Open Edge Crack Research Articles

Aeroelastic flutter of actively controlled nanocomposite beams with an open edge crack

Active control of aeroelastic flutter in composite structures is vital for improving the performance and safety of aerospace systems. Understanding the impact of cracks on flutter behavior of active controlled structures is of importance for early crack detection and accident prevention. The present work investigates the aeroelastic flutter of functionally graded (FG) graphene nanoplatelet (GNP)-reinforced nanocomposite (GNPRC) beams containing an edge crack under active control with an attached piezoelectric patch. The governing differential equations are derived using Hamilton's principle together with the Ritz method, based on the first order shear deformation theory (FSDT) and a rotational spring model. The flutter velocities of the system are determined by numerically solving the eigenvalue problem. Through a comprehensive parametric study, the effects of crack length and location, GNP parameters, and different control actions on the flutter velocities of the FG-GNPRC beams with different end supports are discussed. The results reveal that the presence of a crack reduces the flutter velocities of GNPRC beams, with the extent of reduction depending on the GNP distribution pattern, crack location and support ends. Additionally, the cracked GNPRC beams can be enhanced by attaching piezoelectric actuators with feedback gains at appropriate locations on the beam's surface.

Vibrations of cracked functionally graded beams: General solution and application – A review

This paper presents a unified approach to vibration analysis of functionally graded beams with transverse open-edge cracks based on the so-called vibration shape obtained as a general solution of vibration equations in the frequency domain. The crack is modeled by a pair of translational and rotational springs of stiffness computed from the crack depth in dependence upon functionally graded material parameters. The frequency-dependent vibration shape functions allow one not only to obtain the closed-form solution of both free and forced vibrations for multiple cracked FGM beams but also to develop the well-known methods such as Transfer Matrix Method or Dynamic Stiffness Method for analysis of FGM framed structures. The proposed theoretical developments have been illustrated by their application for modal analysis and frequency response analysis of multi-span and multistep beams.

Investigation of Transverse Vibration Characteristics of Cracked Axially Moving Functionally Graded Beam Under Thermal Load

This article presents a new analysis of the vibration characteristics of open-edge cracks for graded moving beams under thermal load. The material property gradient is based on the distribution of the power law in the direction of the beam thickness. The vibration equation is obtained depending on the precept of Hamilton and resolved by the extension of Galerkin’s approach. A rotational spring is used to represent the cracking in the beam. The effects of the axial velocity, gradient index, thermal load, and cracking parameters on vibration characteristics are observed. Furthermore, the mode shapes of the simple support cracked moving graded beam are determined. The results show that the rise in the axial velocity, the crack depth, and the material property index led to a decrease in the natural frequencies, which indicates the results obtained. HIGHLIGHTS Stability and vibrations analysis of the cracked gradient beams with an axial motion under a uniform temperature rise The effect of axial velocity, gradient index, thermal load, and cracks parameter was studied Galerkin’s technique is developed for vibrational analysis of cracked graded beams with longitudinal motion The Euler-Bernoulli beam model was used taking into account the effect of rotatory inertia GRAPHICAL ABSTRACT

Vibrational power flow analysis of Timoshenko microbeams with a crack

In this paper, an analytical model based on the modified couple stress theory and Timoshenko beam theory is developed to study the vibrational power flow of a microbeam with a crack. The open edge crack on the microbeam is modeled as a rotational spring, which connects the two segments of the microbeam separated by the crack location. The governing equations of the cracked microbeam are derived from Hamilton's principle. By introducing the differential operator method, the differential equations are transformed into algebraic equations, and the governing equations are decoupled. The wave propagation method is applied to solve the vibrational problem of a cracked microbeam under a transverse harmonic excitation. Both the input power flow and the transmitted power flow in the cracked microbeam are computed and analyzed. The size effect of the cracked microbeam in terms of material length scale is firstly analyzed. Subsequently, the effects of crack depth and crack location on the input and transmitted power flows are investigated. It is found that the existence of crack significantly changes the transmission characteristics of the power flow.

Adaptive Probabilistic Optimization Approach for Vibration-Based Structural Health Monitoring

This paper presents a novel adaptive probabilistic algorithm to identify damage characteristics by integrating the use of the frequency response function with an optimization approach. The proposed algorithm evaluates the probability of damage existence and determines salient details such as damage location and damage severity in a probabilistic manner. A multistage sequence is used to determine the probability of damage parameters including crack depth and crack location while minimizing uncertainties. A simply supported beam with an open edge crack was used to demonstrate the application of the algorithm for damage detection. The robustness of the algorithm was tested by incorporating varying levels of noise into the frequency response. All simulation results show successful detection of damage with a relatively high probability even in the presence of noise. Results indicate that the probabilistic algorithm could have significant advantages over conventional deterministic methods since it has the ability to avoid yielding false negatives that are quite common among deterministic damage detection techniques.

Identification and evaluation of cracks in electrostatically actuated resonant gas sensors using Harris Hawk / Nelder Mead and perturbation methods

In this paper we study the static deflection, natural frequency, primary resonance of an electrostatically actuated cracked gas sensor. Besides, a novel hybrid metaheuristic algorithm is proposed to detect the location and depth of possible crack on the microcantilever systems. The gas sensor configuration consists of a microcantilever with a rigid plate attached to its end. The nonlinear effects of the electrostatic force and fringing field are taken into account in the mathematical model. The crack is represented by a rotational spring. In the first part, the effect of crack on the static and dynamic pull-in instability are studied. The equations of motion are solved by the application of the perturbation methods. Next, an inverse problem is formulated to predict the location and depth of the crack in the gas sensor. For that purpose, the weighted squared difference of the analytical and predicted frequency response is considered as the objective function. The location and depth of the crack in the microsystem are determined using the hybrid Harris Hawk and Nelder Mead optimization algorithms. The accuracy and efficiency of the proposed algorithm are compared with the HHO, DA, GOA, and WOA algorithms. Taguchi design of experiments method is used in order to tune the parameters of optimization algorithms systematically. It is shown that the proposed algorithm can predict the exact location and depth of the open-edge crack on an electrostatically actuated microbeam with proof mass.

Improvement of the computational efficiency of metaheuristic algorithms for the crack detection of cantilever beams using hybrid methods

This study examines the capability of various optimization algorithms and proposes novel hybrid algorithms for more precise prediction of open-edge cracks in cantilever beams. The natural frequencies of the beam with a crack are obtained by modal analysis and experimentally validated by impact testing. The performance of Harris hawk optimization (HHO), electrostatic discharge algorithm (ESDA), pathfinder algorithm (PFA) and Henry gas solubility optimization (HGSO) algorithms from the literature is evaluated to determine the location and depth of an open-edge crack for an Euler–Bernoulli beam. Then, hybrid algorithms (HHO-NM, ESDA-NM and PF-NM) are proposed to improve the results of the aforementioned algorithms. Simulation results show that the proposed hybrid algorithms yield much more precise results with fewer function evaluations than the previously introduced algorithms and, therefore, have superior crack detection capability. Statistical post hoc analysis shows that the proposed hybrid algorithm can be considered a high-performance algorithm, which can significantly improve the efficiency of crack detection applications.

Transverse Vibration of Cracked Graded Rayleigh Beam with Axial Motion

The paper presents the transverse vibration of an open edge crack graded Rayleigh beam with axial motion. The vibration equation was obtained relying on Hamilton's precept and resolved by the approach of Galerkin's. The power-law is adopted to represent the gradient of properties of the material composing the beam along the direction of the thickness. Cracks were modeled as rotational massless spring. The effects of axial velocity, material property change index, location, and depth of cracking on the vibration characteristics are observed. Also, the corresponding mode shapes are found for cracked moving graded Rayleigh beam with simply supported, and fixed-fixed end supports. The results clear up that the natural frequencies drop due to the rise in the axial velocity, the crack depth, and the material property index

Laboratory study on the propagation of edge cracks in rock-like material and its implication in coal mining

Rock fracture propagation is a major hazard for mining and tunnel excavation in fractured rock masses or coal seams. A longwall mining panel with a typical dimension of 200m (width)×1000m (length)×3m (height) can be considered as an open edge crack. The fracturing processes in the vicinity of the edge crack (or the longwall panel) particularly in the roof and floor are critically important for the safety of mining operation because fracturing can lead to water inrush and dynamic loading on the working face. It’s therefore important to understand and predict the pre-existing edge crack initiation and propagation in rock masses. This paper describes a study investigating the mechanisms and pathways of rock fracture under uniaxial compression. In this study, a rock-like material which consists of model gypsum, water and diatomaceous earth at a mass ratio of 165:75:2 was used. The uniaxial compression strength of the material decreased with the increase of the length of pre-existing edge crack. During the tests, wing (tensile) cracks were first observed at the tip of the pre-existing edge crack. This was followed by secondary cracks as the loading increased. The final failure of the specimens however was dominated by tensile cracks throughout the specimens. Due to the sudden crack initiations in the specimens, the loading stress in the specimen varies stepwise, and acoustic emission (AE) energy and amplitude showed abrupt changes when crack initiated. When the crack initiation occurred, the loading stress of the specimens showed a notable retreat in the stress-strain curve, and the recorded AE energy and amplitude showed a sharp spike. These findings from this experimental study have been applied to the underground longwall mining to explain the failure mechanisms in the floor of the mining panel. The fracturing process associated with the pre-existing edge crack resembles the formation of flow channels for water inrush during longwall mining.

Nonlinear Dynamic Response of FG Graphene Platelets Reinforced Composite Beam with Edge Cracks in Thermal Environment

This paper presents a numerical investigation on the nonlinear dynamic response of multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) beam with open edge cracks in thermal environment. It is assumed that graphene platelets (GPLs) in each GPLRC layer are uniformly distributed and randomly oriented with its concentration varying layer-wise along the thickness direction. The effective material properties of each GPLRC layer are predicted by Halpin-Tsai micromechanics-based model. Finite element method is employed to calculate the dynamic response of the cracked FG-GPLRC beam. It is found that the maximum dynamic deformation of the cracked FG-GPLRC beam under dynamic loading is quite sensitive to the crack location and grows with an increase in the crack depth ratio (CDR) and temperature rise. The influences of GPL distribution, concentration, geometry as well as the boundary conditions on the dynamic response characteristics of cracked FG-X-GPLRC beams are also investigated comprehensively.

Analytical solution of deflection of multi-cracked beams on elastic foundations under arbitrary boundary conditions using a diffused stiffness reduction crack model

Crack can significantly affect the performance of structures and is one of the crucial indicators of damage in structural health monitoring. In this paper, the deflection behaviors of Euler–Bernoulli beams with arbitrary open edge cracks under arbitrary elastic boundary conditions are investigated. A continuous diffused stiffness reduction crack model is implemented to simulate the cracks in beams, which can incorporate multiple cracks and consider the stiffness reduction effect in the vicinity of a crack. With the proposed diffused stiffness reduction model, the fourth-order differential equation governing the deflection behavior of the multi-cracked Euler–Bernoulli beam is constructed. The powerful variational iteration method is applied to obtain the analytical solution of the multi-cracked beams on elastic foundations. Five shape functions are introduced, based on which the deflection of the multi-cracked beam is proposed. Both the solutions corresponding to the general elastic boundary conditions and the conventional boundary conditions are presented explicitly. The deflection solution is benchmarked and verified against the literature, and encouraging agreements are obtained. Parametric studies are carried out to investigate the influences of crack position, crack ratio, stiffness of the elastic foundation, and boundary conditions on the deflection of the cracked beams. The proposed crack model and the deflection solution overcome some of the limitations in the literature.

Experimental and numerical study on dynamic analysis of cracked glass epoxy composite beam

For the present work, the dynamic response of a cracked-cantilevered glass–epoxy composite beam has been investigated using numerical as well as experimental studies. Linear free vibration of a cantilevered composite beam with an open edge crack is considered. The presence of crack certainly changes the dynamic behaviour such as natural frequencies and natural modes of the system. A proper investigation of this behaviour is essential to understand and perform an improved way of online condition monitoring based on vibration signals of such systems. The primary objective of this work is to convert a continuous system into an equivalent single degree of freedom (SDOF) system by applying the lumped parameter concept. Subsequently, a reduction in the equivalent stiffness has been observed due to the presence of a crack by using fracture mechanics approach. Variation of material properties of glass epoxy composites are along all the three dimensions, however, the properties in transverse direction are of our main concern. The dynamic behaviour of such cracked composite beams is firstly computed using the reduced equivalent dynamical model of the beam with varying crack locations. Subsequently, experiments are performed to obtain the natural frequency of the cracked-composite beam, results are also obtained using finite element packages using numerical computation. Results obtained from the lumped parameter model and numerical simulations are compared with that of experimental results. A strong agreement between the results obtained using various methods was observed. Finally, a wide parametric study is performed using these methods for various geometric and crack parameters.

Nonlinear bending of elastically restrained functionally graded graphene nanoplatelet reinforced beams with an open edge crack

This paper investigates the nonlinear bending behaviours of multilayer functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) beams elastically restrained at both ends and with an open edge crack. The GPLs are uniformly distributed in each individual layer but follow a layer-wise variation along the thickness direction. The effective Young's modulus is predicted by the modified Halpin-Tsai micromechanics model while both the thermal expansion coefficient and Poisson's ratio are determined by the rule of mixture. The finite element method is employed to discretize the edge cracked beam, with a particular focus on the influences of the location and depth of the open edge crack on the nonlinear bending deflections of FG-GPLRC beams. It is found that adding a higher content of GPLs into the matrix, dispersing more GPLs near the top and bottom surfaces of the beam and increasing the elastic stiffness of the end constraints can effectively strengthen the beam stiffness hence considerably reduce the deflection. An increase in the crack depth ratio (CDR) and temperature rise weaken the structure and consequently lead to bigger deflections. The nonlinear bending performance of the beam is also found to be highly sensitive to the location of the crack.

The effect of crack geometry on mode shapes of a cracked cantilever beam

ABSTRACT Due to the limitations of the manufacturing processes, defect like crack is produced in the structures. Crack gives the catastrophic failure of the structures or beams; hence, the detection and classification of the cracks are important issues in the scientific research. For a long time, the free vibration-based crack detection methods have been used for the possible crack detection in the structures. On the other hand, the effect of arbitrary and random defect geometry, i.e. V-shaped, U-shaped open edge cracks on the applicability of these methods has been overlooked. In order to investigate this issue, three crack parameters, i.e. crack geometry, crack depth and crack locations, were considered on the cantilever beam to study its effect on the mode shapes of cracked beams. The stiffness of cracked cantilever beams was evaluated by the deflection method using ANSYS. Theoretical method, Numerical method and Experimental method have been used to compute the mode shapes of cracked beams. Through free vibration study, it is found that spring steel structures are somewhat sensitive to the change in crack geometries as far as the mode shapes are concerned. So, it is obvious that the mode shape based free vibration method can satisfactorily predict the crack depth and location in spring steel structures irrespective of the crack geometries.

Damage Localization in Laminated Composite Beams with Multiple Edge Cracks Based on Vibration Measurements

This study presents identification and localization of open transverse edge cracks in laminated composite beams by using vibration measurements. To this aim, a composite cantilever beam is considered under six damage scenarios. Natural frequencies and mode shapes of the beam for each case are obtained numerically by using a shear-deformable finite element model as well as ANSYS® software. Experimental measurements are then performed to validate the numerically calculated results. To show consistency among the calculated and measured results, modal assurance criterion values are obtained for each case. For determination of the crack locations on the beam, changes in the mode shape curvature and the modal flexibility are employed based on the experimental and numerical modal data. Comparisons showed that the methods considered give reasonable results, and they can be efficiently used for damage localization in laminated composite beams including multiple edge cracks.

Investigation of Crack Effects on Isotropic Cantilever Beam

The effect of an open edge crack on the parameters of an isotropic aluminum cantilever beam was investigated. The rotational stiffness and flexibility of the cantilever beam crack were analytically calculated for various crack depths. The results showed that as the depth of the crack increased, the rotational stiffness decreased and flexibility increased. For the intact cantilever beam, acceptable variation was validated by comparing the analytically estimated natural frequencies of the first three modes of bending vibration, and those obtained through modal analysis using the block Lanczos method of finite element analysis software ANSYS v16. The software was used to perform a structural, modal and harmonic analysis of the cracked cantilever beam under different scenarios. The results showed a reduction in the natural frequencies with the existence of the crack. The amount of the reduction varied based on the location and depth of the crack and the pattern of mode shapes. The calculated value of stiffness of the cantilever beam decreased with the presence of the crack. The amount of the decrease was dependent on the depth and location of the crack. The calculated values of the (SIF) stress intensity factor in mode I of the crack (opening edge crack) were proportional to the depth of the crack and inversely proportional to the distance of the crack from the fixed end of the cantilever beam. Based on these results, it is inferred that changes in the modal and structural parameters of the cracked cantilever beam were evidence which could be used to identify cracks.

Thermal buckling and postbuckling of edge-cracked functionally graded multilayer graphene nanocomposite beams on an elastic foundation

This paper investigates thermal buckling and postbuckling behaviors of functionally graded graphene nanoplatelet (GPL)-reinforced composite multilayer beams containing an open edge crack and resting on a Pasternak-type elastic foundation based on the first-order shear deformation beam theory including von Kármán geometric nonlinearity. The material properties of functionally graded GPL-reinforced composites (GPLRCs), which exhibit piece-wise variation along the thickness direction, are evaluated using micromechanics based models. The bending stiffness of the cracked section is estimated by the rotational spring model. The obtained nonlinear partial differential equations of equilibrium are discretized by the differential quadrature method, and then an iterative method is used to obtain the thermal buckling loads and postbuckling load-deflection curves. Detailed parametric studies are conducted to investigate the effects of crack length, GPL distribution pattern, GPL weight fraction, GPL length-to-width and length-to-thickness ratios, boundary conditions, and foundation stiffnesses on the thermal buckling loads and postbuckling response of the cracked GPLRC beams.

Geometrically non-linear forced vibrations of fully clamped functionally graded beams with multi-cracksresting on intermediate simple supports

The objective of this work is to investigate the non-linear forced dynamic response at large vibration amplitudes of fully clamped functionally graded beams containing a multiple open edge cracks and resting on intermediate simple supports. The theoretical model is based on the Euler-Bernoulli beam theory and the crack rotational spring model. The functionally graded beam properties are supposed to vary continuously through the beam thickness. A homogenization procedure based on the neutral surface approach taking into account the presence of the crack is developed to reduce the problem examined to that of an equivalent isotropic homogeneous multi-cracked beam. In the non-linear analysis, harmonic motion is assumed and the discretized expressions for the beam total strain and kinetic energies are derived by applying Hamilton’s Principle, so as to reduce the problem to a non-linear algebraic system solved using an approximate explicit method previously applied to various non-linear structural vibration problems. Considering the forced vibration case, the non-linear frequency response functions are obtained numerically in the neighbourhood of the predominant non-linear mode shape using a single mode approach. The effects of crack, the beam material gradient and the applied harmonic force are presented and discussed.

Free vibrations of laminated composite beams with multiple edge cracks: Numerical model and experimental validation

Free vibration analysis of laminated composite beams including open transverse cracks is presented by using a shear-deformable thirteen degrees-of-freedom finite element model, which considers extension-twist, bending-twist and bending-extension couplings, and the Poisson's effect. Lagrange's equation is employed to derive the equations of motion. Trial functions are selected as cubic Lagrange polynomials for deflections while quadratic for the others in derivation of element mass and stiffness matrices. Damage is introduced into the beam by reducing stiffness of elements within damaged zone. Comparisons are made with the available literature to show the present element's accuracy. Experimental validation is also performed with through ambient vibration tests on a cantilever laminated composite beam under six damage scenarios. According to the results, the methodology presented in this study provides a simple and quick way in a sufficient accuracy to determine the natural frequencies and mode shapes of laminated composite beams with open transverse non-propagating edge cracks.

Vibration and Buckling Characteristics of Functionally Graded Graphene Nanoplatelets Reinforced Composite Beams with Open Edge Cracks.

This paper investigates the free vibration and compressive buckling characteristics of functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) beams containing open edge cracks by using the finite element method. The beam is a multilayer structure where the weight fraction of graphene nanoplatelets (GPLs) remains constant in each layer but varies along the thickness direction. The effective Young’s modulus of each GPLRC layer is determined by the modified Halpin-Tsai micromechanics model while its Poisson’s ratio and mass density are predicted according to the rule of mixture. The effects of GPLs distribution pattern, weight fraction, geometry, crack depth ratio (CDR), slenderness ratio as well as boundary conditions on the fundamental frequency and critical buckling load of the FG-GPLRC beam are studied in detail. It was found that distributing more GPLs on the top and bottom surfaces of the cracked FG-GPLRC beam provides the best reinforcing effect for improved vibrational and buckling performance. The fundamental frequency and critical buckling load are also considerably affected by the geometry and dimension of GPL nanofillers.