In this study, the solution of the buckling problem of axially loaded laminated cylindrical shells consisting of functionally graded (FG) nanocomposites in elastic and thermal environments is presented within extended first-order shear deformation theory (FOST) for the first time. The effective material properties and thermal expansion coefficients of nanocomposites in the layers are computed using the extended rule of mixture method and molecular dynamics simulation techniques. The governing relations and equations for laminated cylindrical shells consisting of FG nanocomposites on the two-parameter elastic foundation and in thermal environments are mathematically modeled and solved to find the expression for the axial buckling load. The numerical results of the current analytical approach agree well with the existing literature results obtained using a different methodology. Finally, some new results and interpretations are provided by investigating the influences of different parameters such as elastic foundations, thermal environments, FG nanocomposite models, shear stress, and stacking sequences on the axial buckling load.

The free vibration behavior of laminated plates consisting of nonhomogenous orthotropic layers is presented. First, the mechanical properties of laminated plates composed of non -homogenous (NH) orthotropic layers are modelled. After establishing the basic relations of laminated plates within shear deformation theory (SDT), governing equations are derived in the framework of Donnell type plate theory. The solution of the governing equations is carried out by the Galerkin method and the analytical expression is found for the linear frequency of plates composed of nonhomogenous orthotropic layers. Finally, the influences of various factors such as shear stresses, non -homogeneity, number and arrangement of layers on the frequency of rectangular plates are examined.

The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young’s modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson’s ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated.

In this study, the influence of the torsional rigidity of the connected shafts, couplings and the working body of the machine, as well as the damping capacity of the coupling, on the torsional impact moment generated in the machine transmission is investigated. Unlike existing classical calculation models, the torsional stiffness of the connected shafts, the torsional damping ability of the coupling and the effects of the moment ratio are taken into consideration together. Under these conditions an analytical expression for the shock moment or resonance coefficient is obtained. The main novelties in obtaining of this expression are the ratio of the torsional stiffness of the connected shafts with the torsional stiffness of the coupling and the acceptance of the moment of resistance of the working body of the machine depending on the torsional stiffness. It has been found that the considered factors have a significant effect on the resonance zone. Finally, different and overlapping conditions are determined when determining the value of the resonance coefficient characterizing the torque impact moment, calculated according to the classical and proposed models.

In this study, one of the first attempts is made to solve the nonlinear (NL) vibration problem of shear-deformable multilayer plates consisting of nonhomogeneous orthotropic layers (NHOLs) using the Poincaré-Lindstedt method. First, the shear deformation theory (SDT) for homogeneous plates is extended to multilayer plates composed of NHOLs. In the framework of von-Karman type nonlinear theory, the basic relations of the plates in question are established and then NL equations of motion based on four functions such as rotation angles, Airy stress and deflection functions are derived. Then, NL-partial differential equations (NL-PDEs) are reduced to NL-ordinary differential equations (NL-ODE) and the solution of NL-ODE is performed for the first time by the modified Poincaré −Lindstedt method, yielding new amplitude dependent expressions for NL frequency, and for the ratio of NL frequency to linear (NL/L) frequency for multilayer plates consisting of NHOLs. Finally, detailed parametric studies are carried out to gain insight into the effects of various factors such as shear strains, non-homogeneity, number and array of layers on the NL frequencies under different rectangular plate characteristics.

This work is dedicated to the modeling and solution of eigenvalue problems within shear deformation theory (SDT) of laminated cylindrical shells containing nanocomposite plies subjected to axial compressive load in thermal environments. In this study, the shear deformation theory for homogeneous laminated shells is extended to laminated shells consisting of functionally graded (FG) nanocomposite layers. The nanocomposite plies of laminated cylindrical shells (LCSs) are arranged in a piecewise FG distribution along the thickness direction. Temperature-dependent material properties of FG-nanocomposite plies are estimated through a micromechanical model, and CNT efficiency parameters are calibrated based on polymer material properties obtained from molecular dynamics simulations. After mathematical modeling, second-order time-dependent and fourth-order coordinate-dependent partial differential equations are derived within SDT, and a closed-form solution for the dimensionless frequency parameter and critical axial load is obtained for first time. After the accuracy of the applied methodology is confirmed by numerical comparisons, the unique influences of ply models, the number and sequence of plies and the temperature on the critical axial load and vibration frequency parameter within SDT and Kirchhoff–Love theory (KLT) are presented with numerical examples.

The buckling behavior of functionally graded carbon nanotube (FG-CNT) reinforced polymer-based moderately-thick plates subjected to in-plane biaxial compressive loads in elastic and thermal environments in the framework of first-order shear deformation plate theory (FSDPT) is investigated. First, the temperature-dependent properties of CNTs and nanocomposites are defined and their constitutive relations are established, then the stability and strain compatibility equations in elastic media are derived in the framework of the FSDPT. Then, by applying the Galerkin method to the basic equations, a closed-form solution is obtained for the critical biaxial compressive loads. The specific numerical analyzes and interpretations are made for various plate sizes and CNT patterns on the Winkler elastic foundation and in thermal environments within FSDPT and classical plate theory (CPT).

This study presents the thermoelastic stability of carbon nanotube (CNT) patterned composite conical shells in the framework of shear deformation theory (ST). The study includes two different boundary value problems. As the material properties are independent of temperature, the truncated conical shell is assumed to be under thermal load, and when the material properties are temperature dependent, the conical shell is assumed to be under axial compressive load. The modified Donnell-type shell theory is used to derive the basic equations for CNT patterned truncated conical shells. The Galerkin method is applied to the basic equations to find the critical temperature and critical axial load expressions of CNT patterned composite truncated conical shells in the framework of ST. The effect of changes in CNT patterns, volume fraction, radius-to-thickness and length-to-thickness ratios, as well as the half-peak angle on critical parameters within the ST, are estimated by comparison with classical shell theory (CT).

The aim of the study is to present a new approach to the analytical solution of the vibration and stability problem of clamped sandwich cylindrical shells (SCSs) covered by functionally graded (FG) coatings under an axial compressive load in the framework of shear deformation theory (ST). After modeling the micro and macro mechanical properties of FG coated SCSs with various configurations, the constitutive relations and basic equations are derived depending on the stress, deflection and two angles of rotation functions using modified Donnell type theory. An attempt is made to analytically solve the fundamental differential equations for SCSs covered by FG coatings using novel approximation functions satisfying the clamped boundary conditions. Three different shear stress functions (SSFs) such as parabolic shear stress function (Par-SSF), cosine-hyperbolic shear stress function (Cos-Hyp-SSF) and uniform shear stress function (U-SSF) are used in the analysis. After confirming the accuracy of the obtained results, the influences of coating profiles, volume fractions and layer arrangement variations on the critical parameters for three different transverse shear stress functions are investigated in detail.

The widespread use of structural elements consisting of functionally graded (FG) materials in advanced technologies has led to extensive research. Due to the difficulties encountered during modeling and problem solving, the number of studies on the dynamic behavior of structural elements made of FG viscoelastic materials is quite limited compared to the number examining FG elastic materials. This study is one of the first attempts to solve the dynamical problem by the mathematical modeling of functionally graded viscoelastic plates (FG-VE-Ps) and viscoelastic media together with different initial conditions. FG-VE-Ps on viscoelastic foundations (VE-Fs) are assumed to be under compressive edge load in the longitudinal direction. The governing equations for FG-VE-Ps on VE-Fs are derived using Boltzmann and Volterra concepts. The problem is reduced to the solution of integro-differential equation system using the Galerkin method. Then, by performing Laplace transforms, new analytical expressions for the time-dependent deflection function and critical time at different initial conditions are found. The loss of stability of FG-VE-Ps on VE-Fs is modeled to cover three time-varying ranges: the first is the range in which the deflection function decreases; the second is the transition interval; the third is the increase range of deflection function, which leads to the loss of stability. The time corresponding to the sharp increase of the deflection function is defined as the critical time, and is determined both theoretically and numerically. The results are compared with the results obtained by various methods to confirm their accuracy. Finally, the effects of VE-Fs, VE material properties, and FG profiles on the critical time behavior of plates are studied numerically.

The mathematical modeling of the stability problem of nanocomposite cylindrical shells is one of the applications of partial differential equations (PDEs). In this study, the stability behavior of inhomogeneous nanocomposite cylindrical shells (INH-NCCSs), under combined axial compression and hydrostatic pressure in the thermal environment, is investigated by means of the first-order shear deformation theory (FSDT). The nanocomposite material is modeled as homogeneous and heterogeneous and is based on a carbon nanotube (CNT)-reinforced polymer with the linear variation of the mechanical properties throughout the thickness. In the heterogeneous case, the mechanical properties are modeled as the linear function of the thickness coordinate. The basic equations are derived as partial differential equations and solved in a closed form, using the Galerkin procedure, to determine the critical combined loads for the selected structure in thermal environments. To test the reliability of the proposed formulation, comparisons with the results obtained by finite element and numerical methods in the literature are accompanied by a systematic study aimed at testing the sensitivity of the design response to the loading parameters, CNT models, and thermal environment.

In this work, the propagation of planar waves in a homogeneous micropolar thermoelastic medium is studied while the entire body rotates with a uniform angular speed. The coordinate system of the rotating medium is assumed to be stationary, and therefore the kinematic equations have two additional terms, namely, the gravitational and the Coriolis accelerations. The problem is addressed based on the two-temperature thermoelastic model with higher-order time derivatives and dual-phase lag, which can explain the effect of microscopic features in nonsimple materials. With certain boundary conditions and the normal mode approach, the variations in temperature, displacement, microrotation, and thermal stresses induced by heating are derived. In the absence of rotation and two-temperature factor, comparison is made with the results of classical thermoelastic models.

In this study, the stability behavior of multilayer cylindrical shells made of functionally graded nanocomposite layers (FG-NCLs) subjected to the lateral pressure in thermal environments is investigated. It is postulated that nanocomposite layers forming layered cylindrical shells are made of single-walled carbon nanotube (SWCNT)-reinforced polymers that have four types of profiles based on the uniform and linear distributions of mechanical properties. The material properties of SWCNTs are assumed to be dependent on location as well as temperature and are obtained from molecular dynamics simulations. The governing equations are derived as partial differential equations within shear deformation theory (SDT) and solved in a closed form, using the Galerkin procedure, to determine the lateral critical pressure (LCP) in thermal environments. The numerical representations relate to the buckling behavior of multilayer cylindrical shells made of functionally graded nanocomposite layers under the uniform lateral pressure for different CNT patterns and temperatures within SDT and Kirchhoff-Love theory (KLT).

In this study, the solution of the nonlinear forced vibration (NFV) problem of double curvature panels consisting of inhomogeneous (INH) nanocomposite (NC) layers is discussed within first order shear deformation theory (FSDT), taking into account the viscous damping effect. First, the mechanical properties of laminated double curvature panels composed of carbon nanotube patterned layers are modeled mathematically. Then, based on FSDT with a von K ' arm ' an-type nonlinearity derived the nonlinear basic relationships and partial differential equations (PDEs). The expression for the NFV frequency of multilayer panels made of inhomogeneous nanocomposite layers (INHNCLs) is obtained within FSDT, using the multi-scale method to the nonlinear PDEs for the first time. Finally, the influences of the external excitation, nonlinearity, transverse shear strains, number and arrangement of layers and CNT-models on the forced vibration frequencies are studied in detail.

In this study, the stability of inhomogeneous nanocomposite cylindrical shells (INCCSs) under hydrostatic pressure in a thermal environment is presented. The effective material properties of the inhomogeneous nanocomposite cylindrical shell are modeled on the basis of the extended mixture rule. Based on the effective material properties, the fundamental relations and stability equations are derived for thermal environments. In this process, the first-order shear deformation theory (FSDT) for the homogeneous orthotropic shell is generalized to the inhomogeneous shell theory. This is accomplished using the modified Donnell-type shell theory. The analytical expressions are obtained for hydrostatic buckling pressure of INCCSs in the framework of FSDT and classical shell theory (CST) by obtaining a solution based on Galerkin's procedure. The numerical examples presented include both comparisons and original results. The last section shows the influences of carbon nanotube (CNT) models, volume fraction, and shell characteristics on the hydrostatic buckling pressure in the thermal environment.

In this study, the stability problem of heterogeneous orthotropic (HTO) truncated conical shells with clamped edges subjected to external pressures (lateral and hydrostatic) within shear deformation theory (ST) is solved using a new approach. After the mathematical and visual design of HTO-truncated conical shells, modified Donnell-type governing equations including transverse shear stresses are derived for them. Stability equations are solved analytically for the first time in this study by constructing new approximation functions depending on an unknown parameter for stress, deflection and two angles of rotation functions under clamped boundary conditions. In addition, the unknown parameter contained in the analytical formulas for the clamped HTO- truncated conical shells within ST is found from the minimum conditions of the critical external pressures. After confirming the accuracy of the results, the influences of shear stresses, orthotropy, heterogeneity and conical shell characteristics on critical lateral and hydrostatic pressures are examined in detail in the presence of clamped boundary conditions.

In the current paper, a generalized thermoelastic model with two-temperature characteristics, including a heat transfer equation with fractional derivatives and phase lags, is proposed. The Caputo–Fabrizio fractional differential operator is used to derive a new model and to solve the singular kernel problem of conventional fractional models. The suggested model is then exploited to investigate responses of an isotropic cylinder with variable properties and boundaries constantly exposed to thermal or mechanical loads. The elastic cylinder is also assumed to be permeated with a constant magnetic field and a continuous heat source. The governing partial differential equations are formulated in dimensionless forms and then solved by the Laplace transform technique together with its numerical inversions. The effects of the heat source intensity and fractional order parameter on the thermal and mechanical responses are addressed in detail. To verify the integrity of the obtained results, some comparative studies are conducted by considering different thermoelastic models.

The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the two-parameter elastic foundation (T-P-EF). It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs, based on a generalized first-order shear deformation shell theory (FSDST) which includes shell-foundation interaction. By adopting the extended mixing rule, the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters. Three carbon nanotube distribution in the matrix, i.e. uniform distribution (U) and V and X-types linear distribution are taken into account. The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads (CBLs) of the structure selected here. The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF. Finally, a parametric study is carried out to study the influences of the foundation parameters, the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.

Revolutionary advances in technology have led to the use of functionally graded nanocomposite structural elements that operate at high temperatures and whose properties depend on position, such as cylindrical shells designed as load-bearing elements. These advances in technology require new mathematical modeling and updated numerical calculations to be performed using improved theories at design time to reliably apply such elements. The main goal of this study is to model, mathematically and within an analytical solution, the thermoelastic stability problem of composite cylinders reinforced by carbon nanotubes (CNTs) under a uniform thermal loading within the shear deformation theory (ST). The influence of transverse shear deformations is considered when forming the fundamental relations of CNT-patterned cylindrical shells and the basic partial differential equations (PDEs) are derived within the modified Donnell-type shell theory. The PDEs are solved by the Galerkin method, and the formula is found for the eigenvalue (critical temperature) of the functionally graded nanocomposite cylindrical shells. The influences of CNT patterns, volume fraction, and geometric parameters on the critical temperature within the ST are estimated by comparing the results within classical theory (CT).

This study presents the solution for the thermal buckling problem of moderately thick laminated conical shells consisting of carbon nanotube (CNT) originating layers. It is assumed that the laminated truncated-conical shell is subjected to uniform temperature rise. The Donnell-type shell theory is used to derive the governing equations, and the Galerkin method is used to find the expression for the buckling temperature in the framework of shear deformation theories (STs). Different transverse shear stress functions, such as the parabolic transverse shear stress (Par-TSS), cosine-hyperbolic shear stress (Cos-Hyp-TSS), and uniform shear stress (U-TSS) functions are used in the analysis part. After validation of the formulation with respect to the existing literature, several parametric studies are carried out to investigate the influences of CNT patterns, number and arrangement of the layers on the uniform buckling temperature (UBT) using various transverse shear stress functions, and classical shell theory (CT).