Flexible Plate Structure Research Articles

Mayfly Algorithm for Modelling a Horizontal Flexible Plate Structure

Flexible plates are widely used in engineering and the industry, primarily due to the lightweight nature compared to rigid counterparts. These structures offer benefits such as cost savings, lower energy consumptions and improved operational safety. However, a notable drawback is that flexible structures are vulnerable to unwanted vibrations, which can cause structural damages. Hence, the development of specialized models are essential to effectively addressing this challenge. Researchers have devised various approaches to suppress unwanted vibrations, with contemporary studies often employing system identification techniques utilizing swarm intelligence algorithms to construct dynamic models of flexible structures. Therefore, this research employs the potent mayfly algorithm (MA), known for its effectiveness in optimization tasks. The developed models using MA were then compared with traditional approach known as recursive least square (RLS) through a comparative analysis. The outcome reveals that RLS exhibited the lowest mean square error (MSE) at , while MA had an MSE of Yet, MA adeptly depicted the characteristics of the system, outperforming the RLS in these validation by indicating a 95% confidence level in the correlation test and exhibiting robust stability in the pole-zero diagram. Consequently, MA serves as a fitting algorithm to accurately depict the real behaviour of the flexible plate structure.

Intelligent proportional-integral-derivate controller using metaheuristic approach via crow search algorithm for vibration suppression of flexible plate structure

Proportional-integral-derivate (PID) controller has gained popularity since the advancement of smart devices especially in suppressing the vibration on flexible structures using different approaches. Such structures required accurate and reliable responses to prevent system failures. Swarm intelligence algorithm (SIA) is one of the optimization methods based on nature that managed to solve real-world problems. Crow search is a well-known algorithm from the SIA group that can discover optimum solutions in both local and global searches by utilizing fewer tuning parameters compared to other methods. Hence, this study aimed to simulate a PID controller tuned by SIA via crow search for vibration cancellation of horizontal flexible plate structures. Prior to that, an accurate model structure is developed as a prerequisite for PID controller development. After the best model is achieved, the proportional-integral-derivative-crow-search (PID-CS) performance was compared to a traditional tuning approach known as the Ziegler Nichols (ZN) to validate its robustness. The result revealed the PID-CS outperformed the proportional-integral-derivative-Ziegler Nichols (PID-ZN) with attenuation values of 44.75 and 42.74 dB in the first mode of vibration for single sinusoidal and real disturbances, respectively. In addition, the value of mean squared error (MSE) for PID-ZN and PID-CS for single sinusoidal disturbance are 0.0167 and 0.0081, respectively. Meanwhile, PID-ZN and PID-CS achieved 2.3981 × 10−4 and 2.3737 × 10−4 when they were exerted with real disturbance. This proves that the PID-CS is more accurate compared to the PID-ZN as it achieved the lowest MSE value.

A Single Objective Crow Search for Modelling of Horizontal Flexible Plate Structure

The magnificent features of flexible plate structure, including lightweight and high-speed response, resulted in additional market demand, especially in the automotive and manufacturing industries. Nevertheless, the structure may incur structural damage and performance degradation when the system encounters excessive vibration. Therefore, a system identification approach utilising a metaheuristic algorithm via crow search to develop a horizontal flexible plate (HFP) model for vibration control is introduced in this paper. Crow search (CS) is a modern algorithm inspired by a crow’s intellectual operation to store additional food and memorise the food storage location. In this study, CS is employed to optimise the objective function, which is the mean squared error for accomplishing a precise predicted model in replicating the dynamic response of the actual structure. Hence, the preliminary action for modelling using this approach is designing and fabricating an HFP rig for experimentally gathering the real input-output vibration data. After that, the mathematical modelling utilising the CS algorithm was implemented using a parametric model structure. Finally, the best-fit model is chosen for the representation of the HFP based on the lowest mean squared error, correlation test within a 95% confidence level and stability in a pole-zero plot. The simulation result reveals that the CS algorithm with a second-order estimated model accomplished a minimum MSE of 1.1168 × 10-5, an unbiased correlation test and excellent stability for the HFP structure.

Advanced Finite Elements for Geometrically Nonlinear Analysis of Rectangular Plates under Various In-Plane Loadings Accounting for the Boundary Conditions of the Stiffeners

Highly flexible plate structures are subjected to various loading and edge conditions in many engineering applications, such as in the aerospace and civil industries. In this paper, the post-buckling response of rectangular plates subjected to axial and shear loadings is investigated by employing the Carrera Unified Formulation (CUF). As in previous works, only isolated plates have been considered, regardless of the effects of the stiffeners and boundary conditions imposed by the surroundings. However, in this research, different plate models are implemented, and the effects of boundary conditions imposed by the stiffeners are evaluated precisely. Comprehensive assessments are provided for the geometrically nonlinear equilibrium curves of the plate structures using the Newton–Raphson linearization method with the path-following constraint. Furthermore, the comparisons of different geometrically nonlinear assumptions according to the full Green–Lagrange nonlinear model and von Kármán nonlinear plate theory are presented. The importance of strain–displacement relationships and stiffeners’ effects in the nonlinear response of plate structures is highlighted. As a result, the accuracy and effectiveness of the presented CUF-2D model are demonstrated.

Displacement field reconstruction technique for plate-like structures based on model superposition method

To achieve real-time sensing and deformation reconstruction of flexible plate structure, a 3D reconstruction technique based on a quasi-distributed fiber grating sensor network and order-optimized modal superposition method is proposed. Graphic visualization is introduced to the field of deformation monitoring, then the displacement field reconstruction of the typical structure of spacecraft is realized. Firstly, a finite element model of the four-sided fixed-supported plate structure is constructed, and the conversion matrix of surface strain and displacement are obtained based on modal analysis, and then the modal parameters are optimized through static simulation experiments; Secondly, the influence of the number and position of sensors on the reconstruction accuracy is studied, then a high-density distributed fiber grating sensor network is attached to the surface of the plate to construct an experimental FBG model of the spacecraft; Finally, concentrated loads are applied to the structure at different positions, and structure’s surface strain information is collected by FBG network, then the morphological reconstruction of the deformed structure is realized based on the improved model superposition method, which proves the feasibility of the algorithm. The results show that the reconstruction method’s average absolute error is less than 0.13 mm, so this method can be used to displace field reconstruction problems of flexible structures.

Proportional integral derivative controller based on ant colony optimization for vibration cancellation of horizontal flexible plate structure

<p>Flexible plate structure provides many benefits as compared to their rigid counterparts including lower energy consumption, effective, lightweight, and quick response. However, the vibration easily affects the flexible plate structure resulting in structural damage. This study introduces the modelling of a flexible plate structure based on a system identification technique known as ant colony optimization (ACO) algorithm for vibration control. Firstly, the input-output vibration data that represent the actual structure of flexible plate was achieved from the experiment. Next, the acquired vibration data was used to develop a dynamic model of the flexible plate structure. The performances of the ACO algorithm were assess based on mean squared error (MSE), pole-zero plot and correlation test in order to get a precise and reliable outcome. The results show that ACO algorithm achieved the minimum MSE which was 6.7613×10<sup>−6</sup>, high stability of pole-zero plot and excellent correlation test. Subsequently, the best model of ACO was chosen to create controller based on an active vibration control technique. It was noticed that the controller managed to obtain a 6.19 dB reduction at the first mode vibration in which the percentage of attenuation of the controller was 10.63% for sinusoidal disturbances and 9.64% for multiple sinusoidal disturbances.</p>

Optimization of the gravity support in CFETR vacuum vessel

The China Fusion Engineering Test Reactor (CFETR) is developed as the next tokamak device in China. The gravity support of CFETR VV is designed with a flexible plate structure to allow radial thermal expansion of the vacuum vessel (VV) system and to withstand various design loads. In this paper, the design optimization is developed with Multi-Objective Genetic Algorithm (MOGA) to balance design parameters contributing to stability and strength for the VV gravity support. In this optimization procedure, a parametric FE model is generated to study the structural response of the support corresponding to each design point. Besides, the effects of the design variables on objective function are quantitatively assessed using sensitivity analysis. Through the optimization procedure, optimal design parameters of the VV gravity support are obtained. Compared to the initial design, an improvement of about 50.4 and 401% for the peak stress and buckling load factor of the support plates, respectively.

Vibration suppression of the horizontal flexible plate using proportional– integral–derivative controller tuned by particle swarm optimization

This paper presents the development of an active vibration control for vibration suppression of the horizontal flexible plate structure using proportional–integral–derivative controller tuned by a conventional method via Ziegler–Nichols and an intelligent method known as particle swarm optimization algorithm. Initially, the experimental rig was designed and fabricated with all edges clamped at the horizontal position of the flexible plate. Data acquisition and instrumentation systems were designed and integrated into the experimental rig to collect input–output vibration data of the flexible plate. The vibration data obtained through experimental study was used to model the system using system identification technique based on auto-regressive with exogenous input structure. The plate system was modeled using particle swarm optimization algorithm and validated using mean squared error, one-step ahead prediction, and correlation tests. The stability of the model was assessed using pole zero diagram stability. The fitness function of particle swarm optimization algorithm is defined as the mean squared error between the measured and estimated output of the horizontal flexible plate system. Next, the developed model was used in the development of an active vibration control for vibration suppression on the horizontal flexible plate system using a proportional–integral–derivative controller. The proportional–integral–derivative gains are optimally determined using two different ways, the conventional method tuned by Ziegler–Nichols tuning rules and the intelligent method tuned by particle swarm optimization algorithm. The performances of developed controllers were assessed and validated. Proportional–integral–derivative-particle swarm optimization controller achieved the highest attenuation value for first mode of vibration by achieving 47.28 dB attenuation as compared to proportional–integral–derivative-Ziegler–Nichols controller which only achieved 34.21 dB attenuation.

Fluid—Structure Interaction Analysis of Flexible Plate with Partitioned Coupling Method

The development and rapid usage of numerical codes for fluid–structure interaction (FSI) problems are of great relevance to researchers in many engineering fields such as civil engineering and ocean engineering. This multidisciplinary field known as FSI has been expanded to engineering fields such as offshore structures, tall slender structures and other flexible structures applications. The motivation of this paper is to investigate the numerical model of two-way coupling FSI partitioned flexible plate structure under fluid flow. The adopted partitioned method and approach utilized the advantage of the existing numerical algorithms in solving the two-way coupling fluid and structural interactions. The flexible plate was subjected to a fluid flow which causes large deformation on the fluid domain from the oscillation of the flexible plate. Both fluid and flexible plate are subjected to the interaction of load transfer within two physics by using the strong and weak coupling methods of MFS and Load Transfer Physics Environment, respectively. The oscillation and deformation results have been validated which demonstrate the reliability of both strong and weak method in resolving the two-way coupling problem in contribution of knowledge to the feasibility field study of ocean engineering and civil engineering.

Analysis and modeling of a flexible rectangular cantilever plate

Flexible plate structures with large deflection and rotation are commonly used structures in engineering. How to analyze and solve the cantilever plate with large deflection and rotation is still an unsolved problem. In this paper, a general nonlinear flexible rectangular cantilever plate considering large deflection and rotation angle is modeled, solved and analyzed. Hamilton's principle is applied to obtain the nonlinear differential dynamic equations and boundary conditions by introducing a coordinate transformation between the Cartesian coordinate system and the deformed local coordinate system. Stress function relating to in-plane force resultants and shear forces is given for the first time for complex coupling equations caused by coordinate transformation. The nonlinear equations and the solving method are validated by experiments. Then, harmonic balance method is adopted to get the nonlinear frequency-response curves, which shows strong hardening spring characteristic of this system. Runge–Kutta methods are used to reveal complex nonlinear behaviors such as 5 super-harmonic resonance, bifurcations and chaos for general nonlinear flexible rectangular cantilever plate.

Active vibration control of a horizontal flexible plate structure using intelligent proportional–integral–derivative controller tuned by fuzzy logic and artificial bee colony algorithm

This paper presents the development of an intelligent controller for vibration suppression of a horizontal flexible plate structure using hybrid Fuzzy–proportional–integral–derivative controller tuned by Ziegler–Nichols tuning rules and intelligent proportional–integral–derivative controller tuned by artificial bee colony algorithm. Active vibration control technique was implemented during the development of the controllers. The vibration data obtained through experimental rig was used to model the system using system identification technique based on auto-regressive with exogenous input model. Next, the developed model was used in the development of an active vibration control for vibration suppression of the horizontal flexible plate system using proportional–integral–derivative controller. Two types of controllers were proposed in this paper which are the hybrid Fuzzy–proportional–integral–derivative controller and intelligent proportional–integral–derivative controller tuned by artificial bee colony algorithm. The performances of the developed controllers were assessed and validated. Proportional–integral–derivative–artificial bee colony controller achieved the highest attenuation for first mode of vibration with 47.54 dB attenuation as compared to Fuzzy–proportional–integral–derivative controller with 32.04 dB attenuation. The experimental work was then conducted for the best controller to confirm the result achieved in the simulation work.

Modelling of Horizontal Flexible Plate Structure Using Artificial Bee Colony Algorithm

This paper presents the performance of system identification for modeling the horizontal flexible plate system using artificial bee colony and recursive least square algorithms. Initially, the experimental rig of flexible plate was designed and fabricated with all edges clamped boundary condition at the horizontal position. Then, the instrumentation and data acquisition systems were integrated into the rig for acquiring the input-output vibration experimentally. The collected data in the experiment will be used later for modeling the dynamic system of horizontal flexible plate system using system identification. The effectiveness of the developed model will be validated using mean squared error, one step ahead prediction, correlation tests and pole zero diagram stability. The estimated of the developed models were found are acceptable and possible to be used as a platform of controller development for vibration suppression of the undesirable vibration in the flexible plate structure. It was found that the artificial bee colony algorithm has performed better in this study by achieving the lowest mean squared error, good correlation test and high stability in the pole zero diagram.

Sound Radiation of Aerodynamically Excited Flat Plates into Cavities

Flow-induced vibrations and the sound radiation of flexible plate structures of different thickness mounted in a rigid plate are experimentally investigated. Therefore, flow properties and turbulent boundary layer parameters are determined through measurements with a hot-wire anemometer in an aeroacoustic wind tunnel. Furthermore, the excitation of the vibrating plate is examined by laser scanning vibrometry. To describe the sound radiation and the sound transmission of the flexible aluminium plates into cavities, a cuboid-shaped room with adjustable volume and 34 flush-mounted microphones is installed at the non flow-excited side of the aluminium plates. Results showed that the sound field inside the cavity is on the one hand dependent on the flow parameters and the plate thickness and on the other hand on the cavity volume which indirectly influences the level and the distribution of the sound pressure behind the flexible plate through different excited modes.

Fiber Bragg grating plate structure shape reconstruction algorithm based on orthogonal curve net

A space curved surface shape reconstruction algorithm is proposed for shape perception and reconstruction of flexible plate structure. First, biorthogonal strain data measured by optimal distributed Fiber Bragg grating sensor network are converted to discrete curvature data. Second, interpolation is done to achieve curvature continuity for structural deformation. Third, moving coordinate systems are established in two orthogonal directions of the orthogonal curved network on the plate surface. Then, all nodal coordinates are computed using the given boundary conditions and nodal curvature. Coordinate transformation is done for two orthogonal coordinates according to the coupling relationship. Finally, a square flexible smart Fiber Bragg grating plate is constructed by implanting fiber grating sensor network, and a visualization experimental platform is constructed. Experimental analysis and verification were done. The experimental results show that the proposed shape reconstruction algorithm has good reconstruction performance for pure bending deformation, torsional deformation, and low-frequency dynamic vibration shape.

Development of a Real-time Dynamics-Estimation System for Flexible Plate Structure Based on Telemetry Data

Development of a Real-time Dynamics-Estimation System for Flexible Plate Structure Based on Telemetry Data

Subsonic Flutter of Cantilever Rectangular PC Plate Structure

Flutter characteristics of cantilever rectangular flexible plate structure under incompressible flow regime are investigated by comparing the results of commercial flutter analysis program ZAERO©with wind tunnel tests conducted in Ankara Wind Tunnel (ART). A rectangular polycarbonate (PC) plate, 5 × 125 × 1000 mm in dimension, is used for both numerical and experimental investigations. Analysis and test results are very compatible with each other. A comparison between two different solution methods (g-methodandk-method) of ZAERO©is also done. It is seen that thek-methodgives a closer result than the other one. However,g-method results are on a conservative side and it is better to use conservative results, namely,g-method results. Even if the modal analysis results are used for the flutter analysis for this simple structure, a modal test should be conducted in order to validate the modal analysis results to have accurate flutter analysis results for more complicated structures.

Parametric modelling of flexible plate structures using continuous ant colony optimization

This paper presents parametric modelling of flexible plate structures using ant colony optimization (ACO). The global optimization technique of ACO is utilized to obtain a dynamic model of a flexible plate structure based on one-step-ahead prediction. In this paper a proposed ACO with roulette wheel selection known as ACO2 is compared with a previous modified ACO which is denoted as ACO1. The comparison is to recognize the optimum performance and to enhance the fast convergence. The flexible plate structure is subjected to random disturbance signal types. Fitness function for the ACO optimization is the mean-squared error between the measured and estimated output of the plate. The validation of the algorithm is presented in both time and frequency domains. Simulation results show that the proposed approachis better and has a fast convergence rate than ACO1. The developed ACO modelling approach will be used for active vibration control systems design and development in future work.

Experiments on resonant vibration suppression of a piezoelectric flexible clamped–clamped plate using filtered-U least mean square algorithm

This article investigates the adaptive filtered-U least mean square feed-forward algorithm for active resonant vibration control of a clamped–clamped flexible piezoelectric plate structure under persistent harmonic excitation. Different from the widely used filtered-X least mean square algorithm based on the finite impulse response filter, the filtered-U least mean square algorithm uses the infinite impulse response filter. An infinite impulse response filter can be constituted simply by using two adaptive transversal filters. The filtered-U least mean square algorithm can model the system accurately with much fewer coefficients. Moreover, the filtered-U least mean square algorithm has better control performance and stability in the presence of vibration control feedback, owing to the inherent zero-pole structure of the infinite impulse response filter. In this investigation, the filtered-U least mean square algorithm is implemented only in experiments. Two experimental cases are carried out, including the reference signal extracted from the function signal generator and the lead zirconate titanate sensor. A proportional–derivative feedback control algorithm is also applied as a comparison. The experimental results demonstrate the feasibility and performance of the designed proportional–derivative controller and filtered-U least mean square controller.

Minimization of vibration power transmission from rotating machinery to a flexible supporting plate

This paper deals with the problem of optimum design of a foundation for rotating machinery with a view to minimize vibration transmission from a machine source to its supporting structure. The problem of analysis and optimization of the installation systems of machinery has been extensively researched on the assumption of a rigid supporting structure. The design based on a rigid supporting structure model is reasonable for the installation of machinery in many real engineering situations. However, this rigid support based model may not be appropriate for the problem studied herein where the machinery is to be installed on a relatively flexible supporting plate. Thus, a generalized mathematical model of mobility power flow is developed in this paper, with a rotating machine as vibration source, resilient mounts as isolator, and a flexible supporting plate as receiver. The objective of minimizing vibration transmission is realized by optimization of stiffness coefficients of resilient mounts with a constraint on the vibration level of the machine. The design objective is chosen as the minimization of the power flow transmitted to the flexible supporting plate through the resilient mounts at the excitation frequency of the machinery. Both a single excitation frequency and a range of excitation frequencies are considered. A gradient-based mathematical programing method is selected for its advantage of efficiently solving the current type of optimization problem with multiple mounts and multi-degree-of-freedom vibration transmission. The sensitivities of the objective and the constraint functions with respect to the design variables are derived analytically. The design and performance of the optimized machinery foundation is illustrated and discussed using several numerical examples. The optimized mounting system is suitable for the installation case of a rotating machine with a low or medium service speed on a flexible supporting plate structure.

Experimental Study of Adaptive Fuzzy Sliding Mode Control for Vibration of a Flexible Rectangular Plate

In this paper, an approach is developed for active vibration control of flexible rectangular plate structures using control theory. The flexible rectangular plate system is first modeled through a new type of modeling method—discretization and reduced-order modeling method (DROMM); and second, the validity of the obtained new model is investigated by comparing the plate natural frequencies, static analysis, and forced vibration response analysis between a finite-element model and the new model. After validating the model, an adaptive fuzzy sliding mode multiple-input multiple-output (MIMO) controller is applied to the plate dynamic equation through the MATLAB/Simulink platform. The simulation and experimental results clearly demonstrate an effective vibration suppression capability that can be achieved using an adaptive fuzzy sliding mode MIMO controller.