Composite Laminate Beam Research Articles

Novel results in vibration analysis of nonlinear laminated composite beams (LCBs)

Novel results in vibration analysis of nonlinear laminated composite beams (LCBs)

A concerted experimental and numerical approach for frequency based non-destructive analysis of Bi-directional cracked laminated composite beams

ABSTRACT The effects of single and multiple transverse open cracks on the dynamic properties of woven fibre laminated composite beam (LCB) under free vibration by experimental and numerical approaches are explored in this research work. The experimental modal testing is performed n laminated glass/epoxy composite beams using vibration Fast Fourier Transformation (FFT) analyser system. The finite element simulation software ABAQUS is used as the platform for numerical modal analysis to arrive at the natural frequencies. Within the test domain of modal analysis, the simulated results are finely agreed with the empirical test results. The effects of crack location, relative crack depth, boundary conditions and fibre orientations on the modal frequency of the cracked LCB are explored under free vibration. The results of the study conclude that the maximum decrease in frequencies is observed for 0° ply oriented single and multi-cracked LCB. Furthermore, the results elicit that the presence of crack positioned nearer to the restrained end exhibits more reduction in vibration frequencies for any particular crack depth. Within the frequency domain, the present research approach can be employed as an effective tool for the detection and analysis of crack or crack-like defects in LCB structures in any applied field of engineering.

Damage Detection in Composite Materials by Flexural Dynamic Excitation and Accelerometer-Based Acquisition

Composite materials provide many advantages over more conventional materials. However, their susceptibility to impact damage can question their use in critical load-bearing structures, and efficient methods are needed for early damage detection. To this purpose, the nonlinear vibro-acoustic modulation (VAM) technique applies a low-frequency pump excitation and a high-frequency probe excitation to exploit the onset of harmonic components around the probe frequency of the damaged structural response. The VAM technique has been widely studied on structures instrumented with piezoceramic transducers used for both actuation and sensing, but few attempts have been made to use equipment typical of modal testing, such as shakers and accelerometers. In this study, the VAM technique is applied to a composite laminate beam by employing an electro-dynamic shaker to generate low-frequency flexural excitation, a low-profile piezoceramic transducer to introduce the probe wave, and a micro-accelerometer to sense the structural response. Three resonance low frequencies and two acoustic frequencies are considered in different testing scenarios, at increasing levels of excitation amplitude. The results show a general good performance of the technique with the adopted experimental setup, the choice of the probe frequency and the higher level of the pump excitation having a significant impact on its sensitivity.

Preparation and characterization of hybrid laminated composite beams

ABSTRACT Composite materials are age-old materials used to fulfill different needs in different applications. Polymer matrix composites can be laid layer-wise to fabricate laminated composite beams (LCBs). The physical and mechanical properties of these LCBs can be enhanced by altering the constituent materials and sometimes by adding fillers. The aim of the current research is to fabricate a group of layered laminated composites with hand lay-up process with low-cost equipment and to characterise their mechanical and physical properties. Graphene and industrial flyash is used as fillers. A variety of reinforcing schemes of the fillers are used to fabricate nine LCBs. The mechanical and physical properties are observed through experimentation and reported according to the weight percentage of filler and material scheme. Also, carbon fibre is reinforced to fabricate a composite variant and compared with the result of other variants of composites.

Free transverse vibration analysis of laminated composite beams with arbitrary number of concentrated masses

In this study, a new closed-form solution for transverse free vibration analysis of laminated composite beams (LCBs) with arbitrary number of concentrated masses is developed. The LCB is modeled based on the Euler–Bernoulli beam theory and concentrated masses are simulated considering Dirac delta function. Obtained governing equations are, then, solved semianalytically, while the frequency equation and mode shapes are extracted for two different boundary conditions, i.e., clamped-free and simply supported. In order to verify the closed-form solution, the represented model is simplified for a beam without concentrated mass and outcomes are compared with available results in the literature. Finally, the effects of mass as well as location and number of concentrated masses on the free vibration response of the beam are investigated in detail. The results highlight that with increase in the value of point masses, the natural frequencies decrease. Also, it was revealed that the number of point masses influences on the vibration of cantilever beam more than the simply supported one. These outcomes would practically be used to minimize detrimental effects of vibrational noises, leading to increase in the structural components’ lifetime.

Effect of lamination schemes on natural frequency and modal damping of fiber reinforced laminated beam using Ritz method

The current study focussed on analysing natural frequency and damping of laminated composite beams (LCBs) by varying fiber angle, aspect ratio, material property and boundary conditions. Ritz method with displacement field based on the shear and normal deformable theory is used and the modal damping is calculated using modal strain energy method. Effects of symmetric angle-ply and cross-ply, anti symmetric cross-ply, balanced and quasi-isotropic lay up schemes on modal damping are presented for the first time. Results revealed that influence of lay-up scheme on natural frequencies is significant for the thin beams while the modal damping of the thin beams are not sensitive to lay-up scheme. However, the lay-up scheme influences the damping significantly for the thick beams. Similarly, high strength fiber reinforced LCBs have higher natural frequency while low strength fiber reinforced LCBs have higher damping due to the better fiber-matrix interaction.

Free vibration analysis of composite laminated beams with curvilinear fibers via refined theories

In this article, free vibration finite element analysis of variable stiffness composite laminate (VSCL) beams is carried out. The variable stiffness of laminated beams is acquired by using laminates with curvilinear fibers instead of straight fibers. The analysis is based on the higher-order theories that have been presented by Carrera Unified Formulation (CUF). Equivalent Single Layer (ESL) model, which is independent of the number of constitutive layers, has been utilized to consider a number of unknown variables. Several numerical results for the analysis of VSCL beams are presented and the effect of the fiber orientation angle and various boundary conditions on the natural frequencies are demonstrated.

Haar wavelet discretization method for free vibration study of laminated composite beam under generalized boundary conditions

Investigation on vibration of laminated composite beam (LCB) is an important issue owing to its wide use as fundamental component. In the present work, we study the free vibration of arbitrarily LCB with generalized elastic boundary condition (BC) by using Haar wavelet discretization method (HWDM). Timoshenko beam theory is utilized to model the free vibration of LCB. The LCB is first split into several segments, and then the displacement for each segment is obtained from the Haar wavelet series and their integral. Hamilton's principle is applied to construct governing equations and the artificial spring boundary technique is adopted to obtain the general elastic boundary and continuity conditions at two ends of LCB. The vibration characteristics of beam with different fiber orientations and lamina numbers is investigated and its displacements are compared with those in previous works. Numerical results are shown graphically and demonstrate the validation of our method.

Experimental and numerical studies on vibration of laminated composite beam with transverse multiple cracks

Abstract Composite beams are increasingly used in aerospace, automobile, and other applications. Crack is the most common defect in structures during its service life. The cracked composite beams are subjected to dynamic loads and the vibration of the cracked beams is of technical significance to the structural integrity of systems. The objective of the present investigation is to demonstrate the vibration characteristics of a laminated composite beam (LCB) with multiple transverse cracks. Finite element method (FEM) is used for the frequency-based crack analysis in this study. A computer program is developed in MATLAB environment for numerical analysis. First-order shear deformation theory (FSDT) is adopted for the finite element analysis. Natural frequencies of vibration are computed through the eigenvalue solver. Composite specimens are fabricated using hand lay-up technique and are tested for its material constants under tensile test. Experiments are conducted using woven roving Glass/Epoxy laminated beam samples with pre-defined cracks. The obtained test results from the experimental work using FFT analyzer are validated with the numerical results obtained through MATLAB. The effects of natural frequencies with respect to the various boundary conditions, crack depth and locations are investigated to support in real applications. A fine agreement is accomplished between the numerical and test results. Both the studies showed that natural frequencies in the LCB are significantly influenced by the location and size of the cracks. The results show that natural frequencies are decreased with cracks and an increase in fiber orientation.

Dynamic analysis of laminated composite beam using Timoshenko beam theory

The uses of laminated composite beams are increasing day by day in many industries. This laminated composite beam has been exposed under different dynamic loadings in mechanical operation. Therefore, the dynamic investigation of laminated composite beams (LCB) is very much necessary to forecast the catastrophe fail of the LCB components. At present, dynamic investigation of the LCB is carried out by the determining of fundamental frequency and mode shape. The special attentions like; in the design of geometry, orientation of fibres, layup of sections and boundary conditions are also analysed with referring the dynamical loadings and industry uses. The analysis procedures and results are validated with the reference results using finite element analysis software. Present research deals with the consequence of different volume fraction, boundary conditions and geometrical variation like aspect ratio, geometric ratio and length of E-glass polyester LCB. By altering different stacking sequences and these effects on mechanical properties as well as natural frequency are also analysed.

Response of Composite Laminate Beam Using Higher Order Beam Theory

The present work proposes the composite laminate beam behaviour using higher order beam theory (HBT). The higher order displacement field with twelve degrees of freedom and nine node isoparametric element is used for the finite element formulation. The finite element model for linear static analysis is developed using MATLAB code. The numerical results are obtained for the deflection of beam for arbitrary boundary conditions, stacking angle, aspect ratio and different loading conditions. The results are validated using the literature and it shows good agreement.

The Effect of Various Fiber Orientations and Boundary Conditions on Natural Frequencies of Laminated Composite Beam

This paper investigates the free vibration characteristics of laminate composite beam for various lamination schemes and under various boundary conditions. A beam model with the aspect ratio (length to thickness) of 25 to 150 made of carbon/ epoxy laminates under free vibration were constructed using a commercially available finite element software (ANSYS). The varied parameters are the lamination schemes (cross ply, angle ply and unidirectional ply) and boundary conditions (Clamp-Free (C-F), Clamp-Clamp (C-C), Clamp-Hanger (C-H), Free-Free (F-F) and Hanger-Hanger (H-H) ). For each case, finite element simulations were performed and the natural frequencies were determined. Mode shapes were also analyzed to observe the beam’s deformation behavior. Results showed that increasing aspect ratio will decrease natural frequencies for the first seven mode shapes. In terms of lamination scheme, the unidirectional ply produced the highest frequency (34.26 Hz), followed by cross ply (34.05 Hz) and angle ply (13.60 Hz) at the aspect ratio of 25. In terms of boundary conditions, the Hanger-Hanger boundary condition produced the highest natural frequency (2272.52 Hz) at the aspect ratio of 25, while Clamped-Free boundary condition produced the lowest frequency (2.28 Hz) at the aspect ratio of 150. In general, it can be concluded that the current study is useful and has contributed significant knowledge to better understand of effect of various fiber orientations and boundary conditions on the natural frequencies of laminated composite beam.

A beam finite element for analysis of composite beams with the inclusion of bend-twist coupling

Material-induced bend-twist coupling in laminated composite beams has seen applications in engineered structures for decades, including airplane wings and turbine blades. Numerical studies and analytical formulations of the dynamics of bend-twist coupled laminated beams and plates have been investigated in recent years, yet can be cumbersome to implement quickly and efficiently. In early stages of design, employing a stiffness method approach to predict the load-deformation relationship and structural natural frequencies can be more efficient than developing a shell finite element model for each design iteration.A weak-form approach to the development of an accurate bend-twist coupled composite laminate beam element is presented herein. Comparisons are made between the stiffness matrix terms using the presented method and a shell finite element model of an idealized beam; the proposed method shows good agreement for a suite of beams with varying degrees of bend-twist coupling. The method is then extended to the calculation of natural frequencies by combining the new stiffness matrix with a corresponding consistent mass matrix to formulate the eigenvalue problem and shows very good agreement with both analytical and shell element solutions.

Linear and nonlinear resonant techniques for characterizing cyclic fatigue damage in composite laminate

In the present work, the linear and nonlinear resonance experiments are performed on composite laminate beam with cyclic loading damage. The effect of different cyclic loading damage on the linear and nonlinear resonance response is analyzed. The nonlinear resonance studies the amplitude dependence of different modes. The frequency and the loss factor as function of the amplitude are determined for each cyclic loading damage. For the linear resonance, the specimens are tested at low amplitude excitation. The frequency and loss factor are evaluated for each cyclic damage. The nonlinear parameters are quantified as function of the damage. The linear parameters are compared with the nonlinear parameters.

Nonlinear vibration of unsymmetrical laminated composite beam on elastic foundation

In this paper, nonlinear vibrations of the unsymmetrical laminated composite beam (LCB) on a nonlinear elastic foundation are studied. The governing equation of the problem is derived by using Galerkin method. Two different end conditions are considered: the simple-simple and the clamped-clamped one. The Hamiltonian Approach (HA) method is adopted and applied for solving of the equation of motion. The advantage of the suggested method is that it does not need any linearization of the problem and the obtained approximate solution has a high accuracy. The method is used for frequency calculation. The frequency of the nonlinear system is compared with the frequency of the linear system. The influence of the parameters of the foundation nonlinearity on the frequency of vibration is considered. The differential equation of vibration is solved also numerically. The analytical and numerical results are compared and is concluded that the difference is negligible. In the paper the new method for error estimation of the analytical solution in comparison to the exact one is developed. The method is based on comparison of the calculation energy and the exact energy of the system. For certain numerical data the accuracy of the approximate frequency of vibration is determined by applying of the suggested method of error estimation. Finally, it has been indicated that the proposed Hamiltonian Approach gives enough accurate result.

Simulation of Low Velocity Impact Induced Inter- and Intra-Laminar Damage of Composite Beams Based on XFEM

In this paper, the Inter-Fiber Fracture (IFF) criterion of Puck failure theory based on the eXtended Finite Element Method (XFEM) was implemented in ABAQUS code to predict the intra-laminar crack initiation of unidirectional (UD) composite laminate. The transverse crack path in the matrix can be simulated accurately by the presented method. After the crack initiation, the propagation of the crack is simulated by Cohesive Zoom Model (CZM), in which the displacement discontinuities and stress concentration caused by matrix crack is introduced into the finite element (FE) model. Combined with the usage of the enriched element interface, which can be used to simulate the inter-laminar delamination crack, the Low Velocity Impact (LVI) induced damage of UD composite laminate beam with a typical stacking of composite laminates [05/903]S is studied. A complete crack initiation and propagation process was simulated and the numerical results obtained by the XFEM are consistent with the experimental results.

Elastic-damage deformation response of fiber-reinforced polymer composite laminates with lamina interfaces

The single-layer and multi-layer finite element models are developed and examined for adequacy in predicting the elastic-damage response of fiber-reinforced polymer composite laminates. A new experimental-computational approach featuring a two-tier mesh convergence analysis of the finite element models is developed. A 12-ply carbon fiber-reinforced polymer composite laminate beam specimen with anti-symmetric layups is designed and loaded to induce matrix damage under significant deflection without catastrophic fracture. A constitutive model incorporating Hashin’s equations for damage initiation criteria, along with an energy-based damage propagation law is employed in the finite element simulation. The results shows that the multi-layer finite element model predicts well the load–deflection curve of the carbon fiber-reinforced polymer composite laminate, while the single-layer model overestimates the elastic flexural stiffness of the specimen by 47 %. During the flexural deformation, matrix damage initiates in the central and edge regions of the critical laminas under compressive and tensile stresses, respectively. The multi-layer finite element model also predicted the matrix-induced interface delamination along the edges of the critical laminas under tension, as observed experimentally. The model demonstrates the adequacy in representing the role of lamina interface in dictating the elastic-damage response of carbon fiber-reinforced polymer composite laminates manufactured by prepreg layups method.

Numerical model of postbuckling behavior of GFRP beams subjected to pure bending

ABSTRACTThis article deals with numerical calculations of thin-walled composite laminate beams with closed cross-section subjected to pure bending. Thin-walled beams with square cross-section made of eight-layer GFRP laminate have been taken into consideration. An FEM model has been prepared using four-node multi-layered shell elements governed by first-order shear deformation theory. Linear buckling analysis and nonlinear static analysis including large displacements have been performed. A Newton–Rapson algorithm has been employed. The FEM calculations have been conducted using Ansys® software. Three following layer arrangement were considered: [45/−45/0/0]S, [45/−45/45/0]S and [45/−45/45/0/0/−45/45/−45]T. The influence of number of load steps and geometrical initial imperfection on course of equilibrium paths has been checked. The results of calculations have been compared with experimentally performed four-point bending tests. Comparing results of tests and numerical calculations, it was observed that, in some cases, the deflection of beams does not correspond to the bifurcation buckling mode but corresponds to the lowest buckling load; the geometrical imperfection that corresponds to the higher buckling mode should be taken into consideration to obtain similar postbuckling equilibrium paths from tests and FEM calculations. As is well known, the buckling load and failure load for real structures depend on course of equilibrium paths. Taking above considerations into account, the author of this article tries to show some problems in obtaining numerical calculations results that are similar to experimental tests.

Critical Aspects of Experimental Damage Detection Methodologies Using Nonlinear Vibro-ultrasonics

Nonlinear ultrasonics has become a major research focus in non-destructive testing (NDT) in recent years. Techniques using higher harmonics or cross-modulation of two excitation frequencies have been developed and have shown to be extremely sensitive and to allow measuring defects that are undetectable using conventional ultrasonic NDT. This paper reports on the application of nonlinear vibro-ultrasonics to detect delamination damage in composite laminate beams. In addition, measurement and data analysis requirements are evaluated to ensure optimal sensitivity, reliability and robustness of nonlinear vibro-ultrasonic damage detection systems. The importance of the individual components of the measurement chain is demonstrated, and a measurement system is described that has a dynamic range of more than 120 dB and 24-bit amplitude resolution, which enables the measurement of sideband frequencies with unprecedented sensitivity and accuracy. The influence of the selection of input variables such as excitation frequencies and input voltages on the sensitivity of the system is also demonstrated. It highlights the challenges of reliable damage evaluation in the case of materials and structures with unknown damages. The conclusion of the paper is that nonlinear vibro-ultrasonics has great potential as NDT technique with unmatched sensitivity, but that measurement systems and experimental parameters and processes have to be selected and optimised with extreme care to ensure that damage detection results are reliable.

Vertical beam modal response in a broadband energy harvester

We examined energy harvesting using a vertical composite laminate beam with an additional moving mass subjected to kinematic harmonic excitation. The gravity effect and the moving tip mass applied to the system cause considerable changes in effective spring-mass characteristics of the bending beam. Simultaneously, we observed dynamical beam damping by an additional degree of freedom and non-linear effects including friction between the moving mass and the beam structure. The experiments were performed on the beam excited kinematically by a shaker, while beam velocity measurements were made by a scanning laser vibrometer. We applied modal analysis in the limit of a fairly low excitation level. The selected modal vibrations are illustrated by corresponding output time series.