A spectral finite element for wave propagation and structural diagnostic analysis of composite beam with transverse crack (original) (raw)
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Composite Structures, 2005
A spectral finite element model for analysis of flexural-shear coupled wave propagation in delaminated, multilayer composite beams is presented. Concept of obtaining the exact spectral element dynamic stiffness matrix for delaminated beam is discussed. Computation is performed in the Fourier domain at FFT sampling points over broad frequency band. Post processing of the response is made in the time domain, which is suitable for structural diagnostics and broad-band wave propagation problems. Implemented numerical examples illustrate the influence of delamination on wave propagation in cantilever multilayer laminated composite beams.
Composite Structures, 2005
A spectral finite element model for analysis of flexural-shear coupled wave propagation in delaminated, multilayer composite beams is presented. Concept of obtaining the exact spectral element dynamic stiffness matrix for delaminated beam is discussed. Computation is performed in the Fourier domain at FFT sampling points over broad frequency band. Post processing of the response is made in the time domain, which is suitable for structural diagnostics and broad-band wave propagation problems. Implemented numerical examples illustrate the influence of delamination on wave propagation in cantilever multilayer laminated composite beams.
Flexural-Shear Wave Propagation in Cracked Composite Beam
Science and Engineering of Composite Materials, 2004
A spectral finite element model for analysis of flexural-shear coupled wave propagation in a multilayer composite beam with a transverse open and not propagating crack is presented. The concept of obtaining the exact spectral element dynamic stiffness matrix is discussed. Computation is performed in the frequency domain at FFT sampling points over a broad frequency band. Post processing of the response is made in the time domain, which is suitable for structural diagnostics and broad-band wave propagation problems. Implemented numerical examples illustrate the influence of crack on wave propagation in cantilever multilayer laminated composite beams. INTRODUCTION Composite materials play an increasing role in many engineering applications. High performance, strength, stiffness and low weight are the attractive factors which increase the use of these materials in aerospace, automobile, marine and rail industries. One of the major concerns associated with composites is their susceptibility to damage, which may occur during manufacture, service or maintenance. Among others, delamination, matrix and fibre cracking are the most common damages occurring in composite materials. Although such damages are barely visible, they can severely degrade the mechanical properties and the load carrying capability of the structure. Any growth of this damage can lead to fracture of the material. Most of the structural health monitoring methods can be classified into model-based and signal-based approaches. The former utilises structural physical parameters for damage detection and is rather related to modelling and identification problems; any change of structural physical parameters can indicate damage /I/. The signal-based approach uses different vibration, strain, acoustical and ultrasonic signals for damage detection and is related to signal processing. It is usually based on a relationship between a structure condition and a damage symptom or feature, where the problem is to find symptoms which are sensitive to damage and damage evolution. The paper is devoted to utilizing wave propagation as an efficient tool for damage detection in composite structures. Many numerical methods are applied for wave propagation modelling. The most efficient and convenient among them is spectral element method (SEM) 121. The SEM is based on exact solution to governing Partial Differential Equations (PDE) in the frequency domain /3/. This exact solution is used as interpolating function for spectral element formulation. The use of an exact solution in the element formulation ensures exact mass and stiffness distribution. As a result, the element directly yields the exact dynamic 55 Unauthenticated Download Date | 7/8/16 12:31 AM Vol. 11, No. 1, 2004 Flexural-Shear Wave Propagation in Cracked Composite Beam Unauthenticated Download Date | 7/8/16 12:31 AM
Applied and Computational Mechanics, 2020
Due to the limitation that the classical beam theories have in representing transversal shear stress fields, new theories, called high order, have been emerging. In this work, the principal high order theories are unified in single kinematics and applied to the Equivalent Single Layer Theory. The governing equations and the boundary conditions for laminated beams are consistent variational obtained. From the equilibrium equations, the high order spectral finite element model was developed using the polynomial functions of Hermite and Lagrange, with interpolants in the zeros of Lobatto's polynomials. Finally, to demonstrate the finite element model's outstanding efficiency, numerical results (static and dynamic) are shown and compared with the elasticity theory solution
Frequency response analysis of laminated composite beams
Mechanics of Composite Materials, 1995
Fibre composite materials are widely used in structural applications requiring high stiffness-to-weight and strength-toweight ratios and a high damping. The significance of damping to the dynamic performance of structures is broadly recognized. Passive damping is an essential dynamic parameter for vibration and sound control, fatigue endurance, and impact resistance. Because of the increased need for highly damped structures, significant progress has been recently achieved in the analysis of damping of composites. Recent works on the damping mechanics of composite laminates [1-4] and structures [5][6][7][8] have shown that composite damping is anisotropic, highly tailorable, and depends on an array of micromechanical, laminate, and structural parameters, including constituent material properties, fibre volume ratios, ply angles, ply thicknesses, ply stacking sequence, temperature, moisture, and existing damage.
Modelling of wave propagation in composite plates using the time domain spectral element method
Journal of Sound and Vibration, 2007
This paper presents results of numerical simulation of the propagation of transverse elastic waves corresponding to the A0 mode of Lamb waves in a composite plate. The problem is solved by the Spectral Element Method. Spectral plate finite elements with 36 nodes defined at Gauss-Lobatto-Legendre points are used. As a consequence of the selection of Lagrange polynomials for element shape functions discrete orthogonality is obtained leading to the diagonal form of the element mass matrix. This results in a crucial reduction of numerical operations required for the solution of the equation of motion by time integration. Numerical calculations have been carried out for various orientations and relative volume fractions of reinforcing fibres within the plate. The paper shows how the velocities of transverse elastic waves in composite materials depend on the orientation and the relative volume fraction of the reinforcement.
Composite materials are used in many years ago and now days they are very use full. Since 4000 B.C straw was added soil to increase the resistance of the bricks. Although the benefits brought by the composite materials are known for thousands of years, just some years ago the right understanding of material behavior as well as the technology for designing composites war started to be developed. F111 airplane is the first model to incorporate this technology. Another example, of an airplane Boeing 767 has 2 tons in composite materials. The main possibility of material to combine with high strength and stiffness with low weight has also got the attention of the automobile industry. The Ford device or motor Company was developed a car in 1979 with some components made from composite materials. The type of modal was simply 570 kg lighter than the version in steel, only the transmission shaft had a reduction of 57% of its original weight. Since then Recently, Chrysler developed a car which was completely based on composite materials, and it " s known as CCV (Composite Concept Vehicle). Laminated composite materials are, generally lighter and stiffer than other structural materials. It consists of several layers of a composite mixture combination of matrix and fibers. Each and every layer can have similar (or) dissimilar material properties with having different fiber orientations under varying stacking sequence. Because of composite materials are produced in many several combinations and forms, the design engineer must consider many design alternatives. The structural components can made of composite materials such as different aircraft wings, helicopter blades, vehicle axles and turbine blades. This type of materials are used widely in structural applications where high strength-to weight and stiffness-to-weight ratios are required. In the composite " s fiber orientations by altering lay-up, composite beam material can be tailored to meet the particular requirements of stiffness and strength .The ability to manufacture a composite material are due to high strength of the material, low weight ratio, resistance in fatigue and low damping factor. The composite materials have wide range of applications in car and aircraft industries. Research work in the design of mechanical, aerospace and civil structure and development of composite materials has grown tremendously in few decades. The main thing is designing and modeling of industrial products for finding the free vibration characteristics of Laminated Composite Beam (LBC). Composites beam analysis is main important in mechanical and civil structural design such as railways, car suspension system and structural foundation. V. Tita, J. de Carvalho and J. Lirani [1] contributed for better understanding of the dynamic behavior of components made from fiber reinforced composite materials, specifically for the case of beams. In order to investigate the influence of the stacking sequence on the dynamic behavior of the components, using the Finite Element work has been carried out by experimental and numerical analysis and then results are presented and discussed. Subramanian [2] has investigated free vibration analysis of LCBs by using two higher order displacement primarily based on shear deformation theories and finite elements. Each theory is assumed as quantic and quartic variation of in-plane and transverse displacements within the thickness coordinates of the beam respectively. Results are indicating that application of those theories and finite element model leads to natural frequencies with higher accuracy. Banerjee [3] has investigated the free vibration of axially laminated composite Timoshenko beams using dynamic stiffness matrix technique. L Santosh Sreekanth, and m kumaraswamy [4] used to two different fibers analyze the critical buckling loads at relative cracked and non-cracked beam including crack depth. In this present work the fabrication of E-glass fiber reinforced beam dimensions 200mmX40mmX9mm was carried out by hand lay-up technique. The natural frequencies of these beams ware evaluated for different boundary conditions like Cantilever, Simply supported, Fixed-Simply supported and Fixed-Ended. The evolution of the natural frequencies for above conditions was carried out using accelerometer, impact hammer and FFT analyser which been ABSTRACT: In the present work E-glass fiber reinforced composite beams were fabricated by hand lay-up method having three layers with orientations (0 0 , 30 0 ,-45 0). The first three natural frequencies of these beams ware evaluated experimentally using accelerometer, impact hammer and FFT analyzer, which is being operated by DEWESOFT software. The dimensions of the beams are 200mmX40mmX9mm. The first three natural frequencies were obtained for different boundary conditions like Cantilever, Simply supported, Fixed-Simply supported and Fixed-Ended conditions. The numerical analysis was also carried out to find the first three natural frequencies of the beam for the above boundary conditions using Euler beam equation. The process of find the first three natural frequencies was repeated by simulating the composite beam using ANSYS 16.2.The Results thus obtained in three methods were compared.
2010
The necessity of the aerospace industry to reduce the cost, but to keep good safety standards has brought to the improvement of Structural Health Monitoring (SHM) applications. The objective of a SHM system is to allow an easily an low-cost detection of damages, before critical levels. As the diffusion of composite materials poses relevant problem regarding damage tolerance and damage detectability, SHM is one of the most promising technique for the development of lighter, more efficient and more reliable structures. Guided waves are one of the most interesting instruments for damage identification, basing on in-situ actuation and acquisition and on the possibility to correlate anomalies in wave propagation with internal damage. Modeling this kind of waves with a versatile approach as the Finite Elements (FE) allows great improvements in the SHM field of research, because this approach can reduce the experimental analyses and thus the development costs of a SHM system. Since the complex nature of the guided waves, especially in composite laminates, a validation of these FE models must be provided. This is the objective of this thesis. To accomplish this task the results obtained by the FE models are compared with the ones provided by another numerical technique expressly developed to model waves in plates. Such a technique is known as Semi-Analytical Finite Element (SAFE). This comparison is only possible after a particular post-processing technique, which involve the recursive use of the Fourier transform, of the displacements measured in the FE models. Finally these data are compared with the ones obtained from an experimental analysis of three different type of laminates. Since the results of the FE, of the SAFE and of the experiments are very similar, it is demonstrated that the FE models provided are well-suited to represent wave propagation in composite plates.
Free Vibration Analysis of Laminated Composite Beams using Finite Element Method
First order shear deformation (FSDT) theory for laminated composite beams is used to study free vibration of laminated composite beams, and finite element method (FEM) is employed to obtain numerical solution of the governing differential equations. Free vibration analysis of laminated beams with rectangular cross – section for various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency parameters are evaluated and compared with previous work available in the literature. The good agreement with other available data demonstrates the capability and reliability of the finite element method and the adopted beam model used.
Journal of Vibroengineering, 2018
This study developed to solve the problem of prediction of the natural frequencies of free vibration for laminated beams. The study presented the natural frequencies of composite beams with four layered and different boundary conditions. In each boundary condition, two cases are assumed: movable ends and immovable ends. Numerical results are obtained for the same material to demonstrate the effects of the aspect ratio, fiber orientation, and the beam end-movements on the non-dimensional natural frequencies of beams. Two aspect ratios are given in the numerical results, one is for relatively short-thick beams, while the other is for slender beams. It was found that the results of the non-dimensional frequencies obtained from the short-thick beams are generally much less than those obtained from the other slender beams for same fiber orientation and generally, the frequencies of longitudinal vibration increase as the aspect ratio increased. It was also found the values of the non-dimensional frequencies of the transverse modes are not affected by the longitudinal movements of the ends since these modes are generated by lateral movements only. However, the values of the natural frequencies of longitudinal modes are found to be the same for all beams with movable ends since they are generated by longitudinal movements only.