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• Study focuses on analyzing the free vibrations of doubly curved laminated shells. • C ° finite element based on MHOZT is used for the analysis. • Model incorporates higher order displacement kinematics and accounts for both transverse normal and shear strains. • The formulation includes extended thickness criteria. • Numerical results closely resemble those from 3D elasticity solutions. In this study, the analysis of free vibrations for doubly curved laminated shells has been performed with modified higher order zigzag theory (MHOZT). This approach incorporates higher order displacement kinematics and considers both transverse normal and shear strains. The model assumes that the displacement fields within the plane are a combination of a global cubicly varying field and a locally zigzag linearly varying field. On the other hand, the out-of-plane displacement field varies quadratically with shell thickness coordinates. This formulation considers extended thickness criteria, ensuring the inclusion of the ratio of thickness to the radius of curvature (z / R) in strain displacement relations. Additionally, this model guarantees that there is no transverse shear stress at the extreme surfaces of the shell and that inter-laminar shear stress at interfaces is continuous. To implement this formulation effectively, a C ° finite element is used. The outcomes are compared against a three-dimensional (3D) elasticity solution, as well as other pertinent results available in the literature. The suggested model accurately predicts the vibration characteristics of laminated shells, showing good agreement with the 3D elasticity solutions. [ABSTRACT FROM AUTHOR]

This study presents a free vibration analysis of three different curved laminated composite plates having end-to-end decomposition under fixed opposing straight edges. The curved structures have been mathematically modeled by employing the Classical Laminated Plate Theory and the Finite Element Method to perform the location-based effect of decomposition. Besides, the relation among the decomposition, curvature characteristics, and stacking sequences is examined in terms of natural frequencies. For this purpose, the endto- end decompositions are defined in two different levels and re-positioned along the curved edge for each vibration analysis. The frequency ratio is obtained by proportioning the natural frequency of the damaged structure to that of the healthy structure and considered to interpret the effects of the decomposition location. Cross-ply and angle-ply structures having elliptic, circular, and parabolic curvatures are considered. It is concluded that the effect of the end-to-end decomposition on the natural frequencies varies to its level, the stacking order, and the bending regions of the relevant mode shape. [ABSTRACT FROM AUTHOR]

This paper reports for the first time the experimental investigation on the free vibration characteristics of angle-ply laminated composite stiffened plates along with the numerical investigation. The natural frequencies of these plates are computed experimentally using an FFT analyzer and numerically by employing the finite element method with combination of isoparametric nine nodded plate and three nodded beam elements. Angle-ply laminated stiffened plates are fabricated using woven glass fiber fabrics and epoxy by hand layup technique. The effects of various support conditions; number, orientation and types of stiffeners; aspect ratios of plates and different fiber orientations on the fundamental frequencies of the angle-ply laminated stiffened plates are investigated. These parameters significantly influence the natural frequencies. It is found that there is a very good agreement observed between the fundamental frequencies obtained from both experimental and numerical investigation. Mode shapes are also presented for angle-ply laminated square stiffened plates with three different support conditions to justify the trend of increasing/decreasing of the modal frequency with the addition of stiffeners. It is observed that the enhancement of the frequencies of the angle-ply plates due to addition of stiffeners is influenced significantly by the position of stiffeners and consequently mode shapes. As the research on the free vibration behavior of angle-ply stiffened plates with experimental analysis is very rare, this study can be considered as the benchmark for future research. [ABSTRACT FROM AUTHOR]

Composites have been extensively used in the modern era in wide range of applications. This article deals with the study of vibration characteristics of natural fiber reinforced composite beam in which Aloe vera fiber is reinforced in epoxy matrix and is used in combination with glass-epoxy. Finite element method of analysis is adopted using Ansys software. Effects of several parameters like laminate stacking sequence, support conditions, material hybridization, and number of layers, etc. on the natural frequency of natural fiber reinforced composite beam are analyzed. Experimental study on Aloe vera fiber reinforced composite beam is also conducted for validation.

This article presents a free vibration analysis of laminated sandwich plates under various boundary conditions by using an efficient C0 eight‐node quadrilateral element. This new element is formulated based on the recently proposed layerwise model. The present model assumes an improved first‐order shear deformation theory for the face sheets while a higher‐order theory is assumed for the core maintaining an interlaminar displacement continuity. The advantage of this model relies on its number of variables is fixed, does not increase when increasing the number of lamina layers. This is a very important feature compared to the conventional layerwise models and facilitates significantly the engineering analysis. Indeed, the developed finite element is free of the shear locking phenomenon without requiring any shear correction factors. The governing equations of motion of the sandwich plate are derived via the classical Hamilton's principle. Several examples covering the various features such as the effect of modular ratio, aspect ratios, core‐to‐face thickness ratio, boundary conditions, skew angle, number of layers, geometry and ply orientations are solved for laminated composites and sandwich plates. The obtained results are compared with 3D, quasi‐3D, 2D analytical solutions, and those predicted by other advanced finite element models. The comparison studies indicate that the developed finite element model is of fast convergence to the reference and valid for both thick and thin laminated sandwich plates. Finally, it can be concluded that the present model is not only simple and accurate than the conventional ones, but also comparable with refined analytical solutions found in the literature. [ABSTRACT FROM AUTHOR]

Composites have been extensively used in the modern era in wide range of applications. This article deals with the study of vibration characteristics of natural fiber reinforced composite beam in which Aloe vera fiber is reinforced in epoxy matrix and is used in combination with glass-epoxy. Finite element method of analysis is adopted using Ansys software. Effects of several parameters like laminate stacking sequence, support conditions, material hybridization, and number of layers, etc. on the natural frequency of natural fiber reinforced composite beam are analyzed. Experimental study on Aloe vera fiber reinforced composite beam is also conducted for validation. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration and buckling responses of laminated composite and sandwich microbeams with arbitrary boundary conditions are investigated. The governing equations based on the modified couple stress theory are derived by using the total potential energy of a microbeam and employing a transverse shear-normal deformable beam theory. Extensive analysis results in terms of dimensionless fundamental frequencies and dimensionless critical buckling loads are introduced for various boundary conditions, aspect ratios, orthotropy ratios, fiber orientation angles, thickness to material length scale parameter ratios, and core thickness to face layer thickness ratios. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration of laminated composited cylindrical shells with two kinds of non-continuous supported boundary condition are investigated. The artificial springs are used to simulate the arcs supported and points supported boundary condition. The equations of motion are derived by using the Chebyshev polynomials and the Lagrange equation, and Donnell's shell theory is employed in this process. The accuracy of the present method compared with that of literature, and convergence analysis is carried out at the same time. Then, the influences of spring stiffness, the number of supported point, and the lamination schemes of non-continuous supported laminated composite cylindrical shells on frequency parameter are studied. The results show that the method can accurately deal with the free vibration of laminated shells with arbitrary non-continuous boundary and arbitrary lamination schemes. [ABSTRACT FROM AUTHOR]

Extensive numerical results available in published articles reflect the importance of the effects of geometric parameters, material properties, end conditions, hygrothermal fields, etc. on the behavior of laminated composite and sandwich structures when exposed to environmental conditions. A critical review of available literature for the prediction of the behavior of laminated composites and sandwich structures under hygrothermal conditions is carried out and summarized under different categories namely: static, vibration, buckling, post-buckling and miscellaneous studies (transient, dynamic, impact studies). Each category is further discussed separately in details highlighting the important outcomes of the research. In addition to that, each category is again grouped on the basis of the type of theory used by different researchers in their work. The displacement fields, thermal fields and the method adopted in different papers are also summarized. [ABSTRACT FROM AUTHOR]

Laminated composite shells are used as roofing units in Civil Engineering applications and hypar shells are most popular because of their ease of construction and aesthetic elegance. The aim of the present study is to analyse higher mode free vibration of composite hypar shells. The purpose is to obtain some design guidelines for the practising engineers dealing with such structures. The methodology adopted here is the finite element method based on first order shear deformation theory. Effect of cross curvature is included in the formulation. The isoparametric finite element consists of eight nodes with five degrees of freedom per node is considered. Three noded beam elements with four degrees of freedom per node are used for stiffeners. The generalised Eigen value solution is chosen for the un-damped free vibration analysis. The formulation is validated first by solving standard problems from literature and then new results are obtained for varying boundary conditions, ply orientation and curvature of the shell. The first five modes of natural frequency are presented. In general, it is observed that fundamental frequency increases with the increase in the number of support constraints. There are, however, few departures from this general tendency when two shells of different laminations are compared. Sometimes lamination order may influence the frequency of stiffened composite shell with cut-out more significantly than its boundary conditions. Symmetric lamination exhibits reasonably good performance and may be adopted for all practical purposes. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the eigenfrequencies of rotating laminated composite (LC) and sandwich microbeams with different boundary conditions (BCs) are studied. The size-dependent variational formulation of the problem is obtained based on the Modified Couple Stress Theory (MCST) by employing a transverse shear-normal deformable beam theory and finite element method (FEM) formulation. The convergence and verification studies of the developed code are carried out and computed results in terms of dimensionless fundamental frequencies (DFFs) are compared with the available ones in the open literature. Various BCs, aspect ratios, fiber orientation angles, thickness to material length scale parameter (MLSP) ratios, core thickness to face layer thickness ratios, dimensionless rotation speeds (DRSs) and hub ratios are employed for the extensive analyses. It is found that the DFFs of the LC microbeams are highly affected by the small size effect accompanying with the orthotropy ratios, DRSs, hub ratios and fiber orientation angles. The effect of the small size on the DFFs of the rotating clamped-clamped LC microbeams is more pronounced than on those of the rotating clamped-free LC microbeams. The hub ratio has a significant effect on the DFFs of the rotating LC microbeams than the rotation speed. [ABSTRACT FROM AUTHOR]

Abstract This paper develops a formulation for displacement-only beam elements based on isogeometric analysis, with intended application to laminated composite members. The main purpose of the current study was to overcome some deficiencies of commonly used beam theories, such as shear-locking, the lacking relevance of isotropic materials for multi-layer composites, the incompatibility with other continuum elements, and the limited continuity in interpolation. A bi-variable non-uniform rational B-spline (NURBS) beam element with complete plane-stress elasticity terms and geometrical expressions was developed. Shear-locking, interlaminar stresses, the deep-beam situation, and vibration features were evaluated for several aspect ratios, ply orientations, and NURBS degrees, in order to verify the efficiency and accuracy. h -, p - and k -refinements were used to improve the displacement field. The validity of the solutions was measured based on results from plane-stress finite element analysis, and compared to the alternative Carrera unified formulation. Results show that the isogeometric displacement-only beam theory can provide the interlaminar stress distribution, gives high accuracy for mid and high-range eigen-frequencies, and avoids the shear-locking phenomenon. Highlights • A displacement-only beam element was formulated based on an IGA-approach. • In-plane elasticity was used for a bi-variate NURBS form. • h-, p- and k-refinements were studied for improving results. • Interlaminar stresses in a laminated composite beam could be evaluated. • Formulation gave good accuracy for static and vibration problems. [ABSTRACT FROM AUTHOR]

Abstract This paper examines the free vibration of laminated composite plates in contact with a water-filled cavity. The fluid compressibility is considered in the analysis. The main objective is to evaluate the natural frequencies of the plate-fluid coupled system, compare the results with those obtained assuming an incompressible fluid domain, and examine the influence of the laminate stacking sequence. Classical and refined plate theories are considered in a compact manner. The Ritz method is used to obtain approximations of the kinetic and potential energy of both the fluid and the plate. The accuracy of the formulation is demonstrated by comparing the results to 3D finite element solutions obtained via commercial software. Parametric studies are carried out to examine the influence of the geometry, lamination angles and boundary conditions on the natural frequencies and the error incurred due to neglecting fluid compressibility. The error is higher when thick, stiff plates with rigid supports are considered. The effect of the fluid domain depth on the natural frequencies depends on the symmetric or antisymmetric nature of the mode shape. The orientation of the laminas becomes highly relevant when rectangular plates with mixed supports are considered. Highlights • Vibration of composite plates in contact with compressible fluid. • Free vibration problem of submerged thick rectangular composite plates. • Plate displacement theories using the 2D Carrera Unified Formulation. • The eigenvalue problem of both fluid and the plate is obtained. • The displacement variables are evaluated using the Ritz method. [ABSTRACT FROM AUTHOR]

This paper presents Best Theory Diagrams (BTDs) constructed from non-polynomial terms to identify best shell theories for the free vibration analysis of laminated and sandwich shell. The shell theories have been constructed using Axiomatic/Asymptotic Method (AAM). The refined models are implemented following the compactness of a unified formulation developed. The governing equations are derived from the Hamilton’s Principle. Navier-Type solution technique is used for solving the eigenvalue problem of simply supported shell. The BTDs use 3D equilibrium solutions as a reference. The BTDs built from non-polynomial functions are compared with Maclaurin expansions. The results are compared with Layerwise solutions. Cylindrical and spherical shells with different layer-configurations are investigated. The results demonstrate that the shell models obtained from the BTD using non-polynomial terms can improve the accuracy obtained from Maclaurin expansion for a given order of expansion of a displacement field. [ABSTRACT FROM AUTHOR]

This paper presents a new four-variable refined plate theory for free vibration analysis of laminated piezoelectric functionally graded carbon nanotube-reinforced composite plates (PFG-CNTRC). The present theory includes a parabolic distribution of transverse shear strain through the thickness and satisfies zero traction boundary conditions at both free surfaces of the plates. Thus, no shear correction factor is required. The distribution of carbon nanotubes across the thickness of each FG-CNT layer can be functionally graded or uniformly distributed. Additionally, the electric potential in piezoelectric layers is assumed to be quadratically distributed across the thickness. Equations of motion for PFG-CNTRC rectangular plates are derived using both Maxwell’s equation and Hamilton’s principle. Using the Navier technique, natural frequencies of the simply supported hybrid plate with closed circuit and open circuit of electrical boundary conditions are calculated. New parametric studies regarding the effect of the volume fraction, the CNTs distribution, the number of layers, CNT fiber orientation and thickness of the piezoelectric layer on the free vibration response of hybrid plates are performed.

Highlights • Analytical solution is presented for flutter instability of cracked laminated composite beams subjected to a follower force. • Effect of crack location and length and stacking sequence on the flutter instability are studied. • Crack location has different effect on the natural frequency, buckling and flutter load of a cracked beam. Abstract Free vibration and buckling instability of laminated composite beams and flutter instability of an isotropic beam with different defects have been investigated before, however, still dynamic stability of laminated composite beam with weak section subjected to follower forces has not considered. This paper presents a simple semi-analytical solution to the flutter instability of a laminated composite beam with multi open-edge cracks subjected to a tip follower force. Using classical lamination theory and Euler-Bernoulli beam theory, equation of motion of the beam is derived analytically and characteristic eigenvalue equations of the cracked laminated composite beam are obtained. A Matlab® code is used to solve these equations numerically. After validating the results, a numerical study is performed to investigate the effect of crack depth and stacking sequences on the dynamic stability of the cracked beam. [ABSTRACT FROM AUTHOR]

In this paper, a new higher-order layerwise finite element model, developed earlier by the present authors for the static analysis of laminated composite and sandwich plates, is extended to study the free vibration behavior of multilayer sandwich plates. In the present layerwise model, a first-order displacement field is assumed for the face sheets, whereas a higher-order displacement field is assumed for the core. Thanks for enforcing the continuity of the interlaminar displacement, the number of variables is independent of the number of layers. In order to reduce the computation effort, a simply four-noded C0 continuous isoparametric element is developed based on the proposed model. In order to study the free vibration, a consistent mass matrix is adopted in the present formulation. Several examples of laminated composite and sandwich plate with different material combinations, aspect ratios, boundary conditions, number of layers, geometry and ply orientations are considered for the analysis. The performance and reliability of the proposed formulation are demonstrated by comparing the author's results with those obtained using the three-dimensional elasticity theory, analytical solutions and other advanced finite element models. From the obtained results, it can be concluded that the proposed finite element model is simple and accurate in solving the free vibration problems of laminated composite and sandwich plates. [ABSTRACT FROM AUTHOR]

In this work, two new shear deformation theories namely Trigonometric Deformation Theory (TDT) and Trigonometric-Hyperbolic Deformation Theory (THDT) are developed and implemented for the analysis of laminated and three dimensional braided composite plate. Both models are based upon shear strain shape function which yields non-linear distribution of transverse shear stresses and these models also satisfy the traction free boundary conditions on top and bottom surfaces of the plate. Virtual work principle is used to obtain the governing differential equations and boundary conditions. Both the proposed theories are formulated and validated for the free vibration and buckling of laminated and Three Dimensional (3D) braided composite plate. From the obtained results, the proposed theories are more accurate in predicting the response for free vibration and buckling analysis of laminated and 3D braided composite plates. Intensive numerical studies of 3D braided composite are performed in detail. It is further observed that the geometric parameter (aspect ratio), boundary conditions, fiber volume fraction and braiding angle have significant effect on the free vibration and buckling response of the 3D braided composite plates. In the framework of finite element analysis, both proposed theories anticipate exemplary results for the laminated and braided composite plates compared to existing theories. [ABSTRACT FROM AUTHOR]

This study investigates the vibration transmission and energy flow tailoring of variable stiffness laminated composite (VSLC) plates with curvilinear fibres subjected to harmonic excitation. The free vibration characteristics of VSLC plates are firstly studied. The steady-state dynamic responses are then obtained based on the first-order shear deformation theory. The effects of variable angle fibres on the time-averaged input power and kinetic energy of the plate are examined using the power flow analysis approach. The time-averaged power flow density vector is used to determine the primary energy transmission paths, which are shown to depend on the dominant mode excited by the applied force. Curvilinear fibre designs are found to have a significant influence on the main energy flow transmission paths and vibration level. For enhanced vibration suppression, the fibre angles can be tailored to modify the vibration transmission paths according to a specific excitation. [Display omitted] • Vibration energy flow of variable stiffness laminated composite plates is investigated. • Power flow density vector is used and obtained to identify main energy flow paths. • Influence of fibre orientations on the vibration transmission and vibration levels is revealed. • Effects of curvilinear fibres on the dominant energy transmission paths are examined. • Enhanced vibration suppression by exploiting curvilinear fibre design. [ABSTRACT FROM AUTHOR]

Over the past few decades, composite materials are extensively used in various industries due to their high specific stiffness, strength, weight sensitivity and cost-effectiveness. However, lack of complete control over the manufacturing process results in undesirable uncertainties, which in turn affect the vibrational characteristics of systems. This paper presents a novel approach, referred to as polynomial correlated function expansion (PCFE), for stochastic free vibration analysis of composite laminate. The proposed approach facilitates a systematic mapping between the input and output variables by expressing the output in a hierarchical order of component functions. The component functions are expressed in terms of extended bases and the unknown coefficients associated with the bases are determined by employing homotopy algorithm. The proposed approach has been employed for stochastic free vibration analysis of laminated composite plates. Results obtained using PCFE have been compared with results obtained using radial basis function (RBF) and conventional response surface method (RSM). Compared to RBF and RSM, PCFE yield more accurate result from considerably fewer sample points. Furthermore, case studies with different ply orientations have also been performed. Based on the numerical results, new physical insights have been drawn on dynamic behaviour of composite laminates. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to develop a general mathematical model for laminated curved structure of different geometries using higher-order shear deformation theory to evaluate in-plane and out of plane shear stress and strains correctly. Subsequently, the model has to be validated by comparing the responses with developed simulation model (ANSYS) as well as available published literature. It is also proposed to analyse thermal buckling load parameter of laminated structures using Green–Lagrange type non-linear strains for excess thermal distortion under uniform temperature loading. Design/methodology/approach – Laminated structures known for their flexibility as compared to conventional material and the deformation behaviour are greatly affected due to combined thermal/aerodynamic environment. The vibration/buckling behaviour of shell structures are very different than that of the plate structures due to their curvature effect. To model the exact behaviour of laminated structures mathematically, a general mathematical model is developed for laminated shell geometries. The responses are evaluated numerically using a finite element model-based computer code developed in MATLAB environment. Subsequently, a simulation model has been developed in ANSYS using ANSYS parametric design language code to evaluate the responses. Findings – Vibration and thermal buckling responses of laminated composite curved panels have been obtained based on proposed model through a customised computer code in MATLAB environment and ANSYS simulation model using ANSYS parametric design language code. The convergence behaviour are tested and compared with those available in published literature and ANSYS results. Finally, the investigation has been extended to examine the effect of different parameters (thickness ratios, curvature ratios, modular ratios, number of layers and support conditions) on the free vibration and thermal buckling responses of laminated curved structures. Practical implications – The present paper intends to give sufficient amount of numerical experimentation, which may lead to help in designing of finished product made up of laminated composites. Most of the aerospace, space research and defence organisation intend to develop low cost and high durable products for real hazard conditions by taking combined loading and environmental conditions. Further, case studies might lead to a lighter design of the laminated composite panels used in high-performance systems, where the weight reduction is the major parameter, such as aerospace, space craft and missile structures. Originality/value – In this analysis, the geometrical distortion due to temperature is being introduced through Green–Lagrange sense in the framework of higher-order shear deformation theory for different types of laminated shells (cylindrical/spherical/hyperboloid/elliptical). A simulation-based model is developed using ANSYS parametric design language in ANSYS environment for different geometries and loading condition and compared with the numerical model. [ABSTRACT FROM AUTHOR]

A modified Fourier series method is applied to study the free vibration of laminated composite and four-parameter functionally graded sector plates with general boundary conditions. The first-order shear deformation plate theory is employed to include the effects of rotary inertias and shear deformation. Regardless of the boundary conditions, each of the displacement and rotation components of the sector plates is described as a linear superposition of a double Fourier cosine series and several supplementary functions introduced to accelerate the convergence of series representations. The Rayleigh–Ritz procedure based on the energy functions of the sector plates is adopted to solve the exact solutions. In order to verify the accuracy and reliability of the present method, comparisons of the present results with those published are presented. New numerical results for laminated composite and functionally graded sector plates with elastic restraints are given. The effects of the boundary conditions and material and geometrical properties on the frequencies of the sector plates are investigated. [ABSTRACT FROM AUTHOR]

In this paper, a new layerwise plate formulation based on a C 0 higher-order finite element model is presented for static and free vibration analyses of laminated composite and sandwich plates. The proposed layerwise theory which is developed for a three layered composite plates, assumes higher-order displacement field for middle layer and first-order displacement field for top and bottom layers. Compatibility conditions are imposed at the layer interface to satisfy the interlaminar displacement continuity. An eight-noded isoparametric element is used to model the plate. The accuracy of the proposed formulation is assessed for linear static and free vibration analyses by comparing the authors’ results with available 3D elasticity, finite element and analytical solutions. It has been shown here that the present finite element formulation is much simpler, straightforward and accurate for static and free vibration analyses of laminated composite and sandwich plates. [ABSTRACT FROM AUTHOR]

The present article reviews the recent research done on the free vibration analysis of multilayered laminated composite and sandwich plates using various methods available for the analysis of plates. Displacement fields of various displacement based shear deformation theories have been presented and compared. Also, some numerical results related to fundamental flexural mode frequencies of laminated composite and sandwich plates are presented using a trigonometric shear and normal deformation theory. The theory involves six unknown variables and does not require problem dependent shear correction factor. Governing differential equations and associated boundary conditions of the theory are derived by employing the dynamic version of the principle of virtual work. Navier-type closed-form solutions are obtained for simply supported laminated composite and sandwich plates. The present results are compared with exact elasticity solution and other higher order shear deformation theories wherever applicable. This article cites 391 references. [ABSTRACT FROM AUTHOR]

A theoretical analysis for the free vibration of magneto-electro-elastic (MEE) laminated plates with generalized membrane-type interfacial imperfections is proposed. The wave motion characteristics, such as the dispersion curves and mode shapes, are investigated. The pseudo-Stroh formalism and the propagator matrix method are employed to derive the analytical solutions for an orthotropic and multilayered MEE plate with imperfect interfaces. The effect of generalized membrane-type interfacial imperfections on the dispersion curve, mode shape, and magnetoelectric coupling factor for piezoelectric BaTiO 3 and piezomagnetic CoFe 2 O 4 sandwich plates are studied in detail. Numerical calculations show that the membrane-type interfacial imperfection has a significant effect on the dispersion curve, mode shape, and magnetoelectric coupling factor in layered MEE composites. This exact solution provides important insight to assess the wave characteristics of the MEE laminated composites with membrane-type interfacial imperfections. [ABSTRACT FROM AUTHOR]

In this work, inverse hyperbolic zigzag theory and inverse trigonometric zigzag theory, recently developed by the authors, are extended for the free vibration analysis of the laminated composite and sandwich plates. The developed plate models satisfy the condition of transverse shear stress continuity at the layer interfaces and the zero traction boundary conditions on the surfaces of the plate obviating the need of shear correction factor. They consider shear strain shape function assuming the nonlinear distribution of transverse shear stresses. The less numbers of independent variables makes the solution computationally effective. An efficient C0 continuous isoparametric serendipity element is employed for the usual discretization of the plate structure. In order to demonstrate the capabilities of the developed models in predicting the structural free vibration response, some representative results are obtained covering different features of laminated composite and sandwich structures such as boundary conditions, aspect ratios and span-to-thickness ratios and the results are compared with those in the literature wherever available. The excellent agreement of the evaluated results with the three-dimensional exact results conclude that the presented models are not only accurate but also efficient. [ABSTRACT FROM AUTHOR]

In this paper, the NURBS-based isogeometric analysis is developed for the free vibration analysis of the generally laminated Timoshenko-type of deep curved beams with arbitrary curvature. The equivalent modulus of elasticity is utilized to account for the material couplings of the beam and the deepness term is exactly integrated into ABD parameters of the curved beam. The geometry and the curvature of the laminated free-form curved beams are modeled by NURBS so that the gap between the analysis of the laminated curved beam with constant curvature and the analysis of that with variable curvature is bridged. All the effects of the axis extensibility, the shear deformation and the rotary inertia are taken into account. Results of the non-dimensional frequencies for the laminated elliptic and circular curved beams with different lay-ups are compared with other available results in order to demonstrate the validity of the present isogeometric model. The free vibration analysis of the laminated parabolic curved beams and the laminated elliptic ring are presented. Particularly, the laminated Tschirnhausen’s cubic curved beam is considered to study the dynamic responses as an example of the laminated free-form curved beam. [ABSTRACT FROM AUTHOR]

Using the layerwise theory in conjunction with the differential quadrature method (DQM), an accurate and efficient solution procedure for the free vibration analysis of thick skew laminated composite plates is introduced. By employing Hamilton's principle and the layerwise theory, the discretized form of the equations of motion in the thickness direction is obtained. Then, the DQM is used to solve the resulting system of differential equations. The fast rate of convergence and high accuracy of the method is established. Then, some new results for skew laminated plates are presented, which can be used as a benchmark solution for future works. [ABSTRACT FROM AUTHOR]

In this work, a new trigonometric zigzag theory is proposed for the analysis of laminated composite and sandwich plates. The theory is based upon shear strain shape function assuming non-linear distribution of transverse shear stresses. It satisfies the necessary conditions of inter-laminar stress continuity at the layer interfaces as well as the condition of zero transverse shear stresses at the top and bottom surfaces of the plates. The theory has the same number of unknown field variables as that of FSDT and the number of unknowns is layer independent which makes the solution computationally more efficient. A C0 continuous isoparametric serendipity element is employed to solve the discrete eigenvalue equations arising in both the problems. The accuracy and the efficiency of the theory are thus demonstrated through numerical experiments on the free vibration and stability analysis of laminated composite and sandwich plates with different modular ratio, aspect ratio, span to thickness ratio, loading and boundary conditions, ply orientations, lay-up number, eigen modes, etc. Higher modes with corresponding mode shapes of vibration and buckling are also represented for laminated composite and sandwich plates. An elegant performance of the proposed theory is observed when it is validated with relevant numerical examples. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the effects of laminate scheme, crack ratio (a/h) and crack position (L1/L) on the free vibration and lateral buckling of a cantilever slender rectangular beam such as an airplane wing or a wind turbine blade with a single edge crack. The local flexibility approach is adopted to model the crack, based on linear fracture mechanics and the Castigliano theorem. The governing matrix equations for free vibration and buckling load are derived from the standard beam element and cracked beam element combined with the local flexibility concept. The results are obtained numerically using the finite element method, based on the energy approach and are given for crack ratios up to 0.5 at crack positions up to 0.9 ratio. Polynomial approximation for displacements gives results with reasonable accuracy. [ABSTRACT FROM AUTHOR]

Abstract: In This study hydrostatic vibration analysis of a laminated composite rectangular plate partially contacting with a bounded fluid is investigated. Wet dynamic transverse displacements of the plate are approximated by a set of admissible trial functions which are required to satisfy the clamped and simply supported geometric boundary conditions. Fluid velocity potential satisfying fluid boundary conditions is derived and wet dynamic modal functions of the plate are expanded in terms of finite Fourier series for compatibility requirement along the contacting surface between the plate and the fluid. Natural frequencies of the plate coupled with sloshing fluid modes are calculated using Rayleigh–Ritz method based on minimizing the Rayleigh quotient. The proposed analytical method is validated with available data in the literature. Using numerical data provided, effect of different parameters including boundary conditions, aspect ratio, thickness ratio, fiber orientation, material properties of the laminas and dimensions of the tank on the plate natural frequencies are examined and discussed in detail. [Copyright &y& Elsevier]

Free vibration behavior of laminated composite non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with rectangular cross-section is investigated. The effect of the warping deformation of wire cross-section on natural frequencies is first considered in the formulations. The differential equations of motion for the springs including warping, which consist of 14 first-order partial differential equations with variable coefficients, are derived using naturally curved and twisted anisotropic beam theory. The natural frequencies of the springs are determined using improved Riccati transfer matrix method. The element transfer matrix is calculated by using the Scaling and Squaring method and Pade's approximations. Calculated results show that the warping deformation has a significant influence on the natural frequencies, which should be considered in the free vibration analysis of the springs. Finally, the effects of various parameters on the natural frequencies for symmetrically laminated composite hyperboloidal springs with rectangular cross-section have been studied. [ABSTRACT FROM AUTHOR]

In this paper, free vibration analysis of cross-ply layered composite beams (LCB) with finite length and rectangular cross-section rested on an elastic foundation is investigated by finite element method. Based on the Timoshenko beam theory which includes the shear deformation and rotary inertia, the stiffness and mass matrices of a LCB are obtained using the energy method. Then, the natural frequencies are calculated by employing eigenvalue technique. The obtained results are verified against existing data in the literatures for a LCB with no foundation and uniform cross-section. Good agreements are observed between these cases. In the same way, the natural frequencies of a specific case, i.e. the stepped beam are calculated and finally, free vibrations of a symmetric and non-symmetric LCB are compared with each others. [ABSTRACT FROM AUTHOR]

Natural frequencies of laminates during its progressive failure are investigated using finite element method. The finite element formulation is based on seven degrees of freedom displacement field, deduced for an orthotropic material. Free vibration analysis is carried out during ply-by-ply failure for a laminate subjected to uniformly distributed load. The variation of fundamental frequency with material and geometric properties is also presented. This study illustrates the effect of ply failure on the natural frequencies of a laminate. The prediction of failed ply and failure mode is accomplished via. Hashin failure criterion. Ply-discount material degradation model is adopted to modify the elastic constants of the failed ply. The effect of fibre orientation, failure mode and failed-ply on natural frequencies is highlighted in this paper. Jacobi iterative method is used to evaluate the natural frequencies of laminate. For the analysis, a computer code is written using FORTRAN based on the finite element formulation. • Natural frequencies of laminates during progressive failure is presented using Jacobi iterative method. • Transverse UDL in conjunction with Hashin failure criterion is considered to model the progressive failure. • Ply-discount material degradation model is implemented for stiffness reduction. • Effect of fibre orientation, number of plies, failed ply-number and failure mode on natural frequencies is highlighted. [ABSTRACT FROM AUTHOR]

This investigation deals with the numerical and experimental study on the free vibration of woven glass fibre laminated composite stiffened plates. Thirty-four stiffened plates fabricated from woven glass fibre and binder (epoxy and hardener) by varying the parameters, such as numbers, types and orientation of stiffeners; depth of stiffener to thickness of plate ratio; and aspect ratio and boundary conditions of plates; are tested in FFT analyser to obtain their natural frequencies. A finite element model is used for vibration of laminated composite stiffened plates for validation of the experimental results. The experimental and numerical results are compared, which shows a very good agreement between them. From this study, it is observed that the above-mentioned parameters significantly influence the fundamental frequency. Since, the experimental investigation on laminated composite stiffened plates is scanty; this study can be considered as a reference for the future work. [ABSTRACT FROM AUTHOR]

This paper presents a new four-variable refined plate theory for free vibration analysis of laminated piezoelectric functionally graded carbon nanotube-reinforced composite plates (PFG-CNTRC). The present theory includes a parabolic distribution of transverse shear strain through the thickness and satisfies zero traction boundary conditions at both free surfaces of the plates. Thus, no shear correction factor is required. The distribution of carbon nanotubes across the thickness of each FG-CNT layer can be functionally graded or uniformly distributed. Additionally, the electric potential in piezoelectric layers is assumed to be quadratically distributed across the thickness. Equations of motion for PFG-CNTRC rectangular plates are derived using both Maxwell's equation and Hamilton's principle. Using the Navier technique, natural frequencies of the simply supported hybrid plate with closed circuit and open circuit of electrical boundary conditions are calculated. New parametric studies regarding the effect of the volume fraction, the CNTs distribution, the number of layers, CNT fiber orientation and thickness of the piezoelectric layer on the free vibration response of hybrid plates are performed. [ABSTRACT FROM AUTHOR]