Vibration Response Of Structure Research Articles

Internal resonance induced nonlinear vibration and acoustic radiation of a hyperelastic cantilever structure immersed in fluid

Hyperelastic structures can exhibit peculiar nonlinear vibration and acoustic behavior due to the existence of geometric and material nonlinearities. In order to comprehend the nonlinear vibro-acoustic responses of a hyperelastic cantilever structure configured with internal resonances, a finite element model that considers both the geometric and material nonlinearities in the structure and the finite-amplitude acoustic waves has been developed. The vibro-acoustic problem is described in an arbitrary Lagrangian-Eulerian frame with perfectly matched layers. Based on the finite element model, a loosely coupled serially staggered procedure is applied to solve the nonlinear governing equations. It is found that with large harmonic axial excitation applied to the hyperelastic cantilever structure, the structural vibration undergoes an axial-to-bending transition due to the 2:1 internal resonance, resulting in the variation of acoustic directivity and frequency characteristics. This transition of vibration form occurs quickly when the excitation amplitude is larger or the excitation frequency is closer to the frequency of the axial mode. A threshold of dissipation energy is proposed to determine the transition of the structural and acoustic responses due to nonlinear internal resonance. Saturation of the structural vibration and acoustic responses is observed in the frequency components associated with the first axial mode of the hyperelastic structure, which only exists in the case of the occurrence of the axial-to-bending transition.

Feature extraction and classification of multiple cracks from raw vibrational responses of composite beams using 1D-CNN network

Structures and components need to be constantly monitored to ensure good service life and avoid failures. Structural health monitoring is a wide-ranging concept that tries to ensure the safety of components and structures. Vibration responses of small and large structures contain information about these damages. In the present study, this information is extracted and used to classify the location and severity of cracks. For this purpose, an FE model of Glass Fibre Reinforced Plastic (GFRP) free-free beam is created for beams without any crack and beams with three crack locations and three crack severities. Finite Element (FE) model is validated using modal analysis and is used to generate vibration responses from simulated hammer strikes at different locations on the beam. The vibration data consists of responses of beams that have only one crack present at a time and when two cracks are present. A 1D-CNN network is trained on the generated vibrational responses to classify damage labels assigned for each crack location and crack severity. The network was tested using datasets containing only single crack instances and only dual crack instances. The trained networks were found to be 95% and 93% accurate in determining the damage class respectively. Furthermore, datasets of these two instances combined, containing responses when single cracks and dual cracks are present, were also investigated. These networks had an accuracy of 92%. Hence, in all these instances, the 1D-CNN network classifies the healthy and damaged conditions satisfactorily. There are two advantages of using such a technique. Firstly, this approach simplifies the two-step approach: one for feature extraction and another one for damage prediction into a single step. Secondly, the use of raw vibration data for damage prediction means that real-time damage detection is possible.

Finite element model updating of a plate type structure made of composite material using a network of PZT

Ambient vibrations are one of the most unpredicted, undesired, and uncontrolled destructive causes of sudden failure for many types of structural systems, predominantly those made of FRP thin plates. FRP thin plates may undergo dramatic collapse beneath the periodic ambient loads associated with frequencies, particularly those approaching natural frequencies. Much research has been done over the last few decades to enhance the structural damping behaviour capabilities of thin plates against ambient vibrations via several means and systems of active vibration control. Recent, exceptional advancements in the field of smart materials and their applications in the field of active vibration control have provided a viable alternative to conventional vibration control tools (sensors/actuators). For instance, the coupled properties inherited by PWAS were utilised to develop durable, compact, and efficient actuators/sensors. To minimize the influence of the disparity between the theoretical and actual dynamic structure performances, the numerical FEM has to be updated using real structural data. In the present study, a model update of the structural parameters of a smart beam is carried out by employing PWAS as smart vibration control tools (sensor/actuator) that have been previously installed on the substrate structure. A finite element model is developed to mimic this intelligent beam. Then, laboratory experiments are undertaken to determine system parameters, which are used to update the finite element model. Finally, optimization is done to minimize the FEM variance in the designated structure vibration response from the real one.

A Seven-Parameter Spectral/hp Finite Element Model for the Linear Vibration Analysis of Functionally Graded Shells with Nonuniform Thickness

This contribution presents a finite element shell model capable of performing linear vibration analyses of shell-type structures made of functionally graded material (FGM). The model is based on the seven-parameter spectral/hp finite element formulation, which allows the analysis ofFG shells of either uniform or nonuniform thickness. Equations of motion are derived using the Hamilton’s principle and the material properties of the constituents are considered to follow a power-law volume distribution through the thickness direction. The verification of the present model is carried out by comparing with numerical results available in the literature, and with numerical simulations performed in a commercial software. To demonstrate the capabilities of the present formulation, the free vibration response of different shell structures, with nonuniform thickness, to the variation of the geometrical parameters (e.g., radius-to-thickness ratio) and the mechanical properties is reported.

Theoretical dynamic reduction for steady-state nonlinear vibration responses of complex jointed structures having hysteretic contact behavior

A novel nonlinear dynamic reduction method was developed to determine the steady-state vibration responses of complex jointed structures having hysteretic contact behavior. By using the harmonic balance method to reformulate nonlinear dynamic equilibrium equations into a set of nonlinear algebraic ones, a dynamic reduction technique based on nonlinearity transformation was theoretically developed to iterate nonlinear vibration solutions in the local coordinate that was related only to the degree-of-freedoms of nonlinear joints. Only odd-order harmonic components were truncated to approximate the hysteretic nonlinear contact forces of joint interfaces, which was conducive to further dimension reduction of the nonlinear algebraic equations and iteration matrix. Then, a nonlinear dynamic reduction solver was developed to associate the steady-state nonlinear vibration responses of overall structures with the dynamic characteristics of underlying linear substructures, nonlinear joint models and external excitations. Combined with finite element analysis, the steady-state nonlinear vibration responses of a complex assembled structure with four reduced-order nonlinear joint models were numerically simulated to validate the proposed nonlinear dynamic reduction method by comparing with the literature. The comparative results of nonlinear frequency response functions exhibited good agreement, and the proposed method indicated higher computational efficiency. The experimental investigations of a rubber isolator system were also performed to validate the proposed method, which demonstrated good performance.

Investigating the Ice-Induced Fatigue Damage of Offshore Structures by Field Observations

The oil and natural gas resources of the Bohai Sea are mainly marginal oil fields, and there are currently a large number of structures that are approaching or have reached the end of their service life called aging structures. The interactions between ice and offshore structures could lead to significant ice-induced vibration. Ice-induced vibrations may evoke fatigue damage in tubular joints, which results in severe dangers for offshore platforms in the Bohai Sea. Dynamic ice force models and sea ice fatigue environmental parameters have not been well developed in the current design codes. It is not accurate to evaluate the fatigue damage of structures only with numerical simulation. In this paper, a faster method for evaluating fatigue damage on aging structures is proposed. Firstly, the approximate linear relationship between the fatigue hot spot stress and the vibration response of the deck structure has been discovered using dynamic analysis for jacket platform of Bohai Sea. Then, the procedure of the fatigue damage evaluation of the aging structures in the Bohai Sea is established. Finally, the numerical simulation of the structure is carried out considering ice thickness, ice velocity, ice direction, and action height of sea ice. Fatigue damage is calculated by the fatigue hot spot stress and the Palmgren–Miner rule. The measured data on the platform in the Bohai Sea are selected to obtain the fatigue hot spot stress using a mathematical model. The fatigue damage results considering the actual ice conditions of a jacket structure in the Bohai Sea are compared using the proposed method and finite element analysis. The comparison of the results verifies the rationality of the method proposed in this work.

Research on mapping relationship between environmental load and vibration response of bridge structure based on structural health monitoring data

AbstractWith the increasing lifespan of bridges, various forms of deterioration will inevitably occur. The bridge health monitoring system enables direct monitoring of the loads (such as wind, temperature, and vehicles) experienced by the bridge during operation, as well as the corresponding vibration response of the bridge structure (including main beam deformation, tower top displacement, cable acceleration, etc.). These data provide valuable insights into the safety and durability of the bridge during its operational lifetime. However, the challenge lies in extracting meaningful information from the vast amount of collected data. This article focuses on the Fuyu Bridge as a research case and analyzes the variations in environmental factors, such as temperature, humidity, wind load, and structural vibration responses (main beam and cable), obtained from the Fuyu Bridge's structural health monitoring system. It also conducts a structural safety assessment during the operational period of the bridge. Furthermore, the research explores the relationship between environmental factors, load effects, and structural response to establish a foundation for future structural safety assessments of the Fuyu Bridge during its operational period. For instance, changes in environmental factors or load effects can be used to predict structural responses. Additionally, this study provides access to the structural health monitoring data of the Fuyu Bridge, facilitating data‐driven research for other scholars in the field.

Full-Field Vibration Response Estimation from Sparse Multi-Agent Automatic Mobile Sensors Using Formation Control Algorithm.

In structural vibration response sensing, mobile sensors offer outstanding benefits as they are not dedicated to a certain structure; they also possess the ability to acquire dense spatial information. Currently, most of the existing literature concerning mobile sensing involves human drivers manually driving through the bridges multiple times. While self-driving automated vehicles could serve for such studies, they might entail substantial costs when applied to structural health monitoring tasks. Therefore, in order to tackle this challenge, we introduce a formation control framework that facilitates automatic multi-agent mobile sensing. Notably, our findings demonstrate that the proposed formation control algorithm can effectively control the behavior of the multi-agent systems for structural response sensing purposes based on user choice. We leverage vibration data collected by these mobile sensors to estimate the full-field vibration response of the structure, utilizing a compressive sensing algorithm in the spatial domain. The task of estimating the full-field response can be represented as a spatiotemporal response matrix completion task, wherein the suite of multi-agent mobile sensors sparsely populates some of the matrix's elements. Subsequently, we deploy the compressive sensing technique to obtain the dense full-field vibration complete response of the structure and estimate the reconstruction accuracy. Results obtained from two different formations on a simply supported bridge are presented in this paper, and the high level of accuracy in reconstruction underscores the efficacy of our proposed framework. This multi-agent mobile sensing approach showcases the significant potential for automated structural response measurement, directly applicable to health monitoring and resilience assessment objectives.

Development of a moving vehicle identification framework using structural vibration response and deep learning algorithms

The accurate identification of vehicle position, velocity, and mass on bridges is crucial in the field of structural health monitoring (SHM). Existing methods for moving vehicle identification primarily rely on staged approaches, which may not adequately address multiple vehicle scenarios. This study is the first to propose a framework that simultaneously considers vehicle velocity, mass, and location as supervised learning problems using structural vibration response. The framework comprises three phases: data generation and preparation, network building and training, and prediction. In Phase 1, a labeling strategy is introduced to convert arbitrary moving vehicle scenarios into a unified, trainable format. Phase 2 presents a novel loss function specifically designed to measure the discrepancy between the network output and the label. Lastly, Phase 3 introduces a data post-processing workflow that converts the network output into moving vehicle information. To demonstrate the effectiveness of the proposed method, the identification accuracy is quantified and analyzed using five different indexes under different vehicle numbers, velocity intervals, and mass intervals. Furthermore, the influences of some key variables, the modeling error and model simplification are discussed in detail. The proposed approach surpasses conventional methods by overcoming staged identification limitations and accommodating multiple vehicles, while efficiently identifying their velocity, mass, and moving range on the bridge without requiring initial conditions.

Electromechanical coupling enriched finite element method for dynamic characteristic of piezoelectric materials structures

To improve the application depth and breadth of intelligent unit devices made from piezoelectric structures, their kinetic properties shall be urgently studied. Herein, based on the basic equations and boundary conditions of piezoelectric materials, an interpolation coverage function of node displacement was introduced into the displacement shape function and potential shape function of coupling electromechanical finite element method (FEM), forming an electromechanical coupling enriched FEM generalized shape function. Together with the variation principle, an electromechanical coupling enriched FEM was put forward, and its motion equations were deduced. Next, the free vibration and transient response of the piezoelectric structure were analyzed, and the accuracy and validity of the new method were validated with numerical cases. Results show this method has high application prospects for analyzing the dynamic properties of piezoelectric material structures.

Active vibration control of composite laminates with MFC based on PID-LQR hybrid controller

Due to the high vibration sensitivity, the flexible composite structure is prone to vibration and structural deformation, thus it is necessary to study active vibration control to improve its performance. Based on the idea of the PID control and LQR control, a PID-LQR hybrid controller is proposed in this article. It is proved that the hybrid controller has better control performance by simulating the structural vibration response under various excitation conditions. Finally, the effectiveness of the hybrid controller is verified by the active control experiment, and the vibration response is reduced by about 31.55% after control.

Joint parameter-input estimation for digital twinning of the Block Island wind turbine using output-only measurements

This paper presents a recursive Bayesian inference framework for digital twinning of an offshore wind turbine (OWT) in the Block Island Wind Farm (BIWF), the first commercial offshore wind farm in the U.S. with jacket substructure. The framework employs a window-based extended Kalman filter (EKF) to jointly estimate the dynamic input loads and unknown model parameters of the finite element (FE) model of the turbine using sparse output-only measurements. The estimation of input loads on the OWT is critical for fatigue life estimation, foundation monitoring and control strategy. In the proposed joint estimation algorithm, unknown input time histories are divided into overlapping windows and the current window of inputs is concatenated with uncertain model parameters to form an augmented state vector. To account for the uncertainty about wind direction and misalignment between wind direction and the turbine yaw angle, two independent horizontal wind load time histories in X and Y directions are estimated at the nacelle level. A numerical validation study is first performed in which wind loads of the OWT are simulated using the multi-physics platform FAST, and structural vibration responses are generated using the FE model in OpenSees. The window-based EKF is implemented using the simulated measurements, and the estimations of structural stiffness as the updating model parameter and input loads are observed to have high accuracy. The proposed algorithm is then validated using in-situ measurements on one of the OWT in BIWF. To investigate the effectiveness and robustness of the method under different environmental and operational conditions, four cases are considered in which the turbine is operating at the rated rotor speed (region 3 of power generation), below the rated rotor speed (region 2), idling rotor state (region 1 or no power), and region 4 beyond cut-out wind speed. Accurate predictions of acceleration and strain data are obtained using the proposed algorithm, and the estimations of model parameter are consistent and close to their nominal value under different conditions. These results from numerical and experimental studies validate the proposed window-based EKF for joint parameter-input estimation and digital twinning for long-term structural health monitoring of the OWT.

Long Short-Term Memory Network for Predicting Wind-Induced Vibration Response of Lightning Rod Structures

Lightning rod structures are susceptible to wind loads due to their high slenderness ratio, high flexibility, and light weight. The wind-induced dynamic response of a lightning rod is critical for structural safety and reliability. The traditional methods for this response, including observation and simulation, focus on structural health monitoring (SHM), wind tunnel tests (WTTs), or fluid–structure interaction (FSI) simulations. However, all these approaches require considerable financial or computational investment. Additionally, problems such as data loss or data anomalies in the sensor monitoring process often occur during SHM or WTTs. This paper proposes an algorithm based on a long short-term memory (LSTM) network to predict the wind-induced dynamic response and to solve the problem of data link fracture caused by abnormal sensor data transmission or wind-induced damage to lightning rod structures under different wind speeds. The effectiveness and applicability of the proposed framework are demonstrated using actual monitoring data. Root-mean-squared error (RMSE), determination of coefficient (R2), variance accounted for (VAF), and the refined Willmott index (RWI) are employed as performance assessment indices for the proposed network model. At the same time, the random forest algorithm is adopted to analyze the correlation between the data of the different measurement points on the lightning rod structure. The results show that the LSTM method proposed in this paper has a high accuracy for the prediction of “missing” strain data during lightning rod strain monitoring under wind speeds of 15.81~31.62 m/s. Even under the extreme wind speed of 31.62 m/s, the values of RMSE, MAE, R2, RWI and VAF are 0.24053, 0.18213, 0.94539, 0.88172 and 0.94444, respectively, which are within the acceptable range. Using the data feature importance analysis function, it is found that the predicted strain data of the measurement point on the top part of the lightning rod structure are closely related to the test strain data of the two adjacent sections of the structure, and the effect of the test strain data of the measurement points that are far from the predicted measurement point can be ignored.

A Semi-Analytical Approach for the Linearized Vibration of Clamped Beams with the Effect of Static and Thermal Load

The geometric nonlinearity due to static and thermal load can significantly alter the vibration response of structures. This study presents a semi-analytical approach to illustrate the nonlinear vibration of clamped-clamped beams under static and thermal loads. The von Karman strain and Hamilton’s principle are employed to derive the nonlinear static equilibrium equation and nonlinear governing equation. The vibration equation’s coefficient is variable. The transfer-matrix method and local homogenization are used to solve the equation. The proposed method’s accuracy is validated by commercial software and literature. The numerical results indicate that uniform stress caused by thermal load only reduces the structural mode frequencies. The geometric nonlinearity of the structural static deformation affects both the mode frequencies and mode shapes. And the mode shapes cannot be approximated by harmonic functions. When the static deformation is significant, the structure’s local RMS response is substantially affected. The combined loads have a more significant impact on the acceleration response than the superposition of individual load effects.

Oil–water two-phase flow-induced vibration of a cylindrical cyclone with vortex finder

Cylindrical cyclones play an important role in oil–water separation and sewage treatment in the petroleum industry. Here, we describe the characteristics of vibration induced by a two-phase rotational flow in a cylindrical cyclone. The cyclone operating parameters together with a dimensional analysis and multiphase flow numerical simulation were used to understand the flow field characteristics. The frequency and amplitude of pressure fluctuation were obtained by measuring pressure changes at points on the axis of the device. It shows that the pressure in a cylindrical cyclone varies periodically during separation and that fluctuation frequency and amplitude are related to the inlet velocity and flow split ratio. The effect of the overflow split ratio on the pressure fluctuation frequency is negligible, but increasing the overflow split ratio will cause greater fluctuation of the flow. For a cylindrical cyclone, the pressure fluctuation frequency can be calculated from the inlet velocity. Adjusting the inlet velocity and the overflow split ratio changes the mechanical response of the structure. The results of a modal analysis show that the structural vibration response is consistent with the response state of the lowest point of the internal central-vortex pressure and that both are in approximate circular motion. Furthermore, the frequency of pressure fluctuation induced by the flow is close to the intrinsic frequency of the structure with a single bottom constraint, which can cause unwanted resonance easily. Therefore, an appropriately added constraint on a cylindrical cyclone should be taken into consideration to avoid the resonance frequency.

Predicting range-dependent underwater sound propagation from structural sources in shallow water using coupled finite element/equivalent source computations

Predictions of underwater sound propagation (USP) from structural sources in complex shallow-water environments are crucial for underwater navigation, communication, and localization. Modeling range-dependent USP in shallow water remains challenging because structural acoustic radiation is coupled with complex waveguide physics. This paper presents a coupled finite element (FE)/equivalent source (ES) computation scheme for predicting the range-dependent USP from a structural source. The scheme involves coupled vibroacoustic FE/ES analyses and waveguide-field ES computations. The former computes the structural vibration response and reproduces the structural-acoustic radiation at arbitrary spatial positions. The coupled vibroacoustic FE/ES analysis provides the input for the waveguide-field ES computations, which couple the structural-acoustic radiation with the shallow-water environment. A multilayer acoustic–elastic ES method (ESM) is developed to accommodate sound speed inhomogeneities and a range-dependent elastic seabed. Numerical simulations demonstrate the interactions of structural-acoustic radiation with two-dimensional topographies and internal solitary waves. The proposed scheme is extended to three dimensions by combining the coupled vibroacoustic FE/ES analysis with a pre-corrected fast Fourier transform-accelerated ESM. The results validate the proposed scheme and demonstrate its benchmark-quality solutions and high numerical efficiency, suggesting great application potential for optimizing the sonar performance at the preliminary design stage.

Self-tuning vibration control using piezoelectric patches and RL shunts set to maximise electric power absorption

This paper presents experimental results on the flexural vibration response of a thin plate structure subjected to a stochastic disturbance. The plate is equipped with five piezoelectric patches connected to shunt circuitry to reduce the resonant response of a target flexural mode. The shunts are synthesized digitally to mimic a resistor-inductor connected in parallel. Firstly, the study assesses the vibration control effects produced by the shunts, contrasting the time-averaged flexural kinetic energy of the panel and the time-averaged electric power absorbed by the shunts filtered in a narrow band centred on the resonance frequency of the target mode. This analysis shows that both cost functions results on the same optimal tuning parameters, which provides a benchmark for the vibration control. Next, it investigates the online tuning of the resistive and inductive components of the shunt by implementing an extremum seeking algorithm set to maximise the time-averaged electric power absorbed locally by the shunt filtered in a narrow band centred on the resonance frequency of a target mode. The study shows that indeed the resistive and inductive components in the shunts connected to the five patches converges to the optimal values with the application of extremum seeking algorithm and this leads to a minimisation of the spectral flexural response vibration at the resonance frequency of the target mode by 18 dB.

Research on Dynamic Response of Cold Rolling Mill with Dynamic Stiffness Compensation

The vibration of the vertical system of a cold rolling mill is a major concern for factory production. In factory production, it is found that the thickness control system with dynamic stiffness compensation of the rolling mill has a significant impact on the rolling mill vibration. In this work, a mechanical hydraulic coupling vibration model of a cold rolling mill with a thickness control system with dynamic stiffness compensation was established. MATLAB/Simulink was used to simulate and analyze the vibration response characteristics of the mechanical structure of the rolling mill and mechanical hydraulic coupling system considering the dynamic stiffness compensation control mode and position control mode of the upper cylinder. We found that the control system changed the vibration response of the mechanical structure, and different control modes have different effects on the vibration response curve. When the rolling mill works in the vibration area, the thickness difference at the strip steel outlet would be larger. Considering the rolling mill vibration and strip surface quality, the excitation of the strip inlet thickness can be achieved by adjusting the dynamic stiffness compensation system and changing the rolling speed reasonably to achieve good vibration suppression and control effects.

Influence of Integrating Stiffening Grid Honeycomb Structure in Syntactic Foam Core on Structural Vibration Response of Sandwich Composites

Influence of Integrating Stiffening Grid Honeycomb Structure in Syntactic Foam Core on Structural Vibration Response of Sandwich Composites

Influence of external load on forced vibration of rectangular plate

Rectangular plate is one typical structure with wild application in engineering, and the force vibration is the basis for analysis of sound radiation of plate. In this work, numerical simulation is conducted for force vibration of rectangular plate, and the influence of external load is also studied. Numerical results show that, the rectangular plate will resonate under external load at certain driven frequency, and it’s strictly related to structural modal frequencies. Structural vibration response will change obvious with the change of location of external load. When the location is fixed, with the increase of action region of external load, the acceleration of plate will decrease and some new resonance frequencies will be observed. Conclusions here will lay foundation for further work on sound radiation of plate.