Laminated Cantilever Beam Research Articles

Vibration Suppression of Graphene Reinforced Laminates Using Shunted Piezoelectric Systems and Machine Learning

The implementation of a machine learning approach to predict vibration suppression, as derived from nanocomposite laminates with piezoelectric shunted systems, is studied in this article. Datasets providing the vibration response and vibration attenuation are developed using parametric finite element simulations. A graphene/fibre-reinforced laminate cantilever beam is used in those simulations. Parameters, including the graphene and fibre reinforcements content, as well as the fibre angles, are among the inputs. Output is the vibration suppression achieved by the piezoelectric shunted system. Artificial Neural Networks are trained and tested using the derived datasets. The proposed methodology can be used for a fast and accurate prediction of the vibration response of nanocomposite laminates.

Free Vibration-Based Delamination Detection in Fiber Metal Laminates Composite Beam

Delamination is a typical flaw in fiber-metal laminated composite structures that, when hidden from view, can significantly lower structural stiffness and alter a structure's ability to respond dynamically to forces like natural frequencies. Delamination is undoubtedly an important topic as it causes the performance of the Fiber Metal Laminate structures in the service to worsen. Delamination detection and severity analysis are essential in the aerospace industry for both safety and cost reasons. Although natural frequencies do not directly reveal the location or extent of damage, they are the most dependable metrics for damage detection. Frequency shifts in various modes are used to solve the inverse problem to pinpoint the damage location and extent. The bending natural frequencies shift brought on by delamination is utilized as an input to predict the delamination parameters. This study used an approach based on machine learning and a regression model to find the delamination parameters, i.e., locations and severity, in fiber metal laminated cantilever beams. FEA simulations using ANSYS were used to get the dataset pertaining to the position, severity, and eigen values (or bending natural frequencies) of the delamination. The results of this study indicate that the delamination locations and severity predictions developed using machine learning and regression models are reasonably accurate and demonstrate good agreement with the observed data.

Nonlinear Dynamic Analysis of an Axially Moving Composite Laminated Cantilever Beam

Nonlinear Dynamic Analysis of an Axially Moving Composite Laminated Cantilever Beam

Nonlinear eccentric bending and buckling of laminated cantilever beams actuated by embedded pre-stretched SMA wires

This paper presents a theoretical approach to analyze the eccentric bending and buckling of laminated cantilever beams actuated by embedded pre-stretched SMA wires. Two mechanisms are involved: phase transition of the SMA wires and the nonlinear bending of the laminated beam. On the basis of material model for shape memory alloy during the phase transition in thermal field proposed by Brison, constitutive relations of the SMA hybrid laminated beams are established to interpret the relationship among the recovery stress, the internal stress, the thermal temperature and the thermal expansion. Governing equations in terms of the slope function and the horizontal displacement are derived according to von-Kaman geometrically nonlinear relationships. The nonlinear bending deformation of the SMA hybrid laminated beams is analyzed by considering the deflection due to eccentric bending moment as an initial imperfection and is solved using perturbation approach. A compatible condition is proposed to ensure consistent deformation between the SMA wires and the laminated beams. By developing Matlab program, parametric studies are carried out to investigate the effect of the pre-strain, the volume fraction and the location of the SMA wires on the deflection, the critical temperature, the recovery stress and the internal stress of the SMA hybrid laminated beams. The efficiency and accuracy of the analytical solutions were expounded by comparing with the results from finite element analysis. It is found that buckling may or may not occur in the SMA hybrid laminated beam relying on the value of the pre-strain of the SMA wires.

Influence of Hole Localization on Local and Global Dynamic Response of Thin-Walled Laminated Cantilever Beam.

In this study, we discuss the effects of the diameter and position of a hole on the dynamic response of a thin-walled cantilever beam made of carbon-epoxy laminate. Eigen-frequencies and corresponding global and local eigen-modes were considered, where deformations of the beam wall were dominant, without significant deformation of the beam axis. The study was focused on the circumferentially uniform stiffness (CUS) beam configuration. The laminate layers were arranged as [90/15(3)/90/15(3)/90]T. The finite element method was employed for numerical tests, using the Abaqus software package. Moreover, a few numerical results of the structure’s behaviour, with and without a hole, were verified experimentally. The experimental eigen-frequencies and the corresponding modes were obtained using an experimental modal analysis, comprising the LMS system with modal hammer. We found that the size and location of the hole affected the eigen-frequencies and corresponding modes. Furthermore, even a small hole in a beam could significantly change the shape of its local modes. The numerical and experimental results were observed to have high qualitative compliance.

Nonlinear vibrations of a rotating thin-walled composite piezo-beam with circumferentially uniform stiffness (CUS)

A rotating system comprising a hub and a thin-walled laminate cantilever beam with embedded nonlinear piezoelectric layers is analysed in the paper. The reinforcing fibres set-up in composite material conforms to circumferentially uniform stiffness lamination scheme. This configuration exhibits the mutual bending couplings in two orthogonal planes. Nonlinear analytical model of a piezoelectric material embedded onto the beam walls is postulated by considering the higher-order constitutive relations with respect to electric field variable. Moreover, to properly model electromechanical structural behaviour, the full two-way coupling piezoelectric effect is considered. To this aim, the assumption of a spanwise electric field variation is postulated in the mathematical model of the structure. Based on previous authors’ research, the system of mutually coupled nonlinear equations of motion is formulated. In the numerical analysis the forced response of the system under zero and nonzero mean value harmonic torque excitation is considered. In particular, the influence of hub inertia, excitation amplitude and mean rotating speed on system dynamics is investigated. The results are presented in the form of appropriate frequency response plots and bifurcation diagrams.

Optimal location of cutout within a cross-ply laminated cantilever beam for maximum lateral buckling load

This paper deals with the location optimization of a cutout within a laminated cantilever beam for maximizing the lateral buckling load. Various shapes of cutout, such as circular, elliptical, triangular, are generally used in structural components as a design requirement or sometime to reduce the overall weight of the structures. In this study, a laminated cantilever beam, with a single cutout, is considered. The beam is subjected to a concentrated load at the free end. The objective is to obtain the optimal location of the cutout which resist maximum lateral buckling load. For this an optimization routine has been used in which a finite element calculation of critical lateral buckling load in ANSYS is coupled with an in-built global optimization tool (Genetic Algorithm) in MATLAB. The optimal results are reported for various cases arising from change of geometry and material properties of the plate. It has been concluded that the position of cutout in the laminated beam plays a significant role while designing against lateral buckling load.

Vibration control with the converse flexoelectric effect on the laminated beams

Flexoelectric material under inhomogeneous electric field can be used as control and actuation systems in engineering applications based on the converse flexoelectric effect. The electric field gradient can be generated by using the atomic force microscope probe placed on the top of flexoelectric layer and coupled with a bottom electrode surface. The induced membrane force and the corresponding control moment in turn influence the dynamic response of the beam. The response of a laminated cantilever beam with initial vibration caused by an external loading is studied. The beam was modelled as a laminated beam to explore the influence of flexoelectric layer stiffness on the dynamic response of the structure. When the flexoelectric layer has higher Young’s modulus and mass density than the elastic layer, with increasing the thickness of the flexoelectric layer, the tip displacement of the laminated beam decreased rapidly. Through case studies, the optimal control positions for each mode of vibration were found to be dependent on the flexoelectric layer properties as well. A displacement-based feedback control was introduced to avoid overactuation caused by open-loop control.

Solution of a Transverse Plane Bending Problem of a Laminated Cantilever Beam Under the Action of a Normal Uniform Load

The paper presents an exact direct solution of a transverse plane bending problem of a laminated cantilever beam of small width under the action of a uniformly distributed load under the absolutely hard contact between the layers. The solution has been constructed with the aid of linear elasticity theory equations: to take into account the heterogeneous structure of the laminated beam, piecewise constant functions of elastic characteristics, which have been described analytically by means of shifted Heaviside functions, have been introduced into the Hooke’s law relationships. During the solution of problem, the normal stresses were expressed from static equations in terms of an unknown function of tangential stress distribution over the cross-section height. The use of the obtained expressions in the Hooke’s law relationships and Cauchy equations for linear strains made it possible to establish relationships between displacements and tangential stresses. The Cauchy equation that remained for angle strains gave a defining integro-differential equation, from which differential equations for the unknown tangential stress function and for all unknown integration functions have been derived. The solution of the derived equations is possible for the entire packet of layers without considering an individual layer, the final relations for stresses, strains and displacements describing the stress-strain state of the entire packet of composite beam layers. The constructed solution satisfies the boundary conditions and the conditions of the absolutely hard contact of the layers and is exact if the load distribution corresponds to the determined stress distribution. Using this solution, we have carried out a theoretical study of the stress-strain state of a three-layer beam. The obtained relation allow one to predict the strength and stiffness of multilayer structural composite elements and to construct application solutions for other elastic bending problems of laminated beams.

A Study on the Natural Frequency of a Laminated Cantilever Beam

A Study on the Natural Frequency of a Laminated Cantilever Beam

Modeling of low frequency dynamics of a smart system and its state feedback based active control

Abstract Major physical systems/structures suffer from unwanted vibrations. For efficient working of such systems, these vibrations have to be controlled. In this paper, mathematical modeling of an aluminum cantilever beam with bonded multiple piezoelectric patches which act as the disturbance generator, sensor as well as control actuator has been presented. This piezoelectric laminate cantilever beam is assumed to be vibrating in a single degree of freedom i.e. in the flexural mode only and the corresponding state space models have been derived analytically using the finite element technique. Dominant modes of flexural vibration are identified from the frequency response of the developed model of the system and finally a state feedback controller based on pole placement technique is designed to actively suppress the vibrations. Through numerous simulations as well as experimental validation, the effectiveness of the active controller in damping the vibrations at various excitation frequencies as well as frequency ranges along the flexural mode is established.

Basic Study on Vibration Properties of the Laminated Cantilever Beam

Basic Study on Vibration Properties of the Laminated Cantilever Beam

Design and development of a model free robust controller for active control of dominant flexural modes of vibrations in a smart system

Real physical vibrating smart systems exhibit a lot of nonlinearities in their dynamics. Undesirable vibrations, particularly in the regions of first as well as second resonance, play a very important role in deteriorating the stability of the system as well as its operational efficiency. The work presented in the paper focuses on an analytical technique of mathematical modeling of a vibrating piezoelectric laminate cantilever beam which is considered to be the smart system. The natural frequencies of the vibrating smart system are determined from the ANSYS simulation studies and experimentally, it is found that the vibrations induced voltage is maximum at the first followed by the second natural frequencies. Hence, the smart system is modeled analytically through finite element technique using the Euler–Bernoulli beam theory for the first two flexural modes of vibrations. To account for the possible nonlinearities, a suitable robust controller is designed based on sliding mode technique. Simulation studies on the developed analytical model indicated a high performance of the designed controller in controlling the vibrations at first and second resonance regions. Also, the designed controller was found to be effective in its operations when the excitation varied over a large range covering the first two natural frequencies. In the final stage, the designed robust controller was successfully prototyped on a Field Programmable Gate Array (FPGA) platform using LabVIEW coupled with Compact Reconfigurable Input Output (cRIO-9022) controller configured in its FPGA interface mode and the resulting robust FPGA controller successfully controlled the occurring system vibrations.

Stress analysis of symmetric and anti-symmetric discretely stiffened laminated cantilever beams using displacement-potential field

The stress field of a laminated cantilever beam is analyzed under the influence of symmetric and anti-symmetric arrangements of discrete stiffeners at the opposing longitudinal surfaces. An efficient finite-difference computational scheme is developed, in which a new displacement potential is introduced to model the problem of laminated composites. Solutions of stresses at different plies of the laminated cantilever are obtained, some of which, especially those around the critical regions of stiffeners are presented. The effectiveness and accuracy of present approach is verified by comparing the results with the corresponding solutions of analytical as well as standard computational methods.

Modeling and design of field programmable gate array based real time robust controller for active control of vibrating smart system

The current paper focuses on accurate mathematical modeling of a vibrating piezoelectric laminate cantilever beam theoretically as well as experimentally so as to obtain the best replication of the system dynamics on the software platform for simulation studies. The developed models were tested for accuracy in time as well as frequency domain by employing the sweep sine test. The focus of the study is on the flexural modes of vibrations of the cantilever beam. Here, modeling is focused on the first vibratory mode as it has been observed that the effects of felt vibrations would be maximum in terms of system stability and its operational efficiency when the excitation frequency matches with the first natural frequency of the system (fn1). This was validated by appropriate non-parametric modeling of the smart system by subjecting it to the Impact Hammer test. Development of accurate system models play an important role in designing and testing various control algorithms for reliable active vibration control (AVC). In the final stage, a real time active vibration robust controller was designed using a proportional derivative sliding mode control (PDSMC) technique and deployed on a Field Programmable Gate Array (FPGA) platform. The efficiency of the developed real time controller was proved in time as well as frequency domains by subjecting the closed loop system to harmonic excitations at first natural frequency as well as sweep sine test focussing on the first vibratory mode with the conclusion that the developed controller will function satisfactorily at higher modes of vibrations.

Reverberation-ray matrix analysis of the transient dynamic responses of asymmetrically laminated composite beams based on the first-order shear deformation theory

This study extends reverberation-ray matrix (RRM) analysis to include the transient responses of laminated composite beams based on the first shear deformation theory (FSDT) subjected to impulse force load. To validate the developed analysis method, we analyze the velocity response of a laminated cantilever beam model under considering the effect of the first shear deformation and rotary inertia. The transient responses of the laminated composite beam under a half-cycle pulse force and a rectangular pulse force are then solved by the reverberation-ray matrix analysis method (RRM). The reverberation-ray matrix that represents the multi-reflected and scattered waves in the laminated composite beam is demonstrated. The influence of the impact load type and the axial–flexural–shear coupled effects due to asymmetric ply stacking sequences are analyzed. The beam model effects on the calculation results for transient responses are also emphasized. In summary, compared with the finite element method, the proposed approach provides results that are in good agreement with previous findings. The advantage of RRM is that the solution process of RRM is simpler and faster, and requires fewer computational elements.

Parametric modeling and FPGA based real time active vibration control of a piezoelectric laminate cantilever beam at resonance

The operational efficiency and life of mechanical systems/structures depends to a large extent on their vibration control. Continuously occurring vibrations on the systems can cause fatigue and the effects of these vibrations are particularly severe if they occur at a frequency matching with that of the concerned system’s natural frequency – a stage called resonance. This paper focuses on achieving active vibration control of a smart cantilever beam at its first resonant frequency as it is at this stage that maximum damage to the system performance is expected. The smart system is modelled in the parametric domain using finite element modeling techniques and the obtained model is validated through experimental means. The active vibration control is achieved by employing two control algorithms namely – output feedback and error based control through general purpose operating system (LabVIEW on Windows 7) as well as in real time operating system (LabVIEW FPGA coupled with compact reconfigurable input output modules) and the performances are compared thereby justifying the importance of the deterministic and reliable real time control over the usual PC based control in experimental studies.

Nonlinear Behavior Characterization of a 3-Layer Laminated Cantilever Beam System

This research aims to characterize the nonlinear responses of a 3-layer laminated composite cantilever beam systemsubjected to evenly distributed dynamic excitations, with the employment of the Periodicity Ratio (PR) method. Periodic, quasiperiodic, chaotic behaviors especially the behaviors in between period and quasiperiod of the cantilever beam system are quantitatively described. A periodic-quasiperiodic-chaotic region diagram is developed to be used for identifying the global behaviors of the cantilever beam system with a large range of parameters. The research approach demonstrates that the PR method is effective and powerful in analyzing the complex dynamical characteristics of nonlinear cantilever beam systems, and the approach shows significances for industrial application and further nonlinear research in this area.

Transient response analysis of balanced laminated composite beams by the method of reverberation-ray matrix

Abstract This study extends the method of reverberation-ray matrix (MRRM) to analyze the transient response of a laminated composite beam subjected to an impulse force load. To validate the MRRM for this application, we first analyze the velocity response of a laminated cantilever beam model, then solve the transient responses of a laminated composite beam under a half-cycle pulse force and a rectangular pulse force using the MRRM. We present the reverberation-ray matrix of multi-reflected and scattered waves in the laminated composite beam, and analyze the influence of the impact load type and the axial–flexural coupling effects due to asymmetric ply stacking sequences. The effects of different beam models on the calculation results for transient responses are also emphasized. Compared with the finite element method, the proposed MRRM approach yields results that are in good agreement with previous findings, and the MRRM solution process is simpler, faster, and requires fewer computational elements.

818 非一様加熱を受ける圧電材料からなる三層積層片持はりの非定常圧電熱弾性解析(GS-3 熱応力・熱弾性(2))

818 非一様加熱を受ける圧電材料からなる三層積層片持はりの非定常圧電熱弾性解析(GS-3 熱応力・熱弾性(2))