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The present study investigates free vibration analysis of cylindrical panels made of porous orthotropic layers. Porous material properties are modeled using uniform and two non-uniform porosity distribution patterns through the thickness. The theoretical formulations are expressed based on the higher-order shear deformation theory. The equations of motion of laminated cylindrical panels are established by performing Hamilton's principle. These fundamental partial differential equations are solved analytically for the laminated cylindrical panels, which are simply supported on all edges. Galerkin's solution procedure is applied to obtain the natural frequency equation. The natural frequencies are compared to results in the literature to verify the obtained frequency equation. Afterward, novel parametric studies are developed to discuss the influence of porosity parameters, porosity distribution patterns, geometrical parameters, orthotropy, and lamination sequences on the free vibration response of porous laminated cylindrical panels. [ABSTRACT FROM AUTHOR]

In this study, the deflection and stress field of perfect and imperfect (with and without porosities) functionally graded (FG) cylindrical panels are determined following the first-order shear deformation theory (FSDT). The panel rested on the twoparameter elastic foundation (Pasternak foundation) under pressure loads and worked in a hygro-thermal environment. Navier's solution has been used for simply supported cylindrical panels to analyze the effects of porosity, geometrical and foundation parameters, as well as temperature and humidity on deflection and stress field. The validated examples demonstrate the reliability of the solution and the self-written Matlab program. Numerical investigations show a significant hygro-thermal effect on the static response of the FG panel. [ABSTRACT FROM AUTHOR]

This paper presents a new semi-analytical approach for the nonlinear vibration and dynamic responses of functionally graded graphene platelet-reinforced composite (FG-GPLRC) panels with complex curvature reinforced by orthogonal and/or inclined stiffeners in the thermal environment resting on the nonlinear viscoelastic foundation with the nonlinearities of von Kármán in the framework of the higher-order shear deformation theory (HSDT). The three curvature types of complexly curved panels are considered to be cylindrical, sinusoid, and parabola panels. Orthogonal and/or inclined stiffeners are modeled utilizing an improved smeared stiffener technique. The stress function form is estimated by applying the like-Galerkin method for complexly curved panels. By applying the Lagrange function and Euler–Lagrange equation, the nonlinear equations of motion of the panels are obtained. The viscous damping effects of the viscoelastic foundation are considered by utilizing the Rayleigh dissipation function. Numerical results are examined utilizing the Runge–Kutta method to acquire the time-deflection curves, and by utilizing the Budiansky–Roth criterion, the critical dynamic buckling loads are determined. From the investigated results, it is possible to evaluate the nonlinear vibration and buckling dynamic responses of three forms of panels with stiffeners. [ABSTRACT FROM AUTHOR]

Purpose: This paper is the first attempt, to the best of the authors' knowledge, to examine the non-linear blast-induced dynamic responses of functionally graded graphene platelets-reinforced composite (FG-GPLRC) porous cylindrical panels in thermal environments. Methods: The mechanical properties of porous FG-GPLRC, including the modulus of elasticity, mass density, coefficients of thermal expansion, and Poisson's ratio, are determined by using the Halpin–Tsai micromechanical model, the extended rule of mixtures, and the open-cell metal foam model. The first-order shear deformation theory, the von Kármán geometric non-linearity, and the standard Lagrange equations are applied to derive the equations governing the motion the FG-GPLRC porous cylindrical panels. Navier's solution is used to model the immovable and simply supported boundary conditions of the cylindrical panels. The Newmark-β scheme for direct integration and the Newton–Raphson iterative technique were used to obtain the non-linear dynamic responses of the FG-GPLRC porous cylindrical panels when they were subjected to various blast-induced loads in a thermal environment. Results and Conclusions: A parametric study is performed and indicates that the dependence of the properties of the material on the temperature influenced both the matrix and the GPLs, and thus had a significant influence on the non-linear dynamic responses of the structure. Enhanced structural performance can be achieved by either dispersing more GPLs, or introducing denser pores near the upper and lower surfaces of the structure. [ABSTRACT FROM AUTHOR]

In this study, free vibration and damping behavior of cylindrical sandwich panel with electro-rheological core and graphene platelets reinforced composite (GPLRC) facing sheets based on first-order shear deformation theory of thick cylindrical shells referred by Qatu (FSDTQ) is investigated. Effective material properties of graphene platelets reinforced composite are determined according to the Halpin–Tsai micromechanical model. The governing equations of motion with required boundary conditions are derived using Hamilton's principle. Afterward, these equations are solved analytically using the Fourier series solution for simply-supported boundary conditions, and for the other edges boundary conditions, we used the generalized differential quadrature method. The exactness and correctness of the present formulation are validated by comparing the results with those of existing literature. Finally, the influences of various parameters such as the electric fields, geometrically parameters, boundary conditions, the volume fraction of GPL, and GPL distributions pattern on vibration behavior and modal loss factor is examined. According to the results, the influence of the GPL volume fraction and electric field on the frequencies and modal loss factor is significant. This achievement can help design intelligent controlling structures for various applications. [ABSTRACT FROM AUTHOR]

In the framework of 3D elasticity theory, the static behavior of functionally graded viscoelastic cylindrical panels with piezoelectric layers under electro-mechanical loads is investigated. The viscoelastic material is modeled using Boltzmann's integral model, and its Poisson's ratio is constant, and for its time-dependent Young's modulus, spatially, the power distribution in the radial direction is considered. Modulus time changes are also expressed using the Prony series. For simply supported edges, the state space method and Fourier expansion, and for other boundary conditions, the semi-analytical approach by the state space differential quadrature method (DQM) are used. Equations of motion are solved in the Laplace domain and by the Laplace inverse technique, results are transferred back to the time domain numerically. Also, the results of this research have been validated with other similar research. Finally, the effect of different parameters such as the type of supports, the relaxation time constant, thickness of the piezoelectric layer, and other important parameters on the static response of the panel have been investigated. Results demonstrate that if the ratio of the total layer thickness to the piezoelectric thickness exceeds a specified value, the effect of the thickness of the piezoelectric layer on mechanical behavior can be disregarded. Furthermore, when relaxation time constant increases, the amount of stress remains constant for a constant thickness and equals the amount of stress in the elastic panel. However, the amount of displacement decreases. [ABSTRACT FROM AUTHOR]

This paper presents and analyzes the nonlinear buckling responses of three types of shallow imperfect panels (cylindrical panel, parabolic panel, and half‐sinusoid panel) made from functionally graded graphene reinforced composite (FG‐GRC) on nonlinear elastic foundations subjected to axial compressive load in thermal environments. The nonlinear governing equations are formulated on Reddy's higher‐order shear deformation shell theory (HSDST) and take into account von Karman‐type nonlinearity. A new approximation technique to determine the stress function in average sense is developed and Galerkin's method is used to obtain the algebraically nonlinear equation system. Then, the simple calculation process can be used to solve the obtained equation systems, and the formulations to calculate the critical buckling loads and postbuckling load‐deflection curves are expressed in explicit form. The results can be flexibly applied to FG‐GRC panels with different curvatures in engineering designs. The effects of panel types, geometrical parameters, temperature increase, initial imperfection, and nonlinear elastic foundations on the critical buckling loads and postbuckling curves of cylindrical, parabolic, and half‐sinusoid FG‐GRC panels are discussed in numerical results. Numerical results also show a small disadvantage in the load‐carrying capacity of cylindrical panels compared to parabolic panels and half‐sinusoid shallow panels. Highlights: Postbuckling of cylindrical, parabolic, and half‐sinusoid panels are studied.The panels are made of functionally graded graphene reinforced composite.Reddy's higher‐order shear deformation shell theory is applied.A new approximation technique to determine the stress function is developed.Critical buckling loads and postbuckling expressions are explicitly obtained. [ABSTRACT FROM AUTHOR]

Using the system of equations corresponding to the classical theory of orthotropic cylindrical shells, the free vibrations of thin elastic orthotropic cylindrical panels with arbitrary fastening of the ends arc investigated. To calculate the natural frequencies and to identify the respective natural modes, the generalized Kantorovich-Vlasov method of reduction to ordinary differential equations is used. Dispersion equations for finding the natural frequencies of possible types of vibrations are derived. An asymptotic relation between the dispersion equations of the problems at hand and the analogous problems for a rectangular plate is established. An algorithm for separating possible vibrations is presented. As examples, the values of dimensionless characteristics of natural frequencies arc derived for orthotropic cylindrical panels. [ABSTRACT FROM AUTHOR]

This work presents an analytical study on the dynamic instability of rotating functionally graded porous cylindrical panels subjected to periodic axial load under simply supported boundary conditions. Considering the Coriolis acceleration, centrifugal component, and hoop stress, the partial general equations of motion have been derived based on first-order shear deformation theory (FSDT) and by using Hamilton's principle. The excitation frequencies of rotating functionally graded porous cylindrical panels were calculated by substituting all motion equations for the transverse displacement and then applying the Galerkin method to the resulting equation. Numerical results are employed to validate the analytical results and show good agreement. The influences of the porosity distribution method, porosity coefficient, static and dynamic load factors, angular velocity, Coriolis acceleration, initial hoop stress, circumferential wave number, angle of the cylindrical panel, and cylindrical panel dimensions on the dynamic instability of rotating functionally graded porous cylindrical panels were investigated. Some of the important outputs that were reached in this study are that static and dynamic loads increase the width of the instability zone and that the structure is more stable when the porosity moves away from the surface and when the angular velocity increases. In addition, the cylindrical panel has a large frequency when the panel's angle is small (i.e., θ0 = 30°), but it is less sensitive to dynamic load when the angle is large (i.e., θ0 ≥ 100°).Please confirm if the author names are presented accurately and in the correct sequence (given name, middle name/initial, family name). Author 1 Given name: [specify authors given name] Last name [specify authors last name]. Also, kindly confirm the details in the metadata are correct.Thank you for this inquiry, author names have been given accurately and in the correct sequence. [ABSTRACT FROM AUTHOR]

• A novel third-order shear deformable model was developed. • Porous functionally graded graphene platelet reinforced cylindrical panels. • A blast pressure acted on the structures. • Temperature-dependent mechanical responses. In this paper, a novel shear deformable model is developed to investigate the temperature-dependent thermo-mechanical responses of porous functionally graded graphene reinforced composite (FG-GPLRC) cylindrical panels subjected to an initial blast pressure. An improved third order shear deformation theory, which has more rigorous kinematic of displacement, is implemented in the construction of the proposed model. Then, the current model is used to predict the thermo-mechanical responses of the nanocomposite panels made of metal foams reinforced by graphene platelets (GPLs). Lagrange equations are used to derive the governing equations corresponding to thermal buckling as well as the free and forced vibrations of the porous FG-GPLRC cylindrical panels. A Navier-type solution, which is free from computational errors, is implemented. Validation works demonstrate that the present model provides accurate predictions of mechanical responses for composite structures. A comprehensive parameter study is carried out to explore the influences of several key parameters regarding the thermo-mechanical behaviors of the porous FG-GPLRC cylindrical panels. [ABSTRACT FROM AUTHOR]

This paper deals with the nonlinear vibration behavior of sandwich panels composed of Graphene platelet reinforced composite (GPLRC) skins and auxetic core embedded with piezoelectric layers subjected to the thermo-magneto-electric loading. The nonlinear equations are obtained by applying Hamilton's principles in the framework of higher-order shear deformation theory (HSDT) and von Karman's nonlinear theory. Linear and nonlinear equations of motion are solved by applying the differential quadrature method (DQM) and homotopy perturbation technique, respectively. In the numerical illustration, at first validation of the present formulation is carried out by comparing the numerical results with those available in the open literature. Then the effects of several parameters such as geometric parameters of auxetic core, applied voltage, magnetic potential, GPL volume fraction, different boundary conditions, and temperature rise on the nonlinear frequency response of sandwich panel are studied. From numerical results, it was concluded that the sandwich panel incorporating auxetic core and piezoelectric layers could increase the magneto-electrical power output. [ABSTRACT FROM AUTHOR]

This work presents an analytical study of the parametric instability of cylindrical panels containing functionally graded porous exposed to static and dynamic periodic axial loads under simply supported boundary conditions. Based on Hamilton’s principle, the governing equation of motion by using first-order shear deformation theory (FSDT) has been obtained. By applying the Galerkin technique, an excitation frequency expression is derived, which helps identify areas of instability of functionally graded porous cylindrical panels. Numerical simulations are used to validate the analytical results. Eventually, the impacts of the porosity coefficient, porosity distribution method, static and dynamic periodic axial loads, panel angle, circumferential wave number, and cylindrical panel characteristics on the region of instability are displayed in the section of results and discussions. The findings show that when the porosity is further from the surface, the more stable the structure is. Furthermore, a small angle of the cylindrical panels gives a better dynamic response than a large angle. In addition, increased static and dynamic loads lead to an expansion of areas of instability.

Influence of geometric imperfections on postbuckling of layered (laminated) composite cylindrical panels has been performed under axial compression load using finite element code, ANSYS and validated experimentally. Finite element code was initially validated with available literature for performing the further analyses on the panel. Eigen imperfection irregularities were considered for predicting postbuckling loads of layered composite cylindrical panels with SSSS and SFSF boundary conditions with different r/t ratio and ply sequence and compared the results. Glass-polyester laminated cylindrical panels were fabricated and tested using fixture which accommodates different boundary conditions for investigating the postbuckling phenomenon. Experimental postbuckling analysis was carried out to validate the finite element analysis results and found satisfactory. The influence of imperfections with different r/t, stacking sequences with SSSS and SFSF boundary conditions were carried out and compared. As the r/t ratio of the cylindrical panel increases the postbuckling load decreases for a given boundary conditions and with magnitude of imperfection sensitivities. It has been observed that SFSF boundary conditions with angle play layup sequences taking more axial loads than SSSS boundary conditions with same layup sequence and imperfection sensitivity.

In this study, torsional buckling behavior of a laminated composite cylindrical shell panel reinforced with graphene nano-sheets is analyzed. Using the theory of linear three-dimensional elasticity and based on the principle of virtual work and finite element method, equilibrium equations are extracted. Buckling loads are obtained based on a generalized geometric stiffness concept. Halpin-Sai equations are also used to obtain the mechanical properties of the composite material. The effects of weight fractions and graphene distribution pattern along the thickness of the shell, and zigzag and armchair layup of graphene platelets on the torsional buckling loads are investigated. Five graphene distribution patterns FG-X, FG-O, FG-Ʌ, FG-V and UD are utilized in this study. The 15 models of GPL distribution and arrangement of composite layers are investigated. [ABSTRACT FROM AUTHOR]

In order to fill the evident lack of investigations on nonlinear response of nanocomposite curved panels under nonuniform temperature, this paper aims to analyze the nonlinear thermoelastic stability of cylindrical panels made of carbon nanotube (CNT) reinforced composite, rested on elastic foundations and subjected to sinusoidal-type in-plane temperature distribution. Reinforcement is carried out through functional rules of CNT volume fraction. An extended rule of mixture is adopted to estimate the effective properties of CNT-reinforced composite. Governing equations are derived based on classical shell theory accounting for von Kármán–Donnell nonlinearity, initial imperfection, interactive pressure from elastic foundation, and preexisting lateral pressure. In addition, the elasticity of in-plane constraints of boundary edges is included. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is adopted to derive nonlinear closed-form relation between thermal load and deflection. Parametric studies are carried out and interesting remarks are obtained. The present study finds that, unlike case of uniform temperature rise, thermal instability of cylindrical panels under sinusoidal temperature distribution still occurs even though all edges are movable and load carrying capacity is the weakest for an intermediate value of CNT volume fraction. Under sinusoidal temperature distribution, the cylindrical panel may be deflected at the onset of loading and, for the most part, has no longer bifurcation-type buckling response. Furthermore, small values of preexisting external pressure have beneficial influences on the stability of nanocomposite cylindrical panels under nonuniform thermal loads. [ABSTRACT FROM AUTHOR]

In this work, the nonlinear free vibration analysis of the imperfect cylindrical panels in contact with discontinuous unilateral elastic base are conducted, evaluating the influence of the type of contact, unilateral or bilateral, and the contact area of the elastic base on the natural frequencies and nonlinear frequency-amplitude relations. For that, the structural cylindrical panel model considers the Donnell's nonlinear shallow shell theory to obtain the partial differential equilibrium equation and the compatibility and continuity equation. To represent the unilateral capability of the elastic base, a signum function is inserted in the reaction force of the elastic base to describe its dependence of the transversal displacement field of the cylindrical panel. To apply the elastic base in certain subdomain of the cylindrical panel, a Heaviside-type function is also inserted into elastic base's reaction forces. The nonlinear equilibrium equation is discretized by the Galerkin method, using a consistent transversal displacement field that it was obtained from a perturbation technique. The discretized set of equilibrium equations is employed to obtain the natural frequencies and the nonlinear frequency-amplitude relations, evaluating the influence of the unilateral contact and the contact region of the elastic base on these results. Depending on the signal of the imperfection's magnitude and the type of contact of the elastic base, the imperfect cylindrical panel can display an initial gap between the cylindrical panel and the elastic base, and this possibility is also investigated in this work. From the numerical results, it is observed that the unilateral elastic base applies less structural stiffness than the bilateral elastic base, decreasing the natural frequencies for the same imperfect cylindrical panel. The localization of the elastic base in the cylindrical panel also affects the natural frequencies, increasing or decreasing them depending on the modifications on the structural stiffness. The frequency-amplitude relations are strongly influenced by both unilateral contact of elastic base and the type of the contact consideration between the cylindrical panel and elastic base, exhibiting an intricated nonlinear behavior. • Inclusion of a discontinuous and unilateral elastic base on the nonlinear equilibrium equation of imperfect cylindrical panels. • Novel results on the influence of the unilateral elastic base on natural frequencies and nonlinear frequency-amplitude relations. • Simultaneous evaluation of the influence of the initial geometrical imperfections and the unilateral elastic base on the nonlinear free vibration analysis. • Results of a detailed parametric analysis confirm that natural frequencies and backbone curves are sensitive to the magnitude of initial geometric imperfections and the unilateral elastic base's parameters. [ABSTRACT FROM AUTHOR]

Purpose: This work investigates a simply supported cylindrical panel (with uncertainties in its thickness, radius and Young's modulus) subjected to a time-dependent transverse load. Methods: The nonlinear equilibrium equations of the panel are obtained from Donnell's shallow shell theory, in terms of the transverse displacement field and Airy's stress function. To discretize this set of equations, the standard Galerkin method is applied in the panel's space domain. For that, a consistent modal solution for the transverse displacement field is chosen from a perturbation method, considering the main modal couplings that occur due to the geometric nonlinearities present in the equilibrium equations. The uncertainties of the parameters are assumed to have a uniform probability density function and are considered in the nonlinear equilibrium equations by a generalized polynomial chaos expansion of the modal amplitudes of the transverse displacement field. Legendre-chaos polynomials are used to describe the random parameters and the stochastic Galerkin method is applied to discretize the expanded nonlinear equilibrium equations in the random parameter space. Results: The mean and variance of the bifurcation diagrams are obtained, evaluating the influence of uncertain parameters on their paths, and the regions, where an intrusive application of a generalized polynomial chaos expansion procedure can be applied. Conclusions: The numerical results show good agreement between the proposed procedure and the results obtained by the Monte Carlo method in the bifurcation diagrams, especially those regions that do not have dynamic jumps and/or competition between the periodic, quasi-periodic and chaotic permanent response. [ABSTRACT FROM AUTHOR]

In this paper, an exact elasticity solution of cylindrical panel under cylindrical bending is presented. The formulation is based on the displacement approach in which 3D elasticity equations are reduced to 2-D equations using plane-strain conditions. In the present formulation, an exact elasticity solution is feasible due to the consideration of simply supported boundary conditions with applied loads expressed in harmonic forms. Single layered and multi-layered orthotropic composite panels subjected to realistic transverse normal loads are analysed. Solutions have been presented for uni-directional, bi-directional, and symmetric three-layered cross-ply laminated composite cylindrical panels. Variation of displacements and stresses through the thickness has been investigated for the panel subjected to single sinusoidal load, uniformly distributed load, hydrostatic load, and strip load. Validation of results is presented using reference results in the literature. The extensive results presented in this paper can be served as benchmark solutions for the assessment of improved panel theories.

Influence of geometric imperfections on postbuckling of layered (laminated) composite cylindrical panels has been performed under axial compression load using finite element code, ANSYS and validated experimentally. Finite element code was initially validated with available literature for performing the further analyses on the panel. Eigen imperfection irregularities were considered for predicting postbuckling loads of layered composite cylindrical panels with SSSS and SFSF boundary conditions with different r/t ratio and ply sequence and compared the results. Glass-polyester laminated cylindrical panels were fabricated and tested using fixture which accommodates different boundary conditions for investigating the postbuckling phenomenon. Experimental postbuckling analysis was carried out to validate the finite element analysis results and found satisfactory. The influence of imperfections with different r/t, stacking sequences with SSSS and SFSF boundary conditions were carried out and compared. As the r/t ratio of the cylindrical panel increases the postbuckling load decreases for a given boundary conditions and with magnitude of imperfection sensitivities. It has been observed that SFSF boundary conditions with angle play layup sequences taking more axial loads than SSSS boundary conditions with same layup sequence and imperfection sensitivity. [ABSTRACT FROM AUTHOR]

In this paper, natural frequency analysis of functionally graded graphene platelet (GPL) reinforced composite cylindrical panel is investigated. Halpin-Tsai equations are employed to obtain the mechanical properties of the structure. The linear three-dimensional elasticity theory based on the Hamilton principle and the numerical finite element method are used for obtaining the governing equations of motion. Four patterns of GPL distributions such as: FG-X, FG-V, FG-O and UD are assumed through the thickness of shell. The effects of various parameters such as different distributions and weight fractions of GPL, zigzag and armchair lay-up, geometry and different boundary conditions on the natural frequencies and mode shapes of shell have been investigated. The results indicate that the maximum and minimum natural frequencies belong to FG-X pattern and FG-O pattern, respectively. [ABSTRACT FROM AUTHOR]

In this paper a numerical solution is presented for free vibration analysis of sandwich cylindrical panels made of a saturated functionally graded porous (FG-porous) core and two similar homogenous face sheets. The panel is modeled based on the third order shear deformation theory (TSDT) and stress-strain relations are considered based on the linear poroelasticity theory of Biot. Natural frequencies are calculated for various boundary conditions and a parametric study is presented to study the effects of various parameters on the natural frequencies including geometrical parameters, porosity parameter, porosity distribution pattern, thickness of the porous core and compressibility of porefluid. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model of complex oscillations of a flexible micropolar cylindrical mesh structure is constructed. Equations are written in displacements. Geometric nonlinearity is taken into account according to the Theodore von Karman model. A non-classical continual model of a panel based on a Cosserat medium with constrained particle rotation (pseudocontinuum) is considered. It is assumed that the fields of displacements and rotations are not independent. An additional independent material parameter of length associated with a symmetric tensor by a rotation gradient is introduced into consideration. The equations of motion of a panel element, the boundary and initial conditions are obtained from the Ostrogradsky – Hamilton variational principle based on the Kirchhoff – Love’s kinematic hypotheses. It is assumed that the cylindrical panel consists of n families of edges of the same material, each of which is characterized by an inclination angle relative to the positive direction of the axis directed along the length of the panel and the distance between adjacent edges. The material is isotropic, elastic and obeys Hooke’s law. To homogenize the rib system over the panel surface, the G. I. Pshenichnov continuous model is used. The dissipative mechanical system is considered. The differential problem in partial derivatives is reduced to an ordinary differential problem with respect to spatial coordinates by the Bubnov – Galerkin method in higher approximations. The Cauchy problem is solved by the Runge – Kutta method of the 4th order of accuracy. Using the establishment method, a study of grid geometry influence and taking account of micropolar theory on the behavior of a grid plate consisting of two families of mutually perpendicular edges was conducted.

• A dynamic model of graphene reinforced cylindrical panel subjected to the pulse or steady-state excitation is proposed. • Distributing more GPLs to the outer surfaces shows the optimal performance for the composite structure. • Nonlinear transient responses, bifurcation and chaotic dynamics are investigated. • Double-parameter maximum Lyapunov exponents are plotted to intuitively judge the chaotic regions. The present paper is concerned with nonlinear vibration of a simply supported functionally graded graphene reinforced composite (GRC) cylindrical panel subjected to the transverse excitation. Functionally graded structure is proposed to distribute more graphene platelets (GPLs) to the most needed layer for the optimal performance. The modified Halpin-Tsai model and the rule of mixture are carried out to predict the effective material properties of the GRC cylindrical panel, such as Young's modulus, Poisson's ratio and mass density. Nonlinear partial differential equations of motion are established within the framework of Hamilton principle in conjunction with first-order shear deformation theory (FSDT) and von Karman geometric nonlinearity. Navier approach is adopted to calculate natural frequencies of the GRC cylindrical panel. Then, considering the external excitation, Galerkin method is applied to realize the model reduction, which is expressed by the ordinary differential equations. Backward Differentiation Formula (BDF) is used to perform nonlinear transient responses of the system subjected to the pulse excitation (step load or triangular load). Finally, Runge-Kutta method is employed to carry out bifurcations and chaotic dynamics of the system subjected to the steady-state excitation. Results are presented in the form of natural frequencies and nonlinear responses to perform the parametric studies, such as distribution types and weight fractions of GPLs, geometry parameters and excitation parameters of the GRC cylindrical panel. [ABSTRACT FROM AUTHOR]

The article deals with a three-dimensional analysis of free vibrations of a homogeneous isotropic, thermally conducting cylindrical panel with voids in the context of a three-phase-lag model of hyperbolic thermoelasticity. After expanding the displacement potentials, void volume fraction and temperature functions with orthogonal series, the equations of the considered vibration problem are reduced to five second-order-coupled ordinary differential equations whose formal solutions can be expressed by using Bessel functions with complex arguments. The corresponding results for the thermoelastic panel without voids and an elastic panel with and without voids have been deduced as special cases. To illustrate the analytical results, the numerical solutions of various relations and equations have been obtained to compare the frequency as a function of different cylindrical panel parameters in the case of different thermoelastic models. The computer-simulated results have been presented graphically to show the effect of voids and phase lag on the frequency. [ABSTRACT FROM AUTHOR]

This research deals with the optimization of buckling and fundamental frequency of a cylindrical panel under various heating conditions, which varies across the surface of the panel. A multi-objective design indicator (MODI) is derived with fiber orientations as a design variable. Finite element analysis is used to calculate temperature variation according to the nature of heating, buckling temperature, and fundamental frequency. In this study, scientific computing software is used to incorporate the finite element method with artificial neural network and particle swarm optimization technique. Five different heating cases, including uniform temperature cases, are considered. It is observed from the analysis that the in-plane temperature field of non-uniform type has a significant influence on the buckling and vibration characteristics of the panel. Further, it is observed that panel with lamination scheme of (θ ° / − θ ° / θ ° / − θ °) S gives the higher value of MODI max compared to other lamination schemes considered. [ABSTRACT FROM AUTHOR]

In the analytic modeling of shell buckling, much attention has been paid to closed cylindrical shells or cylindrical panels with at least two opposite edges simply supported whose solutions are known to be Lévy-type solutions. However, there have been very few reports on analytic solutions of commonly used non-Lévy-type cylindrical panels, which is mainly attributed to the widely acknowledged difficulty in solving the governing higher-order partial differential equations under prescribed boundary conditions. To address this gap, the present study provides some new analytic buckling solutions of non-Lévy-type cylindrical panels within the Hamiltonian-system-based symplectic framework. The buckling of a cylindrical panel is first formulated in the Hamiltonian system to realize a new matrix-form governing equation. An original problem with non-Lévy-type boundary conditions is then treated as the superposition of two elaborated subproblems that are solved by the rigorous symplectic approach. The final solution is obtained according to the equivalence between the superposition of the subproblems and the original problem. For benchmark use, comprehensive buckling loads and buckling modes are presented for typical non-Lévy-type panels with different ratios of in-plane dimensions, different ratios of in-plane dimension to radius of curvature, and different ratios of thickness to in-plane dimension. The present study is the first successful extension of the symplectic superposition method to the buckling analysis of cylindrical panels, which may enable access to more new analytic solutions for similar issues. [ABSTRACT FROM AUTHOR]

Supersonic flutter characteristics of cylindrical sandwich panels made of a saturated functionally graded porous (FGP) core and two homogeneous face sheets are studied in this paper based on the Biot's poroelasticity theory. The third-order shear deformation theory (TSDT) is used to model the panel and the piston theory is hired to estimate the aerodynamic pressure create by the supersonic fluid flow. First, the set of the governing equations are solved numerically via generalized differential quadrature method (GDQM) and natural frequencies are calculated for various boundary conditions. Then, convergence of the solution is confirmed and its accuracy is demonstrated by comparing the results with those reported by other authors. Finally, the effects of geometrical parameters of the panel, thickness of the porous core, porosity distribution pattern, porosity parameter (size of pores), compressibility of pore fluid and yaw angle (fluid flow direction) on the flutter boundaries of FGP sandwich panels are investigated. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear vibration and dynamic buckling responses of the sinusoid, parabola, and cylindrical CNT-reinforced panels with piezoelectric layer stiffened by a CNT-reinforced stiffener system in uniform temperature change with a piezoelectric layer are presented. An improved homogenization technique for the x - or y -direction CNT-reinforced stiffener system is utilized to determine the total stiffnesses of the considered structures. The higher-order shear deformation theory (HSDT) in conjunction with the von Kármán nonlinearities is adopted to formulate the motion equations, while the stress function for complex curvature panels is estimated using the like-Galerkin procedure. The nonlinear equation of motion is acquired by utilizing the Lagrange function and Euler-Lagrange's equations. The numerical examples use the Runge-Kutta technique to acquire the nonlinear time-amplitude curves, and the critical dynamic buckling load is determined using the Budiansky-Roth criterion. These examples evaluate the effects of stiffeners, piezoelectric layer, material, and geometrical parameters on the nonlinear vibration and dynamic buckling responses of the panels. • Nonlinear dynamic responses of the CNT-reinforced stiffened panels are studied. • Sinusoid, parabola, and cylindrical panels with piezoelectric layer are mentioned. • The improved smeared stiffener technique for CNT-reinforced stiffeners is presented. • The like-Galerkin procedure is applied to estimate the approximate stress function. • HSDT, Euler-Lagrange's equation, and Runger-Kutta method are used. [ABSTRACT FROM AUTHOR]

Natural frequency characteristics of functionally graded multilayer hybrid composite cylindrical shell panel reinforced by graphene platelets (GPLs) and carbon nanotubes (CNTs) are scrutinized in the present study for the first time. Effective material properties of the composite media are evaluated using a modified micromechanical model based on the Halpin-Tsai approach and rule of mixtures. First order shear deformation theory of shells, Hamilton's principle and finite element procedure are applied to obtain the effective stiffness and mass matrices of the structure. After validating accuracy of the presented solution procedure with the published literatures, influence of broad range of factors such as number of multilayers, weight fraction and distribution pattern of GPLs and CNTs reinforcements, CNTs and GPLs volume fraction index for the nonlinear distributions, thickness and length ratio of the shell panel, span angle, Winkler elastic foundation stiffness parameter and different boundary condition are presented and their trends are discussed in several tabular and graphical data in detail. Results denotes that cylindrical shells composed of three phases can make use of the advantages of both CNTs and GPLs reinforcing elements and can significantly improve the free vibration behavior of shell. • Investigating the natural frequencies of FG multilayer hybrid nanocomposite cylindrical shell panel reinforced by GPLs and CNTs for the first time. • Studying the effects of Winkler-type elastic foundation on the natural frequencies. • Deriving governing equations based on FSDT, Hamilton's principle and FEM. • A full comprehensive study considering the effects of the number of multilayers, weight fraction and distribution of GPLs and CNTs, CNTs and GPLs volume fraction index, thickness and length ratio, span angle, Winkler elastic foundation stiffness parameter and BCs. [ABSTRACT FROM AUTHOR]

In this study, the vibration and flutter characteristics of the graphene platelets reinforced functionally graded porous cylindrical panels subjected to the supersonic flow are investigated for the first time. The considered panels are constructed of the nanocomposites that made of matrix of open-cell metal foams with graded pore distributions and are reinforced uniformly by the graphene platelets. The typical mechanical properties of porous matrix are determined using open-cell metal foam model, which provides a typical mechanical feature to determine the relationship between coefficients of density and porosity. The effective elasticity modulus of the nanocomposite is determined based on a modified Halpin-Tsai micromechanics model, and the rule of mixture is used to calculate the Poisson's ratio and mass density. A high order shear deformable computational framework is developed with inclusion of the trapezoidal shape factor to eliminate the errors introduced by the curvature of the panels. The standard Lagrange processing in conjunction with the Navier-solution technique, with the help of the first-order piston theory, is applied to derive the equations of motion related to the vibration and flutter characteristics of the cylindrical panel with simple-supported boundary condition. Comparisons of the natural frequencies with the previous works are performed to validate the proposed model. Parameter studies are carried out, and the results in the form of graphs or tables reveal the effects of pore, graphene platelets on the supersonic flutter characteristics of the nanocomposite cylindrical panels subjected to the aerodynamic flow. • Supersonic flutter of GPL-reinforced FG porous panels is studied for the first time. • The total masses of various FG porous cylindrical panels are the same. • A computational framework based on Reddy's TSDT is developed. • The comparisons indicate the proposed method is accurate. • Revealing effects of some important parameters on flutter characteristics. [ABSTRACT FROM AUTHOR]

In this study, experimental investigations carried out to analyze the influences of different in-plane temperature variations on buckling and free vibration responses of metal and fiber-reinforced laminated composite cylindrical panels are presented. Initially, critical buckling temperature is calculated then free vibration analysis is performed as a function of the buckling temperature to analyze the changes in the natural frequencies and mode shapes. Experimental results revealed that the thermal buckling strength of the panel is significantly influenced by the nature of the heating condition. Similarly, significant changes in free vibration mode shapes are observed with the rise in temperature and also according to the heating conditions. It is also observed that, with the increase in temperature, nodal and anti-nodal lines of free vibration modes shifting towards the heating source. The experimental results are compared with the numerical simulation for the studies on the isotropic cylindrical panel and both the results are in good agreement. [ABSTRACT FROM AUTHOR]

This paper develops a new structure dynamic model to investigate nonlinear transient responses of the rotating blade made of functionally graded material (FGM). The rotating blade is simplified as a rotating FGM cylindrical panel with a presetting angle and a twist angle. The geometric nonlinearity effects are taken into account in the strain-displacement relationships, which are derived by Green strain tensor. Based on the first-order piston theory and the first-order shear deformation theory, the equations of motion for the rotating twisted FGM cylindrical panel are acquired by means of Hamilton principle and Galerkin method. Backward Differentiation Formula (BDF) and Runge-Kutta Algorithm are used to solve the nonlinear equations of motion for the system. The effects of four pulse load conditions on the system subjected to the internal pulse load or the external pulse load are fully discussed. A detailed parametric analysis is performed by considering the effects of the rotating speed, volume fraction index and temperature. [ABSTRACT FROM AUTHOR]

On the paper, using the system of equations corresponding to the classical theory of orthotropic cylindrical shells, the free vibrations of thin elastic orthotropic circular cylindrical panel with hinge-mounted end is investigated. To calculate the eigen frequencies and to identify the respective natural modes it is employ the generalized Kantorovich-Vlasov method of reduction to ordinary differential equations. The dispersion equations for finding the eigen frequencies of possible types of vibrations are derived. An asymptotic link betwееn the dispersion equations of problem in hаnd and analogous problem for the rectangular plate is shown. Also, a link between the dispersion equations of the problem in hand and the boundary-value problem for the semi - infinite orthotropic circular cylindrical panel with free edges is shown. [ABSTRACT FROM AUTHOR]

This paper presents an exact solution for the boundary-value problem which describes the linear buckling of axially-compressed cylindrical panels with frames attached to the circular edges. The boundary conditions differ from the classical simply supported ones, often assumed for design purposes, in the sense that the torsion resisted by the frames are also taken into account. The quality of the results reported herein may be valuable benchmark data. [ABSTRACT FROM AUTHOR]

This article investigates the nonlinear stability of composite cylindrical panels (CPs) reinforced by carbon nanotubes (CNTs), resting on elastic foundations and subjected to combined thermomechanical loading conditions. CNTs are embedded into matrix phase through uniform distribution or functionally graded distribution. Material properties of constituents are assumed to be temperature dependent and effective elastic moduli of carbon nanotube–reinforced composite are estimated by the extended rule of mixture. Nonlinear governing equations of geometrically imperfect panels are based on first-order shear deformation theory accounting for elastic foundations and tangential constraint of straight edges. Analytical solutions are assumed to satisfy simply supported boundary conditions and closed-form expressions relating load and deflection are derived through Galerkin method. Numerical examples show the effects of preexisting nondestabilizing loads, distribution patterns, panel curvature, in-plane condition of unloaded edges, thermal environments, initial imperfection, and elastic foundations on the nonlinear stability of nanocomposite CPs under combined loading conditions. [ABSTRACT FROM AUTHOR]

Abstract As a first attempt, the combined application of the differential quadrature method (DQM) and the Newton Raphson method is used to solve the non-Fourier heat conduction equations to obtain temperature, displacements, and stresses in a cylindrical panel made of functionally graded, carbon nanotubes (CNTs) reinforced composite. The heat conduction of a domain made of nanocomposites subjected to heat generation is simulated with a finite heat wave speed. Furthermore, based on the three-dimensional elasticity theory, the thermoelastic analysis of the nanocomposite cylindrical panel subjected to the transient heat conduction is presented. The dynamic Young's modulus of Single-Walled Carbon Nanotubes (SWCNT) can be expressed as a function of loading rate and environmental temperature. All material properties such as heat capacity (C p), thermal relaxation time (τ), density (ρ) and thermal conductivity (K) are considered as a function of both temperature and CNT volume fraction. The hyperbolic heat conduction is solved to obtain temperature in the spatial and temporal domains. Then by implementing the obtained temperature in thermoelastic equations of the cylindrical panel, the displacements and stresses will be obtained at each time step. The proposed method marches in the time direction block by block. In each block, there are several time levels, and the numerical results at these time levels are obtained simultaneously. Through this way, the numerical solution at the (n + 1)th time level depends on the solutions at its previous levels from the 1 st to the n th levels. The final results in the temporal domain are obtained using the Newton–Raphson method. Accuracy of the present solution is confirmed by comparing with some available results in the literature. A detailed numerical study is conducted to examine the effects of heat wave speed and heat flux, CNT volume fraction and the geometrical parameters on the deflection of the cylindrical panel. [ABSTRACT FROM AUTHOR]

Highlights • An efficient reduced order model, based on perturbation procedure, is derived. • An extensive range of geometrical values to cylindrical panel is evaluated. • Different types of bifurcation and loss of stability are determined. • Sensibility to shape of geometrical imperfections are strongly observed. Abstract The aim of this work is to analyse the influence of the nonlinear modal coupling and initial geometrical imperfection on the post-buckling path (perfect case) or nonlinear equilibrium path (imperfect case) of a simply supported, axially loaded cylindrical panel. The cylindrical panel is described by the Donnell nonlinear shallow shell theory and the lateral displacement field is based on a perturbation procedure, generating a precise low-dimensional model that satisfies out-of-plane boundary conditions and considers the forthcoming nonlinear modal coupling due to quadratic and cubic terms in a nonlinear equilibrium equation. The discretized equations of motion are determined by applying the standard Galerkin method. Various numerical techniques are employed to obtain the cylindrical panel's nonlinear static equilibrium path with its structural stability analysis. The results show the influence of geometry on the nonlinear response of the cylindrical panel, unveiling an intricate competition between different types of bifurcation diagrams (stable symmetric, unsymmetrical, and unstable symmetric). Completing the presented results, the initial geometrical imperfection could change the stability of the initial nonlinear equilibrium path (from unstable to stable) depending on the applied amplitude of the imperfection and its shape. It is possible to observe that the influence of the geometrical imperfection on the nonlinear equilibrium path of the imperfect cylindrical panel is determinant. [ABSTRACT FROM AUTHOR]