effective in monitoring the IELS of ancient timber structures.

Spatial and frequency identification of the dynamic properties of thin plates with the Frequency-Adapted Virtual Fields Method

Vibroacoustic inverse methods use the measured response of a vibrating structure to identify a structural parameter or a dynamic load. Two inverse methods are considered, the Force Analysis Technique (FAT) and the Virtual Fields Method (VFM). The Corrected Force Analysis Technique (CFAT) is a variant of FAT that corrects its singularity. This correction allows the method to be applied in the high-frequency domain, when the number of measurement points per flexural wavelength becomes small. In this study, the proposed novelty is the development of a Frequency-Adapted VFM (FA VFM) to the case of a Love–Kirchhoff plate. Thanks to this method, the VFM can now be applied to identify the equivalent bending stiffness and structural damping of a thin plate when the number of measurement points per wavelength is small. The method has previously been developed for an Euler–Bernoulli beam. An experimental identification of the complex bending stiffness of an locally damped aluminium plate using Laser Doppler Velocimetry (LDV) data and the developed method is performed. The experimental study shows for the first time that the FA VFM can be used to map the equivalent bending stiffness and structural damping as a function of position on a plate and identify these parameters as a function of frequency over a large frequency band. The results of the Frequency-Adapted VFM are compared with those of CFAT and the classical VFM approach. FA VFM results are more accurate than those of classical VFM and similar to those of CFAT.

Experimental identification of the bending stiffness and damping of plates using the frequency-adapted virtual fields Method

Inverse vibroacoustic methods can be used to identify the complex bending stiffness of a plate from its vibratory response. This work focuses on the Virtual Fields Method (VFM) and the Force Analysis Technique (FAT). The VFM uses functions called virtual fields to solve the Principle of Virtual Work, a weak form of equilibrium, and identifies complex bending stiffness. Here, the virtual fields are defined as piecewise functions over a surface smaller than the plate (virtual window). FAT uses a finite-difference scheme to discretize the fourth-order spatial derivatives of the displacement in the local equilibrium of the plate and thus estimates the bending stiffness. The application of a finite-difference scheme creates a bias in the identified stiffness, which increases with frequency. The Corrected Force Analysis Technique (CFAT) corrects this bias in the high-frequency domain. In this study, it is proposed to apply the CFAT principles to the VFM to adapt the method, using the virtual window size, so it can be applied it in the high-frequency domain. FAT, CFAT, the VFM and the Frequency-Adapted VFM will be presented. The method was tested on experimental data to identify the complex bending stiffness of an aluminium plate partially covered with a damping material.

Interface stiffness identification of rough and weak bonded interface using developed ultrasonic reflection phase derivative spectrum

The thickness and interface roughness of coatings both affect the interface bonded quality. Existed ultrasonic testing methods based on traditional phase screen approximation or spring model assumption are difficult to simultaneously identify the interface roughness and stiffness of coating. This paper, a new method for integrated identifying coating thickness, interface roughness, and interface stiffness using developed ultrasonic reflection phase derivative spectrum (URPDS) is proposed. A phase-screen-approximated spring-model (PSASM) for ultrasound vertically propagating into rough and weak bonded interface is constructed. On basis of PSASM, a URPDS of coating/substrate structure is developed for identifying the interface stiffness and other parameters of coated parts. Cross-correlation analysis is used to eliminate the phase deviation of URPDS introduced by reference signal and initial phase of tested signal. Sensitivity analysis is used to determine the high-sensitivity regions of URPDS to interface roughness and interface stiffness. Genetic algorithm optimization is used to achieve integrated identification of coating thickness, interface roughness, and interface stiffness. The rationality of PSASM is verified through numerical simulation using a series of coating/substrate models with rough and weak bonded interface, and the relationship between the high-sensitivity regions and the high-precision measurement ranges of interface roughness Rq and interface stiffness Kn is clarified. Ultrasonic experiments are implemented on Nickel-coating samples and coated parts using plane wave probe. The coating thickness, interface roughness, and interface stiffness could be identified accurately, which shows that the proposed URPDS method can identify the interface stiffness of rough contacted dissimilar media or coated parts with rough interface.

Intelligent ultrasonic aspirator: Advancing tissue differentiation through hierarchical classification during hand-held resection

Modern neurosurgery strives to maximize tumor removal while preserving healthy tissue integrity. Accurate intraoperative differentiation between tumor and healthy tissue is crucial yet challenging. Often neurosurgeons rely on their experience and haptic feedback during palpation to distinguish between tumor and healthy tissue. A commonly used hand-held tool for tissue removal during neurosurgery is the ultrasonic aspirator, which changes its electrical properties as it interacts with tissue. The goal is to equip the ultrasonic aspirator with the ability to differentiate between different types of tissue while at the same time not interfering with the surgical workflow and providing comprehensible outcomes. To this end, a hierarchical classification approach is employed as a proof of concept, enabling precise identification of tissue stiffness during resection.The hierarchical approach is compared with the standard flat classification, commonly used in machine learning. Within the hierarchical approach, two strategies are employed: mandatory leaf-node predictions (MLNP) and non-mandatory leaf-node predictions (NMLNP). The NMLNP allows prediction to revert to a parent node when certainty is low. Data are acquired on three artificial tissue models – differing in stiffness – with an ultrasonic aspirator in a hand-held manner. The dataset comprises 1,821 data points for training and 186 for testing after balancing.The results indicate a slight performance advantage for the hierarchical classification MLNP approach over the flat classification approach in the absence of confidence thresholds, with weighted F2-scores of 0.781 and 0.762, respectively. However, the application of confidence thresholds results in both approaches exhibiting comparable performance, with the hierarchical NMLNP approach achieving a weighted F1-score of 0.920, thereby demonstrating superior overall performance. The effects of enforcing these thresholds and excluding data with low certainty are thoroughly investigated. This work emphasizes the feasibility of tissue differentiation using a hand-held ultrasound aspirator while resecting tissue. Moreover, it highlights the capability of hierarchical classification in advancing tissue differentiation accuracy during neurosurgical procedures, which could ultimately aid surgeons and enhance the safety of intraoperative workflows.

Novel Iontronic Pressure Sensor Coupling High Sensitivity and Wide‐Range for Stiffness Identification and Long‐Distance Precise Motion Control

Novel Iontronic Pressure Sensor Coupling High Sensitivity and Wide‐Range for Stiffness Identification and Long‐Distance Precise Motion Control

A least-squares identification method for vehicle cornering stiffness identification from common vehicle sensor data

In this study, we present a robust framework for vehicle tire cornering stiffness identification, leveraging commonly available lateral acceleration and yaw rate measurements. In contrast to most of the state-of-the-art approaches, our methodology does not rely on (augmented) state estimation, but on batch least-squares optimisation of larger time windows. This batch-approach has as a major benefit that many of the observability issues which are encountered in estimation-based methods are completely eliminated. By immediately exploiting the measurement equations, rather than comparing dynamic simulation responses, we obtain a very efficient and sparse formulation which enables online processing. The methodology was validated on (openly available) datasets from two different vehicles – a Ferrari 250LM and Range Rover Evoque, delivering consistent and accurate results for both vehicles. This work shows that batch optimisation can be a very promising alternative for the more common state-estimation approaches for extracting reliable vehicle cornering stiffnesses in various driving scenarios with a much more straightforward tuning.

Experimental Identification of Gear Mesh Stiffness and Verification by Theoretical Models

Experimental Identification of Gear Mesh Stiffness and Verification by Theoretical Models

Stiffness identification of beam structures with elastic foundations through the global mode method and time-domain nonlinear subspace method

Stiffness identification of beam structures with elastic foundations through the global mode method and time-domain nonlinear subspace method

Two-dimensional stiffness identification by inversion of local wavenumbers based on artificial neural network

Impact and fatigue damages in carbon fiber reinforced polymers (CFRP) are unavoidable in severe operating conditions, which will lead to the stiffness properties degrading and redistributing in space. The local wavenumbers of guided waves at a specific point depend on the stiffness at that spatial location. Therefore, the two-dimensional stiffness properties can be determined by inversion of local wavenumbers. In this paper, the relationship between the local wavenumbers and the stiffness coefficients was established by the artificial neural network (ANN) method. For each spatial point, based on the semi-analytical finite element (SAFE) method, the wavenumbers (inputs of ANN) with different frequencies can be obtained at given stiffness coefficients (outputs of ANN). Furthermore, the accuracy of the ANN method was validated by the finite element model. Results show that the predicted two-dimensional stiffness coefficients of the damaged region are close to the true ones, thus demonstrating the accuracy of the two-dimensional stiffness identification method.

Modeling a Milling Dynamometer as a 3DOF Dynamic System by Stiffness Identification

The experimental determination of cutting forces during milling is an important aspect followed in the manufacturing process and involves the use of specialized devices known as dynamometers. These can be made in the laboratory, depending on the type of measurements to be made, or they can be commercial, purchased from specialized companies. In this paper, such a dynamometer made by the authors in the laboratory is analyzed. For the elastic elements, octagonal rings are used. The main problem in the case of these dynamometers, namely the determination of the stiffness of the rings, is solved analytically, using the FEM for comparison, and then experimentally validated. The dynamic model, created based on the obtained values using d’Alembert’s principle, allows for simulating the behavior of this dynamometer in practical applications and determining the field in which it can be used. The frequencies and natural modes of vibration are determined, and the values obtained are compared with those obtained using ANSYS software 2021 R2.

Analysis of Finger Photo Pulse Plethysmography and Body Composition among Low Back Pain Subjects with Lumbar Disc Degenerative Diseases Diagnosed by MRI Analysis

Lumbar disc degenerative disc disease, accompanied by back pain, is a prominent health concern in society. The purpose of the study was to investigate the connection of arterial stiffness and body composition in the patients suffering low back pain with lumbar disc degenerative disorders. A comparative study was performed on 197 patients, both male and female, between the ages of 30 and 70, who were experiencing low back pain. These patients have undergone magnetic resonance imaging of the lumbosacral region to evaluate the intervertebral disc's nucleus and annulus as well as its signal intensity and height. The Pfirrmann grading method was used to determine the extent of disc degeneration. The statistical analysis revealed no significant link between overall body fat and stiffness index in disc bulging and nerve compression groups. However, the group experiencing nerve compression demonstrated a statistically significant association between visceral fat and reflection index in individuals who were overfat and obese. In addition, there was a notable correlation between PWV and the reflection index of the disc bulging groups. So, whole body fat and PWV had a different impact on disc degeneration. The PWV has a robust positive correlation with both the stiffness index and reflection index. The presence of subcutaneous fat and vascular stiffness may not have any impact on low back pain in patients with disc bulging and nerve compression. Early identification of vascular stiffness and study of body composition serve as initial measures to avoid the progression of disc degeneration.

Stiffness identification of reinforced concrete beams using rotation rate sensors

Monitoring flexural stiffness variations of cracked reinforced concrete (r/c) structures is one of the most challenging problems of the dynamics of these structures. In this article, the application of rotation rate sensors for structural health monitoring of reinforced concrete beams is proposed as an alternative SHM method to, e.g. those utilising more expensive and laborious fiber optics. This subject was investigated with progressively damaged 6 m long reinforced concrete beams. During each damage state, the cracks were located and described in detail. Experimental modal analyses were carried out. Translational and rotational vibration modes were acquired using translational accelerometers and rotation rate sensors. The stiffness distributions of the damaged reinforced concrete beams were identified from the modal properties using model-updating techniques. It is demonstrated that stiffness distributions calculated using rotational modes are more accurate than those obtained from the familiar translational natural modes of vibrations. Further improvement of stiffness identification of r/c beams from their vibrations was obtained by combining the directly measured rotational modes and their approximations from translational modes by the central difference method.

Insights into the Mechanical Characterization of Mouse Brain Tissue Using Microindentation Testing

AbstractIndentation testing is the most common approach to quantify mechanical brain tissue properties. Despite a myriad of studies conducted already, reported stiffness values vary extensively and continue to be subject of study. Moreover, the growing interest in the relationship between the brain's spatially heterogeneous microstructure and local tissue stiffness warrants the development of standardized measurement protocols to enable comparability between studies and assess repeatability of reported data. Here, we present three individual protocols that outline (1) sample preparation of a 1000‐µm thick coronal slice, (2) a comprehensive list of experimental parameters associated with the FemtoTools FT‐MTA03 Micromechanical Testing System for spherical indentation, and (3) two different approaches to derive the elastic modulus from raw force‐displacement data. Lastly, we demonstrate that our protocols deliver a robust experimental framework that enables us to determine the spatially heterogeneous microstructural properties of (mouse) brain tissue. © 2024 Wiley Periodicals LLC.Basic Protocol 1: Mouse brain sample preparationBasic Protocol 2: Indentation testing of mouse brain tissue using the FemtoTools FT‐MTA03 Micromechanical Testing and Assembly SystemBasic Protocol 3: Tissue stiffness identification from force‐displacement data

Optimization of stiffness performance of six-axis industrial robots based on posture stiffness evaluation index

Aiming at the problem that the stiffness performance of industrial robots depends on the posture, a method to improve the stiffness performance by optimizing the robot posture is proposed based on the robot posture stiffness evaluation index. The robot joint stiffness identification model is established by using the principle of virtual work and Jacobi matrix, and the stiffness values of six joints are obtained by least-squares. On the basis of revealing the mapping relationship between robot joints and end, the robot end flexibility ellipsoid is obtained, and the volume of the end flexibility ellipsoid is utilized as the global stiffness coefficient of the robot, so as to obtain the robot posture stiffness evaluation index. According to the posture stiffness evaluation index, the robot posture optimization model is established, and the optimized posture is obtained by using genetic algorithm. Taking the QJR6-1 robot as the experimental object, under the maximum load, the deformation of the robot end center is reduced from 0.6238 to 0.3984 mm, which is 36.13%, and the deformation of the end is greatly reduced compared with that before the optimization, which indicates that the robot’s stiffness is improved after the posture optimization, and it verifies the feasibility of the optimization model, and provides a reference to improve the stiffness performance of industrial robots further.

Nonlinear Analysis of Cables with Identification of Flexural-Torsional Stiffness

Nonlinear Analysis of Cables with Identification of Flexural-Torsional Stiffness

Identification of time-varying stiffness with unknown mass distribution based on extended Kalman filter

Although the extended Kalman filter (EKF) provides a promising way for structural state estimation, it cannot effectively track time-varying parameters online. Besides, the structural mass distribution is usually assumed to be known in advance for many EKF-based methods, limiting their applications. In this paper, by using limited observations, an adaptive EKF with unknown mass coefficients (AEKF-UM) approach is proposed for the identification of time-variant parameters and mass distribution at the same time. A real-time updating procedure is presented for improving the process and measurement noise covariance matrices at each time step to assure the stability and accuracy of convergence results. Based on the dramatic increase of measurement noise covariance, an index is defined for determining the damage instant. A covariance resetting technique is then used to enhance the tracking capability for the purpose of effectively capturing the time-varying parameters. The unknown mass coefficients can be estimated at the same time by adding them into the extended state vector. To validate the effectiveness of the proposed approach, two numerical cases are considered, i.e. (i) the Phase I ASCE structural health monitoring benchmark building structure, and (ii) a four-story nonlinear structure equipped with a magneto-rheological (MR) damper. Experimental tests on a four-story building model subject to base excitation are also conducted to investigate the performance of the proposed approach. Results show that the proposed approach is capable of satisfactorily tracking abrupt changes of stiffness parameters with unknown mass distributions.