Vibration Response Of Structure Research Articles

Experimental study on modal analysis and vibration response of tunnel structures under different damage conditions due to subway train loads

Based on a prototype of the Beijing subway tunnel, this research conducts large-scale model experiments to systematically investigate the vibration response patterns of tunnels with different damage levels under the influence of measured train loads. Initially, the polynomial fitting modal identification method (Levy) and the model test preparation process are introduced. Then, using time-domain peak acceleration, frequency response function, frequency-domain modal frequency, and modal shape indicators, a detailed analysis of the tunnel’s dynamic response is conducted. The results indicate that damage significantly amplifies vibration acceleration, with the amplification increasing with the severity of the damage. When the crack lengths are 2 cm, 4 cm, and 6 cm, the peak acceleration increases by 25.12%, 36.35%, and 50.29%, respectively, while adjacent segments show increases of 13%, 29%, and 45%. Damage decreases the tunnel structure’s modal frequency, with the first two modal frequencies showing the most significant reductions of 9.87% and 7.34%, respectively. The adjacent segments show reductions of 7.7% and 4.2%. As the severity of the damage increases, the amplitude of the modal shape at the damaged location also increases, with the first modal shape rising by 43.37% for 4 cm damage compared to 2 cm damage and by 72.21% for 6 cm damage. The second modal shape increases by 9.04% and 26.51%, respectively. Additionally, the effectiveness of the polynomial fitting modal identification method (Levy) for tunnel structural damage detection was validated. Finally, based on the methods outlined above, the tunnel responses measured on-site in the Beijing metro were also analyzed. The findings of this study provide important theoretical support for the assessment and routine maintenance of metro tunnels.

Time-Domain Load Identification and Dynamic Displacement Inversion of Discharge Sluice in Large Hydropower Stations Based on the Conjugate Gradient Least Squares Iteration Algorithm

The identification of flow-induced vibration loads is the key to solving the vibration problem of hydraulic structures induced by high-speed water flow. In this study, a time-domain load identification method for discharge sluices in large hydropower stations based on the conjugate gradient least squares (CGLS) iteration algorithm is proposed. The main idea of this method is to first construct a mathematical model through the response signal and the structural modal parameters for solving the equivalent load acting on the sluice structure. Then, it uses the iterative regularization method to solve the ill-posed problem in the load identification process of the traditional time-domain method. Numerical simulations show that, in comparison to the traditional Tikhonov regularization algorithm, the CGLS algorithm is capable of reducing the relative error of the identified dynamic loads by approximately 100%, with higher accuracy and noise immunity. In this study, the CGLS algorithm is used to identify the external dynamic loads acting on the sluice structure during the flood discharge process of a large hydropower station in China. Three equivalent dynamic loads acting on the pier and the bottom plate are obtained. The positive analysis of the vibration response of the discharge structure is conducted using the equivalent load. The results show that the error between the measured vibration response signals and the vibration response signals obtained from the positive analysis is relatively minor, with the exception of a few individual measurement points. The displacement response mean square error is less than 10%, thereby substantiating the accuracy and validity of the CGLS load identification method proposed in this study in the actual engineering.

Lost data reconstruction for structural health monitoring by parallel mixed Transformer-CNN network

Transformer-based and convolutional neural network-based deep learning methods have been extensively utilized to reconstruct lost data for structural health monitoring. However, the lack of inductive bias in Transformer and the fixed receptive fields of convolutional neural network (CNN) limit their local and global modeling capabilities, respectively. The traditional method of combining the two in series creates a sequential relationship and interdependence, negatively impacting reconstruction accuracy. To address this problem, this paper proposes a novel parallel mixed Transformer-CNN network. By parallel connecting the shifted window transformer and densely connected convolutional block, both can process structural vibration responses simultaneously and independently, leveraging the locality of convolution to address the inductive bias of Transformer. Experiments on real acceleration data from the Canton Tower validate its effectiveness. Compared with models using only Transformer or CNN, the reconstruction errors are reduced by 56% and 17%, respectively. The modal parameters extracted from the reconstructed data are highly consistent with those from the true data, and our model has good robustness to lost rates and noise.

Dynamic performance assessment of offshore wind structures based on root morphology model

Assessing the dynamic performance of offshore wind turbines (OWTs) is crucial for their safe operation and maintenance. To evaluate the structural dynamic performance, traditional methods rely on the reanalysis of damage models, leading to the lack of the real-time capability. Therefore, this paper presents a structural dynamic performance assessment technology based on the root morphology model to address such issue. The approach is developed to synergize data fusion-based and environmental condition classification-based dynamic performance assessment technologies. The data fusion-based method, using optimized VMD for denoising and ARMA models for free response signals, enables real-time dynamic performance assessment by tracking changes in AR coefficients over time. In parallel, the environmental condition classification-based method employs wind speed and wave height monitoring data to classify structural response data into multiple healthy sub-databases. Subsequently, Extenics is applied to compute the correlation between the data to be evaluated and the performance state levels based on the classified data, providing a precise evaluation of the structural dynamic performance. Finally, these two technologies are integrated through root morphology models, which fully consider structural vibration response data and environmental monitoring data. To verify the real-time and reliability of the proposed method, field study has been carried out on a 4 MW monopile OWT during the passage of Typhoon 'In-fa'. Results indicate that the root morphology model-based assessment technique effectively evaluates the impact of typhoons on the dynamic performance of OWTs. Further, a rose diagram for the dynamic performance assessment of OWTs is drawn to achieve real-time evaluation of OWT dynamic performance, which has certain engineering significance to guarantee the safe operation of OWTs and reduce the cost of operation and maintenance.

Influence of bolt preload degradation on nonlinear vibration responses of jointed structures

The clamping performance of bolted joints was gradually degrading under long-term vibration loads, which induced a great impact on the stick–slip friction contact behavior of bolted joint interfaces. In this paper, a time-varying Iwan model was developed to reproduce the tangential hysteresis behavior of bolted joint interfaces by considering preload degradation. A three-degree-of-freedom mass–spring-damper oscillator was numerically simulated to investigate the influence of preload degradation on nonlinear vibration responses, as well as the experimental investigations of a bolted joint structure. The comparison results showed that the proposed model could well describe the effects of preload degradation on the stick–slip friction contact behavior of bolted joint interfaces. The numerical results revealed the nonlinear effects of preload degradation on the frequency response functions (FRFs), which demonstrated good agreement with experimental results.

A strain transmissibility-based analysis approach for operational modal of concrete dam under nonstationary excitation

The transmissibility-based operational modal analysis (TOMA) method is attracting more attentions due to its relaxation of assumptions about excitation properties, making accurately identifying the modes of actual engineering structures possible. However, in specific application on distributed vibration responses of huge hydraulic structures excited by broad-spectrum non-stationary earthquake, more proper selections of data segmentations on two dimensions (along time or spatial axis) are needed. Based on the concept of distributed vibration sensing optical fiber strain transmissibility, the operational modal analysis model based on single reference and poly references transmissibility under the strain format and the corresponding solutions of model and modal parameters are studied. A false mode elimination method combined with the continuity of spatial distribution of optical fiber measurements, a response sequence set optimization method that comprehensively consider amplitude/PSD non-stationarity, and the principle about how to select (non) reference points (sets) considering the spatial distribution of measurement signal-to-ratio are further developed. The case study shows that the proposed combined method could improve the modal parameter identification accuracy of concrete dams under broad-spectrum non-stationary excitation, and the distributed optical fiber vibration sensing technology can provide a rich (non) reference point (set) selection combination for this method.

Flow field characteristics and vibration responses of saddle-shaped membrane structures

Elastically mounted flexible membrane roofs exposed to flows are prone to vortex-induced vibrations and even aero-instability due to the strong fluid–structure interaction (FSI). This study is to investigate the FSI mechanism in the saddle-shaped membrane structure over a range of Reynolds numbers and wind directions in laminar flows, by bridging structural vibration responses and flow dynamics. The aeroelastic characteristics of membrane structures, including statistics of displacement responses, oscillation frequency, and oscillation damping ratios, were identified from the perspective of time and frequency domains. Simultaneously, the particle image velocimetry system was employed to visualize the flow features, including velocity vector, turbulence intensity, and vortex evolution in both space and time. The flow modes were further decomposed by proper orthogonal decomposition (POD) to capture the salient aspects of the flow. Three patterns of POD modes are identified, and the first mode plays the dominant role in POD modes. It showed that as the wind Reynolds number increases, the space between the shear layer and membrane surface would be narrowed, and resultantly the vortices turn out smaller in scale and closer in space. This trend leads to an increase in the frequency of vortex shedding and a stronger FSI effect. When the frequency of vortex shedding approaches the fundamental frequency of structures, the vibration of the membrane would be shifted from turbulent buffeting to vortex-induced resonance, featured with lock-in frequency, significant amplified displacement, and negative aerodynamic damping ratio.

An improved solution of the probability density evolution equation for analyzing stochastic structural responses with adaptive time steps and initial conditions

The probability density evolution method (PDEM) offers an innovative approach for analyzing the stochastic vibration responses of structures. Given the complexities inherent in real-world challenges, the probability density evolution equations (PDEE) often require numerical methods for effective resolution. Consequently, improving computational efficiency and solution accuracy is of paramount importance. Currently, the impulse function discretization method (IFDM) faces several challenges, including limited differentiability in the spatial direction for initial value conditions. Furthermore, the probability density function produced by this method frequently deviates significantly from the true value, undermining the accuracy of the PDEE. Additionally, when addressing vibration responses characterized by rapid evolutionary velocities, the use of a globally fixed uniform time step size (FUTSS) results in a marked decrease in computational efficiency. To tackle these challenges, this study introduces an improved probability density evolution method (IPDEM), which integrates the Gaussian kernel density estimation discretization method (GKDEDM) and an adaptive non-uniform time step size (ANUTSS). The advantages of the IPDEM are illustrated through two numerical simulation examples. The findings indicate that the GKDEDM not only enhances spatial differentiability but also provides a more accurate estimation of the probability density at the initial moment, thereby improving the accuracy of the PDEE. Furthermore, the ANUTSS significantly reduces the number of iterations required while preserving precision, leading to a substantial optimization of computation time.

A boosted deep learning-based approach for near real-time response estimation of structures under ground motion excitations

This article presents an improved Convolutional Neural Network (CNN)-based approach to predict the vibration response of structures under seismic events without installing sensors at different stories. To do so, three different benchmark buildings, including a Single Degree of Freedom (SDOF) system, a two-dimensional three-story steel moment-framed structure, and a three-dimensional three-story steel structure, were used to validate the proposed framework. A suite of 111 ground motion records, which was originally developed by the SAC project and FEMA P695 instruction, was used to generate a generalized dataset. These records were uniformly scaled to 18 different peak ground accelerations, from 0.05 g to 1.7 g, to ensure the generalization of the dataset in terms of seismic intensity. A strengthened CNN was introduced to provide a prediction model capable of estimating the acceleration, velocity, and displacement histories of the buildings under earthquake records. This network receives not only the ground motion records as the input attribute but also catches additional features such as spectral accelerations at 0.2s and 1.0s as RGB values of colourful images. Results indicate that the proposed algorithm is reliable in estimating the response histories of the buildings under linear and nonlinear conditions.

Active Control for Construction Stability of Suspension Arch Rib Segments Based on ARID System

In response to the issues of vibrations affecting the construction safety, speed, and accuracy of suspended structures due to dynamic disturbances during lifting, environmental disturbances, and improper operator actions, this paper investigates the application of the Active Rotary Inertia Driver (ARID) system for double-rope suspended structures, namely analyzes, and applies control to the vibration response of double-rope suspended structures under external excitations. Taking the double-rope suspended structure as an example, a dynamic analytical model of the double-rope suspended structure is established based on D’Alembert’s principle. Through shake table tests, the dynamic response characteristics and vibration control effects of the double-rope suspended structure under various external excitations are studied, and the influence of the twisting radius of the suspended structure on the control effect is analyzed. The experimental results show that the ARID control system achieves significant control effects on the swing and torsional vibrations of the suspended structure, which validates the accuracy of the theoretical model for the ARID control system and demonstrates its feasibility for practical applications.

Numerical Simulation Study on Vibration Characteristics and Influencing Factors of Coal Containing Geological Structure

Accurately determining the natural frequency of coal-containing geological structures is crucial for preventing mine dynamic disasters and utilizing vibration waves to break coal and enhance its permeability. Based on the modal theory of rock, vibration models of coal-containing geological structures, including layering and fractures are established. By analysis, the undamped vibration equation and its characteristic equation for both the layered coal system and the fractured coal system are derived. Subsequently, the Lanczos method is employed to solve the system’s vibration modes using ABAQUS. The effects of the layering position, layering thickness, layering physical properties, crack width, and crack length on the natural frequency and vibration response of coal-containing geological structures are investigated. The results indicate that when a single influencing factor is altered, the displacement response distribution of the coal body vibration system with geological structures remains essentially the same, and these single influencing factors have a minimal impact on the vibration displacement of the coal-containing geological structure. The natural frequency of the system decreases exponentially as the distance between the layering and the geometric center of the coal system with geological structures increases. The presence of layering in the coal system with geological structures significantly reduces the system’s natural frequency. The natural frequency of the coal system with geological structures increases in a power function manner as the layering elastic modulus increases. Conversely, the natural frequency decreases with an increase in crack length. When the change ranges of crack width and bedding thickness are the same, the natural frequency of the fractured coal body system exhibits more significant changes. The natural frequency of the coal system with geological structures initially decreases and then increases as bedding thickness and crack width increase. The trend in the natural frequency changes and the position of the extreme point are related to the ratio of the elastic modulus and density of the geological structure.

Wind-induced vibration response of supertall sightseeing tower evaluation during construction through wind tunnel test of aeroelastic models

Four construction phases of an ultra-high sightseeing tower with a cable-barrel composite structure and their wind-induced vibration response were studied. The first-order natural vibration characteristic of the structure in four different construction phases was calculated through finite element models, and associated aeroelastic models were also designed. Meanwhile, rough strips are applied uniformly on the surface of the model to compensate the Reynolds number of the wind tunnel test. The performance of this method was investigated utilizing the pressure test of rigid segment models. The wind-induced vibration response under four construction conditions, and the effects of wind direction angle, wind speed and structural damping ratio were investigated through the wind tunnel test of aeroelastic models. The results show that sticking rough strips on the surface can effectively improve the Reynolds number of wind tunnel tests. As the wind speed during construction increases, the structural wind-induced vibration response intensifies. A large vortex-induced resonance occurs in the construction phase of a cable-barrel composite structure with the Strouhal number around 0.12 under turbulent conditions in this study. Furthermore, the crosswind-induced vibration response of the structure at a wind deflection angle of 0° is greater than 45° and 90°. Specifically, the mean value of downwind displacement and the maximum value of standard deviation (STD) of downwind and crosswind displacements on the prototype tower top at 0° during construction phases are 1.21 m, 0.35 m, and 0.25 m respectively. Thus, the risk of large wind-induced vibration should be fully considered during construction. Implementing corresponding damping measures to improve the damping ratio of the structure proves effective in restraining its vibration.

Finite element method numerical modeling of the crack's impact on the free vibration of 2D functionally graded beams on the Pasternak-Winkler elastic foundation

The study's contribution is to examine, while taking into account pinned-pinned boundary conditions, the free vibration response of multi-cracks Euler-Bernoulli perfect FG beams structure on Pasternak-Winkler elastic foundations. The finite element approach is used to discretize the equations. The material properties are taken into account using a power-law form, and they differ in the thickness and width directions of the beam structure. The 2D FG beam's reduced cross section is used to calculate the stiffness of the cracked structure. On the other hand, the Pasternak-Winkler type foundation has a longitudinal distribution and makes the system stiffer. For convergence research, the numerical results are compared with the outcomes of earlier investigations in terms of dimensionless fundamental frequencies. Case studies were carried out to examine the effects on the natural frequencies of the beams structure of the power law index, multi-cracks, depths, location, and Pasternak-Winkler-elastic foundation. These studies demonstrate the benefits of the two-dimensional FG beam in the presence of cracks over the unidirectional FG and pure metallic beams.

Research on vibration response distorted similitude of cylindrical shells under modal distribution disorder

Similitude theory enables local-scale models to reflect the dynamic characteristics of full-scale models and is widely employed in engineering experimentation. However, shell structures, constrained by wall thickness, cannot undergo experiments through proportional downsizing. Existing similitude studies with retained wall thickness exhibit only minimal distortion, and accurate prediction of vibration responses is hindered by modal distribution disorder. To address these challenges, a method based on modified frequency response functions of natural frequencies and mode shapes is proposed. Scaling laws for natural frequencies and mode shapes of cylindrical shells with retained wall thickness are established. This method yields a maximum prediction error of 4.29 % for prototype natural frequencies, compared to 50.57 % for existing methods. Predicted prototype vibration acceleration responses correspond well with theoretical calculations in both frequency and amplitude, while existing methods fail entirely. The phenomenon of modal distribution disorder and the effectiveness of the proposed method in mitigating it are verified by modal experiments and response tests. Research reveals that the sensitivity of different modal frequencies to the wall thickness scaling factor varies, serving as the cause of modal distribution disorder. The modal distribution with the same circumferential wave number is unaffected by wall thickness. Modes above the bending frequency, with axial half-wavelength consistent with bending modes, are prone to disorder due to wall thickness distortion. During wall thickness distortion, a mode originally with the lowest frequency is surpassed towards lower frequency by the mode with larger circumferential wave number and the same axial half-wave number, leading to disorder. The proposed method addresses the challenge of minimal distortion in structural vibration response and poor performance, advancing the development of distorted similitude.

Reconstructed source method for underwater noise prediction of a stiffened cylindrical shell

The absence of excitation characteristic parameters significantly hinders the efficacy and precision of underwater noise predictions, especially under multiple excitations. Addressing this issue, a novel noise prediction reconstructed source method has been proposed for the noise analysis of a stiffened cylindrical shell. This method diverts attention from the actual sources and reconstructs the source utilizing the shell's vibrational response and transfer functions. The structural vibration response induced by the reconstructed source remains congruent with the actual behavior. The issue of non-unique solutions inherent in the reconstructed source is resolved through the application of the least squares principle. With the reconstructed sources and the stability of the transfer functions, underwater noise prediction becomes readily attainable. The method has been substantiated via an experiment from a stiffened cylindrical shell. The results indicate that the noise predictions derived from the reconstructed source method exhibit excellent agreement with experimental data, the overall level error of noise prediction is up to 0.7 dB. Furthermore, in comparison to the BEM, this method significantly enhances the efficiency under identical computational settings, with the prediction duration constituting a mere 1% of that required by the BEM.

Influence of surface roughness on vibration response characteristics of flexible structures on offshore floating platforms

The expanding interest in floating offshore renewable energy technologies, including floating wind turbines and solar platforms, is attributed to their multifarious benefits. One pivotal factor influencing the power generation efficiency of these technologies is the vibration response of the flexible structures connected to the platforms, such as mooring systems, dynamic power cables, and flexible pipelines. In this research, a numerical investigation is conducted on the response characteristics of vortex-induced vibration (VIV) of cylinders with varying surface roughness in oscillatory flow. The unsteady Reynolds-averaged Navier-Stokes (URANS) equations and dynamic equation are used for fluid-structure interaction. The results reveal that for rough cylinders, multiple frequencies are involved in the vibration. For most simulated cases, the vibration frequency in the cross-flow (CF) direction is an integer multiple of the frequency of the oscillatory flow and associated with the quantity of shedding vortex pairs during a single period of the oscillatory flow. For rough cylinders, the CF vibration frequency differs by one from the number of shedding vortex pairs within one period of the oscillatory flow. With the increase of surface roughness, the maximum vibration amplitude shows an increasing trend (12%), then a decreasing trend (21%). Furthermore, the vortex shedding flow pattern presents C + S mode or S mode. This study offers valuable insights for analyzing the vibration response characteristics of authentic flexible structures.

Automatic damage detection and data completion for operational bridge safety using convolutional echo state networks

Structural response data might be partially missing during acquisition and transmission by a structural health monitoring (SHM) system, affecting subsequent structural damage identification. Conventional deep learning methods require a substantial amount of data and have low training efficiency. With this in mind, this paper proposes a hybrid approach for data reconstruction and damage identification using an echo state network embedded with convolutional layers. The network has a training-free reservoir layer and focuses on historical information and multi-channel spatial features. As data redundancy occurs in most measured structural vibration responses, the extended Frobenius norm-principal component analysis method is applied to select valuable samples for updating the network, which greatly enhances the training efficiency. Experimental and numerical data from a physical bridge model is used to verify the data reconstruction capability and damage identification accuracy of the proposed method, and its performance is further compared with several existing deep learning methods.

Numerical simulation for pressure fluctuations caused by the growth of a single boiling bubble

The pressure fluctuations caused by the rapid volume changes during the initial growth stage for a single bubble are crucial excitations of boiling induced vibration. Therefore, it is necessary to accurately model the dynamic behavior of bubbles during this stage to obtain reasonable excitation forces, which can be used to estimate the vibration response of structures. The present study develops a dynamics model, which is verified and validated to be applicable to the growth of spherical bubbles in infinite superheated liquid and hemispherical bubbles growing on a vertical heated surface. The effects of mass transfer are considered for the vapor-liquid interface motion, and the temperature variations at the liquid side are determined by the finite difference method. The numerical data match well with the theoretical and experimental results, and the characteristics of the excitation forces caused by a single boiling bubble are obtained and analyzed. In addition, the influences of superheat, accommodation coefficient for phase change, and the temperature gradient at the liquid side on excitation forces caused by bubble growth are studied. The results show that the temperature distributions near the heated surface strongly affect the frequency domain characteristics of the excitation forces.

Multiscale modeling of friction hysteresis at bolted joint interfaces

Friction at connection interfaces plays an important role in understanding the nonlinear vibration response of jointed structures. A reliable friction contact model capable of reproducing nonlinear behaviors at the friction interface is critical in the design and optimization of jointed structures. In this paper, a multiscale friction model is proposed. This approach provides a novel perspective for improving prediction accuracy by combining the predictability offered by a physics-based model and the convenience of a phenomenological model. Specifically, this method considers the actual topography of joint interfaces by measuring the three-dimensional (3D) topography data with high-resolution instruments. The surface topography data is then processed to obtain the geometry data at different scales, and the finite element method is used to determine the physics-based multiscale contact pressure distribution of surfaces. The twofold Weibull mixture model is used to represent the contact pressure distribution and further determine the Iwan density function. The effectiveness of the proposed approach is validated by comparing the model predictions with the experiment results of a new as-built structure. Moreover, the effects of the surface roughness and waviness on the friction behavior are discussed.

Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the finite element method enriched by proper enrichment functions

In this study, a carefully designed enriched finite element method (EFEM) is presented to improve the solution accuracy of the conventional FEM by analyzing the dynamic behavior of the magnetic-electric-elastic (MEE) composite structures, which are frequently used in designing various smart and intelligent devices. By formulating the proper EFEM with ideal numerical performance, different enrichment functions are considered and the corresponding solution quality of different versions of the EFEM is compared and examined in great detail. When the Lagrange polynomial basis functions together with the harmonic trigonometric functions are used as enrichment functions, the obtained EFEM shows extremely powerful and ideal numerical performance, which is obviously better than the other versions of EFEM and the conventional FEM, in studying the free vibration and harmonic frequency responses of the MEE structures. Nearly exact numerical solutions for three-phase physical fields of MEE structures can be generated by the proposed EFEM even if very coarse mesh patterns are used. Intensive numerical studies are conducted to confirm and verify the excellent properties of the proposed EFEM in performing dynamic analysis of the MEE structures.