Effect Of Shear Deformation Research Articles

Dynamic response analysis of a foam-based nanoscale platebased on finite strip method

The present article deals with a dynamic response analysis of a foam-based nanoscale plate based on finite strip method (FSM). The nanoscale plate formulation has been adopted based upon a higher order plate theory and then, a higher order finite strip has been used to solve the problem. The considered finite strip is capable of considering the bending displacement and also shear deformation effects. The foam-based material has been treated as a porous material with some particular pore distribution. The non-uniformity of strain field as well as the nonlocality of stress field have been incorporated with the usage of nonlocal strain gradient elasticity. It is clearly showen that the proposed solution based on finite strip method can accurately simulate the dynamic response of considered plate under external forces. The scale factors due to small size of the plate and foam-based material will show a remarkable impact on the dynamic response.

A dynamic shell model for diagnostics of rotating machinery under periodic excitation

In this paper, a generalized dynamic model of a shell structure has been developed and utilized for diagnostics purposes. The dynamic model is three-dimensional, includes the effects of rotary inertia and shear deformation, and can handle moving loads in radial, tangential and axial directions. The model is utilized to determine in-plane radial displacements of the shell structure under concentrated radial loads for different boundary conditions. The periodic loads are constructed using harmonics obtained through the Fourier series expansion method. The modal expansion technique is implemented for calculation of the steady state forced response of the shell structure. A simplified acoustic radiation model is also implemented in conjunction with the dynamic shell model to predict the noise radiated from a rotating circular cylindrical shell structure under different kinematic, loading and boundary conditions. Moreover, forced vibration response and acoustic radiation predicted will be employed to reveal patterns in the signals that can potentially be used for diagnostics of rotating machinery applications. The shell model is derived using a comprehensive approach and thus can be used to model prevalent engineering applications ranging from electric motors to gears and bearings.

Vibration characteristics of microplates with GNPs-reinforced epoxy core bonded to piezoelectric-reinforced CNTs patches

In the current study, vibration characteristics of a three-layered rectangular microplate with Graphene nanoplatelets (GNPs)-reinforced Epoxy core which is fully bonded to piezoelectric-reinforced single-walled Carbon nanotubes (SWCNTs) patches are provided. The face sheets are subjected to the electric field and the microplate is assumed to be in a thermal environment and also, is located on the visco-Pasternak model of the elastic substrate. The GNPs and SWCNTs are dispersed through the core's and face's thickness according to the given functions. To account the shear deformation effect, tangential shear deformation theory (TGSDT) as a higher-order theory is employed and the modified strain gradient theory (MSGT) with tree independent length-scale parameters is selected to capture the size effect. Using the extended form of Hamilton's principle and variational formulation, the governing motion equations are derived and solved mathematically via Navier's scheme for simply supported edges microplate. By ensuring the validity of the results after comparing them in a simpler state with previously published ones, the effects of the most prominent parameters on the results are investigated. It is seen GNPs and CNTs dispersion patterns play an important role in the microplate vibrational behavior, as well as temperature variations. Since the under consideration microstructure can be accounted as smart structures, therefore, the outcomes of this study may help to design and create more efficient engineering structures, such as sensors and actuators and also micro/nano electromechanical systems.

Effect of tensile and compressive nonlinear edge loads on the buckling performance of hybrid metal composite laminates with cutouts

In the current study, the finite element approach has been used to investigate the effect of compression and tension types of nonlinear edge loads on the vibration and buckling performance of interlaminar hybrid fiber metal laminates (HFMLs) with and without cutouts. The effect of various hybridizations in cross ply, angle ply and quasi isotropic laminate schemes is studied extensively. Toward this a 9-noded heterosis plate element has been used to discretize the plate by taking into account the effect of shear deformation and rotary inertia. Since the stress distribution within the plate is highly non-uniform in nature, the dynamic approach has been used to solve the buckling problems. The present study consists of aluminum metal face sheets bounded with four layered hybrid laminate schemes, which includes glass and carbon layers. In which, six different hybrid configurations have been considered. The performance of each hybrid configuration along with different sized and positioned cutouts is well investigated under various nonlinear loading conditions, which are compressive and tensile in nature.

On the higher-order thermal vibrations of FG saturated porous cylindrical micro-shells integrated with nanocomposite skins in viscoelastic medium

Since the multi-layered structures are widely used nowadays, and due to interesting applications of cylindrical shells, this study is dedicated to analyzing free vibrational behaviors of functionally graded saturated porous micro cylindrical shells with two nanocomposite skins. Based on Biot's assumptions, constitutive relations for the core are presented and effective properties of the skins are determined via the rule of mixture. A sinusoidal theory is used to capture the shear deformation effects, and to account for the scale effects, the modified couple stress theory is employed which suggests a material length-scale parameter for predicting the results in small-dimension. With the aid of extended form of Hamilton's principle for dynamic systems, differential equations of motion are extracted. Fourier series functions are used to obtain natural frequencies and after validating them, a set of parametric studies are carried out. The results show the significant effects of porosity and Skempton coefficient, pores placement patterns, CNTs addition and distribution patterns, temperature variations, material length-scale parameter and viscoelastic medium on the natural frequencies of the microstructure. The outcomes of this work could be used to design and manufacture more reliable micro cylindrical structures in thermo-dynamical environments.

A Comparison Between the Linear and Nonlinear Dynamic Vibration Absorber for a Timoshenko Beam

Dynamic vibration absorbers (DVAs) play an important role in the energy dissipation of a vibrating system. Undesirable vibrations of structures can be reduced by using the absorbers. This paper investigates the effect of an attached energy sink on the energy dissipation of a simply supported beam subjected to harmonic excitation. The aim is to design an optimal linear energy sink (LES) and a nonlinear energy sink (NES) and then compare them with each other. Each absorber includes a spring, a mass, and a damper. For each absorber, the optimum mass, stiffness, and damping coefficients are obtained in order to minimize the beam’s maximum amplitude at the resonant frequencies. The optimization problem is minimizing the maximum amplitude of the beam subjected to an arbitrary harmonic force excitation. For consideration of the effects of rotary inertia and shear deformation, the Timoshenko beam theory is used. The mathematical model of beam with DVA is verified by using the ANSYS WORKBENCH software. Finally, by considering the uncertainty on the DVA parameters it was observed that the LES is more robust than the NES.

Effects of different interlaminar hybridization and cutout sizes on the vibration and buckling characteristics of fiber metal composite laminates under partial edge loads

Fiber reinforced polymer composites are quickly gaining market share in structural applications, but further growth is limited by their lack of toughness. Fiber hybridization is a promising strategy to toughen composite materials. By combining two or more fiber types, these hybrid composites offer a better balance in mechanical properties than non-hybrid composites. This study presents the effect of different interlaminar hybridization and cutout sizes on the vibration and buckling characteristics of hybrid fiber metal laminates (HFMLs) subjected to partial edge loads by developing finite element formulation. Since the stress distribution within the plate element is highly non-uniform in nature, the dynamic approach has been used to solve the buckling problems wherein two sets of boundary conditions are used, one for pre-buckling stresses and other one for buckling load calculations. A 9-noded heterosis plate element has been used to discretize the plate by taking into account the effect of shear deformation and rotary inertia. The present study consists of aluminum metal face sheets bound with four layered symmetric hybrid cross-ply laminate schemes. In this scheme, six different hybrid combinations have been considered. The performance of each hybrid combination is investigated under various loading combinations. Further, the effect of different parameters such as boundary condition, cutout ratio, width and position of localized edge loads, plate aspect ratio, and hybrid configurations are included in this work. It is revealed from the study that the hybrid configurations under different cutouts significantly affect the vibration and buckling characteristics under different localized edge loads.

Application of analytical model in the prediction of dynamic responses and fatigue damage of flexible risers: Part II – Dynamic analysis of flexible risers in large-scale domain using a direct moment correction method

In recent years, the dynamic responses of flexible risers have been the focus of many researchers. Most flexible risers undergo a substantial level of irregular motion from environmental loadings, which involves a continuous slip of helical wires. The slip of helical wires especially leads to a hysteretic effect by reducing the bending stiffness, making it hard to predict the dynamic responses of flexible risers. The current study, as an extension to Part I, presents a new large-scale dynamic analysis method for flexible risers. The suggested method creates a large-scale model for the dynamic analysis that considers a geometric and bending nonlinearity of flexible risers. The kinematics of each beam element is formulated based on a Green-Lagrangian strain and the interaction with the seabed, providing a realistic analysis of flexible risers. In particular, the current study introduces a direct moment correction method that modifies the internal force vector using an improved analytical model. The improved analytical model is assigned at each node of the large-scale model and estimates an accurate bending hysteresis curve considering the effect of shear deformation and varying tension. The suggested method corrects the bending moment and shear force of all beam elements based on the bending hysteresis curves obtained from the improved analytical model, by which a complex bending behavior of flexible risers is reflected in a large-scale domain. As a result, this study achieves a more accurate prediction of the dynamic responses and fatigue damage of flexible risers. A new dynamic analysis program, called OPFLEX, is developed herein based on the suggested analysis method. Using the developed program, the current study conducts several numerical investigations to identify the effect of the shear deformation and varying tension. Consequently, it is confirmed that the shear deformation of internal layers reduces the fatigue damage of helical wires by delaying the increase of internal stress. It is also identified that the effect of varying tension deteriorates the fatigue life of flexible risers through a continuous change of contact pressure during bending.

Impacts of residual stress and shear deformation on 2D steel frames using fiber plastic hinge element: nonlinear behavior and strength

In this study, impacts of residual stress and shear deformation are investigated on 2D steel frames using a new fiber plastic hinge method. Geometry and material nonlinearities, residual stress, shear deformation, imperfections are considered simultaneously in the nonlinear analysis. The proposed method is efficient in computational efforts since the one-element modeling is used for the nonlinear analysis by employing stability functions for capturing the P-small delta phenomenon. The P-large delta phenomenon is considered using the geometric stiffness matrix. Plastic hinges are assumed to be formed at two ends of members. Cross-sections at two ends of members are divided into many fibers. The ECCS residual stress pattern is assigned directly through fibers as initial stress conditions. A finite element program is coded using the Fortran programming language for predicting the nonlinear behavior and ultimate strength of planar steel frames. The behavior and load-carrying capacity of steel frames are predicted precisely and efficiently using the nonlinear inelastic analysis. A case study of a large-scale planar steel frame is investigated for the frame's behavior and strength under the effects of residual stresses and shear deformation. Through numerical examples, we recommend that both residual stress and shear deformation should be considered in the advanced direct analysis and design procedures for steel-framed structures.Article highlightsA nonlinear 2D beam column element is developed successfully using onlyone element per member for modeling.Geometric nonlinearities, material plasticity, residual stress, and sheardeformation are investigated simultaneously.Both residual stress and shear deformation should be considered in the engineering design of steel frames.

Effect of reinforced cutouts on the buckling and vibration performance of hybrid fiber metal laminates

The cutouts are commonly found in fiber metal laminates to facilitate to pass electrical wires, water/fuel lines and sometime to facilitate easy access and inspection. Sometimes, such cutouts need to be reinforced by providing stiffener around the cutouts to avoid pre-mature failures. This article addresses the effects of reinforced cutouts and non-linearly varying edge loads on the vibration and buckling performance of inter laminar hybrid fiber metal laminates (HFMLs) by utilizing finite element approach. Toward this a 9-noded heterosis plate element has been used to discretize both plate and stiffener by taking into account the effect of shear deformation and rotary inertia. The stiffener considered in this study is spread in nature. The displacement compatibility by the plate and stiffener is maintained by using transformation matrix. The effect of eccentricity of the spread stiffener is also incorporated within the transformation matrix. Since the stress distribution within the plate is highly non-uniform in nature, the dynamic approach has been used to solve the buckling problems. The present study consists of aluminum metal face sheets bonded with four layered symmetric hybrid cross-ply laminates, in which six different hybrid configurations have been considered. The performance of each hybrid configuration along with different sized and positioned reinforced cutouts is well investigated under various nonlinear loading conditions.

Effect of compression and tension types of concentrated edge loads on buckling and vibration behavior of interlaminar hybrid fibre metal laminates

The present study deals with the numerical investigation on the buckling and vibration behaviour of interlayer hybrid fibre metal laminates (HFMLs) subjected to different types of concentrated edge compression and tension loads. The term interlayer hybrid represents carbon and glass fibre laminates are sandwiched in between aluminum face sheets. Totally six different hybrid configurations are taken into consideration separately for cross-ply and angle-ply layup schemes. To serve this purpose a finite element code using MATLAB is developed to examine the effects of hybrid configuration, aspect ratio, fiber orientation, type of loading and boundary conditions have been considered to study the buckling responses of HFMLs. The plate is modelled by using 9-noded heterosis elements by considering the effect of shear deformation and rotary inertia. It is revealed from the investigation that the hybrid configurations and loading conditions significantly affect the buckling and vibration characteristics of HFMLs.

Application of analytical model in the prediction of dynamic responses and fatigue damage of flexible risers: Part I – Improvement of analytical model considering shear deformation and varying tension effects

Flexible risers have been widely utilized for the transfer of oil and gas products from a well to production units. The components of flexible risers, unlike steel risers, experience complex contact phenomena during bending. The contact between helical wires and adjacent layers especially causes a significant level of bending nonlinearity, making it hard to estimate the structural responses. Accordingly, a large-scale dynamic analysis of flexible risers usually involves an analytical model that predicts the bending moment and axial stress of helical wires based on theoretical approaches. The analytical model consists of an axis-symmetrical model and a bending model. Among them, the bending model plays a critical role in the prediction of the bending responses of flexible risers. The conventional bending models usually neglect the shear deformation of internal layers and continuity of sliding force, which leads to a significant error of analysis. Furthermore, the previous bending models assume that the contact pressure on helical wires is constant during bending. In real operating conditions, however, most flexible risers experience a considerable change of tension that governs the slip of helical wires. Hence, the current study presents a new dynamic analysis method for flexible risers. The suggested analytical model improves the bending model based on an accurate estimation of the internal strain field considering the shear deformation and continuous sliding force. Also, this study proposes a stiffness update method to reflect the effect of varying tension in the dynamic analysis. The presented method updates the bending property of flexible risers considering the continuous change of the contact pressure from varying tension. For the validation of suggested method, the current study carries out numerical simulations with a pure bending and varying tension for the internal diameter 7 inches flexible risers. It is identified that the suggested analytical model provides accurate analysis results. Moreover, it is found that the effect of varying tension gives a significant impact on the bending behavior of flexible risers by changing the slip condition of helical wires. Part I of this series of papers describes the detailed formulation method for the analytical model and with some verification examples. The suggested analytical model is expanded to the large-scale dynamic analysis in Part II for the investigation of the effect of shear deformation and varying tension.

Effects of Shear Deformation of Struts in Hexagonal Lattices on their Effective In-Plane Material Properties

Two-dimensional lattices are widely used in many engineering applications. If 2D lattices have large numbers of unit cells, they can be accurately modeled as 2D homogeneous solids having effective material properties. When the slenderness ratios of struts in these 2D lattices are low, the effects of shear deformation on the values of the effective material properties can be significant. This study aims to investigate the effects of shear deformation on the effective material properties of 2D lattices with hexagonal unit cells, by using the homogenization method based on equivalent strain energy. Several topologies of hexagonal unit cells and several slenderness ratios of struts are considered. The effects of struts’ shear deformation on the effective material properties are examined by comparing the results of the present study, in which shear deformation is neglected, with those from the literature, in which shear deformation is included.

Dynamic characteristics of a hydraulic curved pipe subjected to random vibration

In this paper, the effects of external random excitation on the dynamic characteristics of a hydraulic curved pipe are investigated. A random vibration motion equation of a curved pipe conveying fluid is determined using Hamilton's principle, in which the fluid-structure interaction (FSI) and the effect of shear deformation are taken into account. The finite element method (FEM) and discrete analysis method of random vibration (DAMRV) are employed to solve these equations. Then, the dynamic characteristics of a curved pipe with different vibration and fluid parameters under two types of supported modes are determined. The numerical results show that the dynamic characteristics of the curved pipe have significant influenced by different parameters. Moreover, the numerical and experimental results are found to have good consistency, which demonstrates that the proposed method can provide theoretical reference and technical support for the design and selection of curved pipes subjected to random vibration.

Enhancing bandwidth of metamaterial plate with linear and nonlinear passive absorbers

In this work, passive vibration absorbers are used to obtain a metamaterial vibrating plate. For this purpose, a set of linear and nonlinear passive absorbers are used. The plate is modeled based on Mindlin’s theory in which the effects of rotary inertia and shear deformation are considered. The metamaterial plate is considered to be both linear and nonlinear, with a set of linear, nonlinear, and viscous absorbers (Maxwell and Maxwell–Voigt). By optimizing the absorber parameters, a noticeable reduction in the vibration amplitude of the plate is obtained, without imparting a significant mass to the original plate. The effects of mass, stiffness, damping of the absorber as well as the number of absorbers are also investigated so that the sensitivity of the behavior of the system with changing the parameters is minimized. The effect of absorbers at lower frequencies is the main focus of this work. There is more than 77% reduction in the vibration amplitude of the plate, while the total added mass is lower than 10%, which is much less than the values given in similar works. Also, the nonlinear effects of the plate have been greatly reduced and no new resonances with sufficient bandwidth have emerged, and linearization of the nonlinear plate with absorber is achieved. Finally, the performances of the used absorbers are compared.

Free vibration analysis of nonsymmetrically laminated cross-ply L-shaped frames

Fiber-reinforced composite laminates can be tailored to produce structural elastic couplings that optimize their response in dynamic environments. It is therefore essential that the free vibration characteristics of structural elements fabricated from fiber-reinforced composites be accurately modeled and investigated. In this work, an analytical wave-based approach is extended to study the in-plane vibrations of nonsymmetrically laminated cross-ply L-shaped frames. The proposed theory accounts for the effects of shear deformation, rotary inertia, and the elastic coupling between in-plane bending and longitudinal deformations. The reflection matrices at the boundaries, together with the reflection and transmission matrices at the corner joint of the L-shaped frame are derived. A traveling wave approach is then used to systematically assemble the small-order matrices into a single expression that can be used to efficiently calculate the exact natural frequencies. An expression for evaluating the mode shapes of the frame for general boundary conditions is also given. The application of the wave-based method is illustrated through several numerical examples and the results are validated using independent finite element models. As part of the numerical analysis, the influence of the number of cross-ply layers on the natural frequencies is investigated.

Out-of-plane free vibration analysis of three-layer sandwich beams using dynamic stiffness matrix

This paper has been devoted to exact calculation of the natural frequencies for out-of-plane free vibration of three-layer symmetric sandwich beams by using dynamic stiffness matrix method. Governing differential equations of motion have been derived using Euler-Bernoulli beam theory and St. Venant’s torsion theory, so that the effects of shear deformation in the face layers and rotary inertia are not taken into account and the cross-section is allowed to warp without restraint. Wittrick-Williams algorithm has been used to calculate the natural frequencies. Accuracy and ability of the dynamic stiffness matrix method have been illustrated in form of several examples. Results are verified through comparison with the natural frequencies obtained from ABAQUS software. Full independence of out-of-plane bending and torsional modes of vibration for three-layer symmetric sandwich beams has been proven.

Dynamic Analysis of Functionally Graded Sandwich Plates under Multiple Moving Loads by Ritz Method with Gram–Schmidt Polynomials

This paper investigates the dynamic behavior of functionally graded sandwich plates under multiple moving loads. The first-order shear deformation theory of plates is adopted with the effects of shear deformation and rotary inertia included. By using Lagrange’s equations, the equations of motion for the dynamic behavior of the plate are derived. Then they are solved by the Ritz and Newmark time integration methods for the free and forced vibrations of the plates with different boundary conditions. To guarantee that all terms in the admissible functions can cope with the essential boundary conditions, the Gram–Schmidt procedure is used to generate the shape functions for the Ritz method. The influences of several factors on the dynamic response of the plates, such as layer thickness ratio, boundary condition, velocity, excitation frequency, phase angle, etc., are examined and discussed in detail. The numerical study indicates that the dynamic deflection has initial fluctuated growth in the low range of moving load velocity before reaching the peak at the critical velocity, which is followed by the considerable decrease in magnitude. Besides, the gaps or distances between the moving loads also play an important role in predicting the dynamic deflections of the plate when subjected to more than one moving loads.

Thermo-mechanical buckling analysis of FG-GNPs reinforced composites sandwich microplates using a trigonometric four-variable shear deformation theory

The current study is aimed to investigate the thermo-mechanical buckling responses of the sandwich microplate with Graphene nanoplatelets (GNPs)-reinforced Epoxy core fully bonded to single-walled carbon nanotubes (SWCNTs)-reinforced piezoelectric patches. The face sheets were exposed to the electric field and the microplate was assumed to locate on the Pasternak elastic substrate. The GNPs and SWCNTs were dispersed throughout the core and face thickness according to some specific functions. To consider the shear deformation effect, tangential shear deformation theory (TSDT), as a trigonometric higher-order theory, was used. The size effects were also included through applying and the modified strain gradient theory (MSGT). The virtual displacement principle was utilized to derive the governing equations and then by employing an analytical method, they were solved. The validity of the results was confirmed by comparing the results for simpler state with previously published ones. A parametric study is provided to observe behavior of the microstructure in different conditions. It was observed that GNPs and CNTs dispersion patterns play an important role in the microplate buckling behavior, as well as temperature variations. The outcomes of this work may help to manufacture more efficient engineering smart structures, such as micro/nanoelectromechanical systems.

In-situ investigation of deformation behavior and fracture forms of Ti/Al/Mg/Al/Ti laminates

In-situ bending and stretching were conducted on hot-rolled and annealed Ti/Al/Mg/Al/Ti laminates, with a focus on crack initiation and propagation of intermetallics and component layers, which helps to clarify their deformation behavior and fracture forms. The results show that delamination is the early fracture form of laminate with or without intermetallics at Al/Mg interface, so Al/Mg interfacial bonding strength determines the mechanical properties of laminate. Various and irregular intermetallics cracks lead to Al/Mg interface delamination in annealed laminate and help to release stress. Necking and fracture of component layers are observed at the late deformation stage, and the sequence is Al, Mg and Ti layers, resulting from their strength. Angle between crack propagation direction and stretching direction of Mg layer both in rolled and annealed laminates is around 45° due to the effect of shear deformation, and crack convergence leads to final complete fracture of Mg layer.