Displacement Mode Research Articles

Mode shape area difference method for sparse damage detection in beam‐like structures

AbstractThis article develops the mode shape area difference (MSAD) method for detecting sparse damage in beam‐like structures under serviceability conditions. MSAD enhances the static deformation area difference (DAD) damage detection method by extending its application to the modal domain. MSAD leverages the sensitivity of mode shapes to the damage, enabling damage detection and localization through the quantification of area differences between functions of modal displacements and their derivatives. To test the applicability of the method to real modal data that is affected by measurement noise resulting in different accuracies on which the modal displacements are estimated, method is evaluated under different levels of artificial noise added to the theoretical mode shapes derived from numerical model of a simply supported reinforced concrete beam. The noise level is defined by a maximum noise amplitude representing the maximal permutation in each component of normalized mode shape. Additionally, the threshold value of noise level from within the reliable estimation of damage based on MSAD method is determined. It is confirmed that MSAD method requires mode shapes with exceptionally low noise levels and demands precise estimation of all mode shape components, thereby reducing its applicability to real experimental data.

A Harmonic Response Topology Optimization Method Based on Hybrid Cellular Automata

Abstract Hybrid cellular automaton (HCA) method is a topology optimization method with high convergence efficiency. Harmonic response topology optimization problem has been widely researched and common frequency-domain methods have been applied to solve this problem. Despite this, little work has so far been undertaken to utilize the HCA method to improve the calculation efficiency of harmonic response topology optimization. In this article, we present a methodology that applies the HCA method to solve harmonic response topology optimization problem. Mode displacement method (MDM), mode acceleration method (MAM), and full method (FM) are common frequency-domain methods that are utilized as harmonic response analysis methods in this study. The examples under rotating loads demonstrate that feasibility of this methodology at one specific frequency excitation and multiple frequencies excitation. This article presents and implements a high convergence efficiency method for harmonic response topology optimization, and this method can converge in 20–30 iterations. This method can extend the application range of the HCA method and improve the optimization efficiency of harmonic response topology optimization.

Large deformation simulation of uprooting of trees with complex root system architectures using material point method with embedded truss elements

Abstract Background and aims Urban trees in coastal cities like Hong Kong may suffer from an uprooting failure when subjected to extreme winds. A proper numerical model for tree uprooting simulation can help to select tree species or soil types that better resist uprooting failure. However, modeling tree uprooting is challenging as it is a cross-disciplinary problem involving complex root system architectures (RSAs) and large deformation of both roots and soils. This study aims to develop a hybrid numerical model that combines truss elements and material point method (MPM) to simulate the entire large-deformation uprooting process of trees with complex RSAs. Methods The tree uprooting model is developed by coupling truss elements in finite element method (FEM) with MPM. Laboratory pull-out tests using artificial roots and real root cuttings are adopted to validate the developed model. A comparative study is performed to investigate the difference between using complex and simplified RSAs in tree uprooting simulations. Results The developed model provides consistent predictions of peak load, critical displacement and failure mode when compared with results from laboratory tests. Moreover, the comparative study shows that the uprooting resistance obtained with a complex RSA is higher than that with a simplified RSA. The difference varies with the soil and root mechanical properties. Conclusion The developed hybrid model offers a novel way for simulating an entire tree uprooting process involving large deformations and complex RSAs. The study shows that using a simplified RSA to approximate the complex RSA might result in misleading failure modes.

Research on Damage Detection of Dual-Rotor Synchronous Excitation Mine Screen Beams Based on Strain Mode Difference Vibration Mode Analysis.

The frame beam structure of the mine screen, subjected to various excitations, is a critical component of mining machinery. Its stress is intricate, the operational environment is severe, and damage can lead to catastrophic failures resulting in machinery destruction and fatalities. Based on the characterization of the vibration response of mine screen frame beams with varying degrees of damage at the same location and with the same degree of damage but at different locations, this paper develops a method of strain modal difference vibration pattern analysis and damage feature extraction for the detection of structural damage in beams. This method is based on the sensitivity of the sudden change in vibration strain modal difference to small deformations. This method solves the problem of using the conventional structural finite element analysis or experimental modal analysis methods to obtain the displacement mode, intrinsic frequency, and other characteristics, which make it difficult to effectively identify the actual engineering, with the damage conditions of the damage state and damage location of the mine screen frame beam problems. The feasibility and validity of the engineering application of the concept are demonstrated through instances.

Bench-scale thermomechanical assessment of carbon fibre reinforced polymer C-channels

This study investigates the thermomechanical response of carbon fibre reinforced polymer (CFRP) C-channels using a bench-scale apparatus that combines mechanical loading and radiant thermal exposure. The study aims to assess the behaviour of pre-loaded CFRP C-channels, representative of aircraft sub-structures when subjected to fire conditions. Woven prepreg CFRP C-channels were tested under cantilever point load deflection while exposed to varying heat fluxes. Key aspects examined during the study include failure times, displacement, temperature distribution, and failure modes. The findings reveal that heated, pre-loaded C-channels experience distinct phases of physico-chemical decomposition and mechanical degradation. The mechanical degradation includes upward shear buckling of the horizontal flanges and vertical web, along with outward buckling of the vertical web towards the heat source. The study shows that thermal decomposition and mechanical degradation occur simultaneously, influenced by heat flux intensity. Higher heat fluxes accelerate decomposition and reduce load-bearing capacity, while lower fluxes slow degradation. Displacement data indicates that heat flux intensity significantly affects structural response. Temperature measurements show higher fluxes lead to elevated temperatures and steeper gradients, impacting failure times and modes. Increased temperatures correlate with shorter failure times, and variability in failure times decreases as heat flux rises. These insights are significant for understanding the thermomechanical response of C-channels in aircraft sub-structures. The knowledge obtained can contribute to developing more robust and safer aircraft designs, particularly for components exposed to fire conditions, enabling engineers to establish more precise safety margins for CFRP structures, potentially preventing catastrophic failures and thereby enhancing overall aircraft safety.

Research on dynamic well control in riserless mud recovery system

In order to promote the development of RMR (Riserless Mud Recovery) system well control technology and ensure the safe operation of deep water drilling operations, the overflow control equation of RMR system considering the lifting force of subsea pump is established and verified, the conventional overflow monitoring method and the overflow monitoring method based on subsea pump parameter variation are compared and analyzed. the dynamic well control process of the RMR system after overflow under the two modes of constant subsea pump displacement and constant inlet pressure of subsea pump is simulated, and the influencing factors of inlet pressure of subsea pump are further analyzed. The results show that although the temperature effect is taken into account in the model established in this paper, the time error of the mud pool increment, the inlet pressure and the displacement of subsea pump after reaching the overflow criterion is less than 22.5% compared with Froyen's model. The conventional overflow monitoring method has fast response and small change, while the overflow monitoring method based on subsea pump parameter change is on the contrary, and the two should be used together. Both the constant inlet pressure of subsea pump mode and the constant subsea pump displacement mode can control overflow, but from the stability of subsea pump, service life and well control safety, the constant displacement mode is better. In the case of large formation pressure, low drilling fluid density, overflow criteria and circulating displacement, the pressure response adjustment speed of the subsea pump inlet is faster, and the back pressure load of the subsea pump inlet can be effectively alleviated by appropriately increasing the circulating displacement and drilling fluid density. This study has enriched the theoretical system of RMR system in overflow control, and has certain guiding significance for the development of deepwater and ultra-deepwater drilling safety technology.

Bandgap characteristics of four component periodic pile barriers in passive vibration isolation

Based on the local resonance theory, the vibration isolation performance of four-component periodic pile barriers consisting of a matrix, an outer pipe, an inner pipe, and a pile core was investigated using the finite element method (FEM). This configuration is contrasted with traditional three-component periodic pile barriers, which are composed of a matrix, a pipe, and a pile core. The four-component systems demonstrate significantly broader bandgaps compared to three-component systems. To validate the efficiency of the FEM, model test on pile barriers were conducted, facilitating a comparison between the FEM and experimental observations of bandgap characteristics. Additionally, the effects of the outer pipe’s density, elastic modulus, and thickness on the complete bandgap characteristics were comprehensively studied within the four-component structure. It is found that the broadest vibration isolation band gaps occur under hexagonal arrangement pattern. In square and hexagonal lattice configurations, the density, elastic modulus, and thickness of the outer pipe pile’s pile have predominantly influenced the upper bound frequency (UBF). There has been a positive correlation between the elastic modulus and the UBF, while the density and thickness have shown inverse relationships. Moreover, there exists a elastic modulus threshold, marking a transition in the displacement mode of the UBF, from the outer irreducible Brillouin zone (M or X) to the inner zone (Γ). Once the threshold is exceeded, both the vibration displacement mode and the width of bandgap remain substantially unchanged. The results obtained in the present paper are very useful for the design and application of periodic pile barriers in ambient vibration reduction.

Flutter Calculations Using the Unsteady Source and Doublet Panel Method

The source and doublet panel method (SDPM) developed by Morino in the 1970s can model unsteady compressible ideal flow around wings and bodies. In this work, the SDPM is adapted to the calculation of aeroelastic solutions for wings. A second-order nonlinear version of Bernoulli’s equation is transformed to the frequency domain and written in terms of the generalized mode shapes and displacements. It is shown that the pressure component at the oscillating frequency is a linear function of the generalized displacements, velocities, and accelerations and can therefore be used to formulate a linear flutter problem. The proposed approach has several advantages over the usual doublet lattice method (DLM) approach: the exact geometry is modeled (including thickness, camber, and twist effects), the motion of the surface can be represented using all six degrees of freedom, the pressure calculation is of higher order, and the aerodynamic mass, damping, and stiffness terms are calculated explicitly. The complete procedure is validated using experimental data from the weakened AGARD 445.6 wing, a NACA 0012 rectangular wing with pitch and plunge degrees of freedom, and an experimental model of a T-tail, yielding flutter predictions that lie closer to the experimental observations than those obtained from the DLM, particularly in the case of the T-tail.

Coupled critical plane-pseudo excitation method for multiaxial fatigue analysis of structures under random vibration

This study proposes a coupled critical plane–pseudo excitation method for assessing multiaxial fatigue damage in mechanical structures subjected to random loads. Within the modal coordinate framework, we derive an expression for the spectral moment of the structural stress response using the pseudo excitation method, which facilitates the decoupling of spatial characteristics from frequency domain properties. For the input power spectral density, represented as an integer power function, we employ eigenvalue decomposition and the residue theorem to derive an analytical expression for the spectral moment of the modal displacement response. By constructing equivalent stress modes based on the maximum shear stress and normal stress criteria, we obtain an expression for the equivalent stress variance. Intelligent optimization algorithms are utilized to determine the critical plane position and the corresponding equivalent stress spectral moments, followed by the application of the Dirlik method for fatigue assessment. A numerical example involving random vibration multiaxial fatigue analysis of an L-shaped thin-walled plate demonstrates the effectiveness of the proposed coupled critical plane–pseudo excitation method in comparison to the traditional critical plane method that relies on the stress covariance matrix for calculating equivalent variance. The results confirm the accuracy and efficiency of our approach, and we further explore the impact of different forms of the excitation power spectral density and the damping ratios on the computational outcomes.

Short and Medium-Range Predictability of Warm-Season Derechos. Part II: Convection-Allowing Ensemble Forecasts

Abstract This study explores convection-allowing ensemble (CAE) forecasts of a subset of 24 warm-season (May–August) progressive derechos from 2012 to 2022. The derecho cases were stratified into low predictability and moderate predictability based on the performance of Storm Prediction Center’s Convective Outlooks. The Model for Prediction Across Scales (MPAS) is used with a global mesh of varying horizontal resolution, with 60 km spacing over most of the globe decreasing to 3 km spacing where the derechos occurred. A 10-member ensemble was initialized at 0000 UTC from 5 days before the derecho (D5) to the day of the event (D1). The CAE is evaluated using objective metrics as well as subjective assessments of convective mode, coverage, initiation timing, and spatial displacement of simulated convection. The objective evaluation indicates that the MPAS CAE has skill in predicting severe wind gusts, even in the medium range (3–5 days before). The skill diminishes faster with lead time in low-predictability cases compared to moderate-predictability cases. Overall, more than half of the ensemble members generated a sustained, progressive bowing mesoscale convective system (MCS) on D1 in both low- and moderate-predictability cases, but the percentages decrease substantially for forecasts with progressively greater lead time. Furthermore, the environmental differences among ensemble members that produce bowing MCSs, multicell clusters, and supercells are minimal. These results indicate that correctly predicting sustained bowing MCSs prior to observed derechos is challenging for the MPAS CAE for lead times longer than 1–2 days, reflecting convective-scale complexity and predictability limits.

Distributed annular diffuse vibration isolator: Isolating shaft vibration of guide roller in printing machine

The operating stability of guide roller in the printing machine is an important factor to affect the paper tape transmission, and the severe vibration of guide roller can becomes erratic the printing quality. In this paper, a novel distributed annular diffuse vibration isolator is proposed to suppress the shaft vibration of the guide roller and improve the printing performance. For discussing isolation performance, dynamic stiffness method is used for establishing the theoretical model of the proposed isolator, and calculate the vibration transmission ratio and normalized modal displacement. The results indicate that three vibration isolation frequency bands, which are 86–140, 182–224, and 236–2000 Hz, can effectively block vibration energy transmission; the normalized modal displacement decreases less between 0 and 50 Hz, decreases significantly between 50 and 1000 Hz. Finally, the experimental platform on vibration isolator of guide roller is set up to verify the vib-isolating performance. These experiment results confirm the vibration transmission ratios obtained from the experiments consistently align with the trends predicted by the theoretical model, and show that vibration acceleration RMS reaches the maximum when the driving frequency is 50 Hz, the maximal RMS before isolator is 122.7 dB; When the driving frequency is 20 Hz, the RMS reaches the minimum, and the minimum is 94 dB. Thus it indicted that the proposed vibration-isolator has excellent vibration isolation performance, can isolate the vibration of the guide roller effectively in a wide frequency range.

Physics-Informed Neural Network (PINN) model for predicting subgrade settlement induced by shield tunnelling beneath an existing railway subgrade

For the shield tunnelling beneath an existing railway subgrade, factors such as disturbance during shield tunnel excavation can cause settlements of the existing subgrade above. Traditional prediction methods for subgrade settlement may not fully reflect the construction site conditions. Recently, machine learning has been widely applied due to its fast computation speed and accurate results. However, data-driven machine learning is considered a “black-box” algorithm, lacking a mechanical theory framework and having weak generalization capabilities. To address the limitations of machine learning and enhance the efficiency and accuracy of subgrade settlement prediction during shield tunnel construction, this paper proposes a prediction model based on a physics-informed neural network (PINN). Firstly, by integrating the non-uniform displacement mode function of the tunnel, the physical equations are constructed for the shield tunnel excavation process. Subsequently, the physical equations are coupled with the machine learning framework to develop a predictive model for shield tunnelling beneath an existing railway subgrade based on the PINN model. The performance of the proposed PINN model is evaluated through the application of two engineering cases and compared with traditional numerical simulations and data-driven machine learning. The results indicate that the proposed model can not only predict the settlement of the existing railway subgrade under scant and noisy monitoring data but also have accuracy in the inversion of tunnel displacement mode parameters. Finally, parametric analyses are conducted to reveal the influence of critical variables on the prediction performance of the PINN model.

An Energy Approach to the Modal Identification of a Variable Thickness Quartz Crystal Plate

The primary objective of modal identification for variable thickness quartz plates is to ascertain their dominant operating mode, which is essential for examining the vibration of beveled quartz resonators. These beveled resonators are plate structures with varying thicknesses. While the beveling process mitigates some spurious modes, it still presents challenges for modal identification. In this work, we introduce a modal identification technique based on the energy method. When a plate with variable thickness is in a resonant state of thickness–shear vibration, the proportions of strain energy and kinetic energy associated with the thickness–shear mode in the total energy reach their peak values. Near this frequency, their proportions are the highest, aiding in identifying the dominant mode. Our research was based on the Mindlin plate theory, and appropriate modal truncation were conducted by retaining three modes for the coupled vibration analysis. The governing equation of the coupled vibration was solved for eigenvalue problem, and the modal energy proportions were calculated based on the determined modal displacement and frequency. Finally, we computed the eigenvalue problems at different beveling time, as well as the modal energies associated with each mode. By calculating the energy proportions, we could clearly identify the dominant mode at each frequency. Our proposed method can effectively assist engineers in identifying vibration modes, facilitating the design and optimization of variable thickness quartz resonators for sensing applications.

Analysis and mitigation of uncertainties in damage identification by modal-curvature based methods

The objective of this paper is to address and reduce the uncertainties associated with measurement noise and discretization in damage identification methods based on modal curvature analysis. The experimental case study considers the local reduction in the bending stiffness of a slender beam under free-free and simply supported boundary conditions. First, the analysis of error sources and their propagation is theoretically set up. Second, the mitigation of uncertainties in damage localization is pursued using a two-stage approach based on multiple hypothesis testing relative to the normalized indices and the definition of a combined macro-index. Finally, the Monte Carlo method is exploited to obtain the statistical error distribution of the experimental damage position and severity predictions by randomizing the numerical displacement mode shapes with the identified noise. The present analysis allows us to find the optimal number of sensors that minimizes the combination of bias and truncation errors, to highlight how sensor spacing and data noise affect damage localization, and to determine the uncertainty bounds of the predicted damage severity. The two-stage approach, enhanced by selecting thresholds related to real noise levels and tuned on SHM objectives, appears to improve identification accuracy compared to the separate use of damage indices based on absolute confidence levels.

Strain response prediction of offshore wind turbine tower under free vibration

Strain monitoring of critical locations in offshore wind turbine tower is essential for fatigue life prediction and safe operation of wind turbine. This paper theoretically analyses the feasibility of predicting tower strain under free vibration using the modal superposition method. A finite element numerical model of the tower is established, and the displacement mode and strain mode parameters of the tower are extracted. The initial displacement and strain of the tower at cut-out wind speed are analyzed, and the first three modal coordinate of the tower are calculated using test points of displacement or strain separately. Subsequently, the full field strain of the tower is predicted using the modal superposition method. Comparative results demonstrate higher accuracy in modal coordinate values calculated using test points of displacement, and the accuracy and errors of strain prediction using different numbers of test points are compared, emphasizing the crucial role of selecting optimal positions and numbers of test points in improving prediction accuracy.

Out-of-plane performance of BFRP reinforced UHPC thin panel: experiment and numerical analysis

In this study, the out-of-plane performance of ultra-high performance concrete (UHPC) thin panels reinforced with basalt fiber reinforced polymer (BFRP) bars was investigated. Eight panels were tested under four-point load, with the investigating parameters including panel thickness, reinforcement ratio, and the presence of steel fibers. The failure mode, crack pattern, load vs. mid-span displacement, and reinforcement strain relationships were studied. Test results revealed that panels with a higher thickness (70 mm) exhibited 178.6% higher initial stiffness, 34.5% higher cracking loads, and 88.7% higher peak loads compared to those with a lower thickness (50 mm). The effects of a larger reinforcement ratio and the presence of steel fibers became more pronounced after concrete cracking, leading to 21.2% and 22.1% higher post-cracking stiffness, respectively. Adding steel fibers helped control the development of diagonal cracks and shifted the panel failure mode from shear to flexural failure. Based on the comparison of test results with design codes, the expressions in CAN/CSA-S806-12 were recommended for predicting the load-carrying capacity of the specimens. Furthermore, a two-dimensional finite element (FE) model was developed to reproduce the test results, which validates the adopted CDP model for UHPC and the bond-slip behaviors between UHPC and BFRP bars.

Bearing performance and failure mechanisms of HSCM piles in marine soft soil under lateral loads

Helix Stiffened Cement Mixing (HSCM) pile represents a novel type of grouted composite pile known for its excellent compressive and tensile performance. Based on field tests, this study introduces a laboratory-based test design methodology and piling technique for HSCM piles. A comprehensive analysis of their horizontal bearing capacity, pile-soil failure mode, optimal piling technique, and reinforcement mechanism is performed. SEM-EDS technology is utilized at a microscopic scale to examine the reinforcement mechanism of HSCM piles. Through ABAQUS finite element simulation, a full-scale model simulating the HSCM pile-soil interaction is developed. The analysis includes pile cross-sectional stress, displacement, and pile-soil failure mode. The p−y curve of the HSCM pile is then plotted, elucidating the reinforcement mechanism of cemented soil. The results indicate that compared to ordinary helical piles, the horizontal bearing capacity of HSCM piles increases by 125.9%. SEM-EDS images reveal that cement and kaolin form a mutual bond, enhancing the strength of the soil around the pile. Additionally, unlike other composite piles, the direction of soil flow around HSCM piles encircles the first helix of the pile core. This research offers a design basis for understanding the horizontal bearing performance and failure mechanisms of HSCM piles in marine soft soil.

A High-Precision Inverse Finite Element Method for Shape Sensing and Structural Health Monitoring

In the contemporary era, the further exploitation of deep-sea resources has led to a significant expansion of the role of ships in numerous domains, such as in oil and gas extraction. However, the harsh marine environments to which ships are frequently subjected can result in structural failures. In order to ensure the safety of the crew and the ship, and to reduce the costs associated with such failures, it is imperative to utilise a structural health monitoring (SHM) system to monitor the ship in real time. Displacement reconstruction is one of the main objectives of SHM, and the inverse finite element method (iFEM) is a powerful SHM method for the full-field displacement reconstruction of plate and shell structures. However, existing inverse shell elements applied to curved shell structures with irregular geometry or large curvature may result in element distortion. This paper proposes a high-precision iFEM for curved shell structures that does not alter the displacement mode of the element or increase the mesh and node quantities. In reality, it just modifies the methods of calculation. This method is based on the establishment of a local coordinate system on the Gaussian integration point and the subsequent alteration of the stiffness integration. The results of numerical examples demonstrate that the high-precision iFEM is capable of effectively reducing the displacement difference resulting from inverse finite element method reconstruction. Furthermore, it performs well in practical engineering applications.

Flexoelectronics of a centrosymmetric semiconductor cylindrical nanoshell

Cylindrical shell-type semiconductors are essential for sensing and energy harvesting when integrated into surfaces of certain equipment, such as spacecraft, marine devices, and portable electronics, where mechanical forces play a significant impact on charge transport. Traditionally, such functionalities are only manifested in piezoelectric or pyroelectric crystals that possess non-centrosymmetry. Here, we theoretically investigate electronic behaviors driven by strain gradient-induced flexoelectric polarization in a centrosymmetric semiconductor cylindrical nanoshell, expanding the flexoelectronics in shell structures. The governing equations and accompanying boundary conditions are formulated simultaneously using the principle of virtual work and the fundamental lemma of the calculus of variation. Electromechanical interactions through static bending and forced vibration analyses of the newly developed model are systematically investigated. Under localized force excitation, the distribution of mobile charges is manipulated by tuning loading magnitudes and areas. The effects of doping levels on electric potentials and mobile charges are explored to show the interaction mechanism between flexoelectric and semiconducting properties. Moreover, the natural frequencies and modes of all mechanical displacements, electric potentials, and carrier concentration perturbations within the shell are identified. This paper provides a new approach for designing shell-shaped sensors and energy harvesters specifically for centrosymmetric semiconductors.

Three-dimensional deformation monitoring of landslides based on combination of two-track InSAR observations and pixel-level surface-parallel flow model

ABSTRACT Landslides are characterized by intricate formation mechanisms and multiple triggering factors, posing serious threats to human life and property. Interferometric synthetic aperture radar (InSAR) has been extensively applied in landslide monitoring due to its all-weather operation, high precision, and wide spatial coverage. However, one-dimensional line-of-sight (LOS) deformation limits the ability to measure actual landslide displacement. Presently, many regions without the latest descending data, but they are in the overlapping position of two adjacent latest ascending track. Compared to using a single track, the method measuring three-dimensional deformation of landslides, combined with two ascending track InSAR datasets and pixel-level surface-parallel flow (PSPF) assumption, is presented. Based on the small baseline subset (SBAS) InSAR, the LOS deformation in two observations in the middle reaches of the Qingjiang River in China was measured. With pixel-level surface-parallel flow model, the three-dimensional deformation was obtained. It was further converted into the slope surface coordinate system, thus determining the direction of landslide movement. The findings effectively elucidate the primary displacement mode of landslides, with deformation rates ranging from −80 to 20 mm yr − 1 , which are significantly influenced by the slope angle and slope aspect. It is highly important to remotely identify the movement direction and analyse the failure mode of landslides.