Displacement Mode Research Articles

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 HCA method to improve the calculation efficiency of harmonic response topology optimization. In this paper we present a methodology which applies 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 which are respectively utilized as harmonic response analysis methods in this study. The examples under rotating loads demonstrate that the feasibility of this methodology at one specific frequency excitation and multiple frequencies excitation. This paper presents and implements a high convergence efficiency method for harmonic response topology optimization, this method can converge in 20–30 iterations. This method can extend the application range of HCA method and improve the optimization efficiency of harmonic response topology optimization.

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.

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.

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.

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.

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.

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.

An isogeometric approach to dynamic structures for integrating topology optimization and optimal control at macro and micro scales

In the context of active vibration suppression, an integrated topology optimization framework is proposed for the optimal control of dynamic structures. This article formulates a new composite objective function by considering the external harmonic excitations with different excitation frequencies and the complex-valued displacement field. Within the proposed optimal control performance function, the symmetric weighting matrix, the magnitudes of which are related to the importance of the control forces, is integrated into dynamic compliance to serve the state displacement. Utilizing the non-uniform rational B-splines (NURBS) basis functions, the material interpolation model defined at control points is described by the NURBS surface, which is incorporated into the optimization formulation for optimal structural and vibration control design. The sensitivity results are deduced in terms of the pseudo-densities and the corresponding weights at control points from both macro and micro perspectives of structural dynamics. To demonstrate the effectiveness of the integrated topology optimization of dynamic structures at macro and micro scales, several numerical examples, including the topology optimization of solid beams in plane stress and Mindlin plates with 3D microstructures, are provided and discussed in terms of structural shape and topology, frequency response curve, and modal displacement.

Review on the research progress of earth pressure on slope retaining structure

The earth pressure of slope retaining structure is one of the problems that are often encountered in geotechnical engineering but have not yet been fully understood and well solved. At present, there are still a lot of problems that need to be solved. For complex conditions such as stratified soil or containing ground water, the distribution law of earth pressure and the displacement mode of retaining structure need to be further studied. This paper summarizes the existing research on earth pressure of slope retain structures. According to the research methods, it is divided into three categories: research on the theoretical calculation method of earth pressure, research on earth pressure by model test, and research on earth pressure by numerical simulation. Focused discussions are carried out respectively, and the previous research results are summarized. At present, there are still a lot of problems that need to be solved in the research of earth pressure of slope retaining structure, and the calculation formula of earth pressure and the assumed fracture surface of earth are lack of experimental verification and engineering measurement.

Study on damage of CRTS II slab tracks in coated-uncoated transition zones subjected to temperature and train loads

The CRTS II ballastless track is sensitive to temperature due to its longitudinal continuity. The application of reflective insulation coating can efficiently lower the temperature of the track slab, thereby decelerating track deterioration. Given the considerable length of high-speed railway lines, the application of reflective insulation coatings leads to numerous transitions between coated and uncoated sections. This study investigates the influence of reflective insulation coatings on the structural damage of coated-uncoated transition zones in railways. To this end, a CRTS II slab track model involving the bilinear cohesive zone model and the concrete plastic damage model is established. The model examines the combined impact of high temperature and train loading, aiming to investigate the damage patterns within the coated-uncoated transition zone of the track. The results indicate: (1) During high temperature loading, the center of the track slab layer is predisposed to warping compared to the sides. (2) If the cohesion parameter falls below 0.04 MPa, augmenting the cohesion model parameter effectively alleviates track slab arching. (3) In instances where the track slab lacks complete coverage of reflective insulation coatings, train loading may shift the location of the maximum vertical displacement and interface failure mode.

Implementation of matrix compression in the coupling of JOREK to realistic 3D conducting wall structures

Abstract JOREK is an advanced non-linear simulation code for studying MHD instabilities in magnetically confined fusion plasmas and their control and/or mitigation. A free-boundary and resistive wall extension was introduced via coupling to the STARWALL and CARIDDI codes, both able to provide dense response matrices describing the electromagnetic interactions between plasma and conducting structures. For detailed CAD representations of the conducting structures and high resolutions for the plasma region, memory and computing time limitations restrict the possibility of simulating the ITER tokamak. In the present work, the Singular Value Decomposition provided by routines from the ScaLAPACK library has been successfully applied to compress some of the dense response matrices and thus optimize memory usage. This is demonstrated for simulations of Tearing Mode and Vertical Displacement Event instabilities. An outlook to future applications on large production cases and further extensions of the method are discussed.

Equivalent static wind load based on displacement mode and load combination for high‐rise buildings

AbstractUnder the action of the fluctuating wind load, the low frequency part produces background response to the structures, while the high frequency part produces resonance response to the structures. In structural design, equivalent static wind load is usually used to equate the fluctuating wind load. Although there are various methods of evaluating the equivalent static wind load, they did not consider the correlation between modal responses or considered them insufficiently. Therefore, in this paper, the correlation between modal response is considered to evaluate the equivalent static wind load, the displacement response is decomposed by proper orthogonal decomposition (POD) method, the correlation between modal displacement is removed, the equivalent static wind load is expressed in the form of displacement mode, and then the correlation between modal response is fully considered in the extreme value combination. This paper combines the equivalent static wind loads in order to make the wind resistance design more reasonable for high‐rise buildings. First, the formulas of equivalent static wind loads expressed by displacement modes of background and resonant response are deduced based on modal decomposition and POD method. Second, the combination formulas of square‐root‐of‐sum‐square (SRSS) and complete‐quadratic‐combination (CQC) rules for the equivalent static wind loads considering the mean wind loads are proposed. Both the linear combination formula of SRSS for the equivalent static wind load and the weighting factor expressions of background and resonance equivalent static wind load are given. Third, the accuracy and validity of the formulas of equivalent static wind load are verified by a wind tunnel pressure test of a high‐rise building. Finally, the simplified combination coefficient formulas for the equivalent static wind loads are proposed, and the combination of the high‐rise building base's fluctuating equivalent static wind loads of along‐wind direction, across‐wind direction, and torsional direction is analyzed.

Multi-modal control and position optimization of solar panels

This paper investigates the impact of the position of piezoelectric actuators on the vibration control effect of the membrane plane composed of solar sail materials with a given unit area. Firstly, the nonlinear vibration equation of the membrane structure is perfected based on the system equation established by Yifan Lu et al. Then, the modal coupling effect pointed out by Liu Xiang is considered, and the fourth-order modal displacement generated by the piezoelectric actuator in vibration control is derived. Subsequently, the sliding mode controller used in vibration control is designed based on Lyapunov stability theory, and its effectiveness is verified through Simulink simulation. The sliding mode controller is used to calculate the required excitation signal and apply it to the piezoelectric patches. The reverse force is generated through the inverse piezoelectric effect of the patches to actively suppress the vibration of the solar sail. By changing the position and size of each piezoelectric actuator on the solar sail plane, this paper compares the impact of different layout positions on vibration control, and proposes an optimal layout scheme for the position of the piezoelectric patches in terms of control effectiveness.

Morphological analysis of a novel scissor-type deployable cable dome structure

A novel deployable scissor-type strut cable dome structure was proposed, which can improve the lateral stiffness of the traditional cable structure and achieve the characteristics of fast unfolding and closing during construction. However, the geometric stability and optimal initial prestressing theory of traditional cable dome structures cannot be applied to the new structure. Based on the equilibrium matrix theory, the geometric stability analysis was conducted and the number of self-stress modes, mechanism displacement modes, and feasible prestress modes was calculated. Then, the formula for the initial prestress distribution of the structure was derived based on the node equilibrium equation. Furthermore, the geometric stability and initial prestress distribution of the structure with different rise-to-span ratios, number of circumferential struts, and hoop cables were studied. Finally, the dynamic properties of the structure are explored by finite element simulation. The analysis results show that the structure has excellent structural stability. The rise-to-span ratios, the number of circumferential struts, and hoop cables are the important factors affecting the geometric stability and the initial prestress distribution. The rise-to-span ratios have no effect on the number of structural modes, while the number of circumferential struts and cables will cause significant changes in the number of self-stress modes. The internal force of the structural members decreases with the rise-to-span ratio and the number of circumferential struts increases, and the number of circumferential struts has the greatest influence on its internal force. The structural natural frequency exhibits a dense distribution, which indicates that the structure has good stiffness. In summary, the research has provided an idea for the application of the deployable scissor-type strut cable dome structure as a new structural system in the field of structural engineering.

Physical model investigation of a hybrid GRS integral bridge abutment under cyclic thermal stresses

GRS integral bridge abutments develop large lateral earth pressure on the facing during seasonal/diurnal thermal expansion/contraction, causing significant surface settlements. To mitigate these issues, researchers prefer the use of different kinds of facing to withstand lateral pressure in conjunction with reinforcing of backfill to reduce surface settlement. The present research investigates the performance of a hybrid integral abutment under lateral movement of the facing due to cyclic thermal expansion/contraction of the bridge deck through scaled down 1 g physical model tests. Using the optimized facing and reinforcement configuration, an integral abutment model was proposed and analyzed under varying rate of loading and different loading offsets for three displacement modes till 100 cycles of excitation. The assessment included the development of lateral pressure on facing, surface settlement, magnitude and location of peak reinforcement forces, followed by evaluating long-term performance in terms of permanent strains, stiffness degradation, and strain energy dissipation. The observations revealed that the proposed model having strong connection between the reinforcement and facing along with inclusion of secondary reinforcements along the entire height of abutment in the bearing zone exhibits rapid dissipation of accumulated strain energy, leading to a 48 % reduction in surface settlement under cyclic thermal stresses.

Mode selection and combination rules of energy-based multimodal pushover method for simply supported beam bridges

The energy-based method (EBM) has been improved as Energy-based Multimodal Pushover Method (EMPM), and is introduced and verified to be effective and convenient for evaluate the seismic performance of the simply supported beam bridges. This paper mainly focuses on the research of vibration mode selection and combination rules of EMPM. Firstly, the longitudinal vibration modes of simply supported beam bridge are categorized into five cases based on mode shapes, and the case definition is emphasized. Then, corresponding to each case, the Pushover loading force are established, and the modal energy, modal displacement, and modal energy capability curve are proposed. After that, the energy-based demand curve and the corresponding energy coefficient for each case is recommended. Finally, only the mode with maximum mode participation factor (MPF) of each case is suggested to take part in the calculation of the seismic response with the proposed mode participation factor combination rule. Case studies of a practice bridge under Chi-Chi and El Centro earthquake waves are used to illustrate the effectiveness and accuracy of the proposed mode selection and combination rules. The study found that the EMPM with the proposed rules could effectively and rapidly assessing the seismic performance of the simply supported beam bridge, resulting in a 70 % decrease in time consumption compared with the Nonlinear Time History Analysis Method (NTHAM). Compared with the CQC and SRSS combination results, the proposed Mode Participation Factor (MPF) combination rule reduced the maximum relative deviation from 39.4 % to 21.09 % between EMPM and NTHAM for peak displacement. Further research showed that the proposed mode selection approach only uses modes with the highest MPF in each case, decreased the number of modes involved more than 50 % and the result accuracy remained almost identical.