Search Results (103)

Functionally graded carbon nanotube reinforced composites (FG-CNTRCs) are a novel breed of polymer nanocomposite, in which the nonuniform distribution of the carbon nanotube (CNT) reinforcement is adopted to maximize the macro-mechanical performance of the polymer with a lower content of CNTs. Composite conical–cylindrical combined shells (CCCSs) are widely utilized as loading-bearing components in various engineering applications, and a comprehensive understanding of the vibration characteristics of these shells under different external excitations and boundary conditions is crucial for engineering applications. In this study, the free vibration behaviors of FG-CNTRC CCCSs supported by an elastic foundation are examined using the Haar wavelet discretization method (HWDM). First, by means of the HWDM, the equations of motion of each shell segment, the continuity and boundary conditions are converted into a system of algebraic equations. Subsequently, the natural frequencies and modes of the CCCSs are achieved by calculating the resultant algebraic equations. The convergence and accuracy are evaluated, and the results demonstrate that the proposed method has stable convergence, high efficiency, and excellent accuracy. Furthermore, an exhaustive parametric investigation is conducted to reveal the effects of foundation stiffnesses, boundary conditions, material mechanical properties, and geometric parameters on the vibration characteristics of the FG-CNTRC CCCS. Full article

In functionally graded polymer foam, mechanical properties and chemical composition vary in a prescribed direction according to a power law distribution. However, most manufacturing methods lack precise control over pore size, limiting their application. In this case, the graded foam structure can be formed from separate layers, with each layer assigned unique values in terms of mechanical properties or chemical composition based on the power law distribution. The hypothesis of the work is that the application of functionally graded (FG) foam materials inside the rotor blades or wings of an unmanned aerial vehicle can provide the ability to vary their stiffness properties. The aim of this work is to conduct an investigation of the static behaviour of a composite box plate with constant and variable heights that simulate the dimensions and changing profile of a helicopter rotor blade. In the numerical analysis, two models of composite box plate are considered and the material properties of graded polymeric foam core are assumed to vary continuously by the power law along the width of cross-sectional structures. It is not possible to model the continuous flow of graded properties through the foam in construction; therefore, the layers of foam are modelled using discontinuous gradients, where the gradient factor changes step by step. The numerical results are obtained using ANSYS software. The results of the numerical calculation showed that the use of graded foam affects the parameters under study. The stiffness of a structure significantly decreases with an increase in the power law index. Full article

Auxetic re-entrant (RE) unit cell-based honeycombs exhibit a negative Poisson’s ratio (NPR) and possess a greater energy absorption capacity than conventional hexagonal honeycombs. The energy absorption capabilities of these structures can be further enhanced through design modifications. This study explores novel double-cylindrical-shell-based RE unit cell (REC) designs with negative Poisson’s ratios (NPRs), and the impact of material variations on NPR is analyzed in detail. The REC structures have two distinct geometric configurations: narrow REC (REC-N) and wide REC (REC-W). To demonstrate that these new geometries exhibit NPR behavior, samples were produced using additive manufacturing (AM) with materials including polylactic acid (PLA), acrylonitrile butadiene styrene (ABS), and functionally graded (FG) PLA-ABS composites. Compression tests were conducted on the samples, following ASTM-D695-15 standards, to determine the Poisson’s ratios. The experimental results obtained were validated against numerical results for all material combinations. It is demonstrated that the NPR can vary by up to 20% with changes in the REC cell geometry design for the same material combination. It is stated that changes in the material composition can alter the NPR by up to 11%. Therefore, it is shown that both the REC cell design and material variations lead to significant changes in the NPR. Full article

The viscoelastic behavior of functionally graded (FG) materials significantly affects their vibration performance, making it necessary to establish theoretical analysis methods. Although fractional-order methods can be used to set up the vibration differential equations for viscoelastic, functionally graded beams, solving these fractional differential equations typically involves complex iterative processes, which makes the vibration performance analysis of viscoelastic FG materials challenging. To address this issue, this paper proposes a simple method to predict the vibration behavior of viscoelastic FG beams. The fractional viscoelastic, functionally graded porous (FGP) beam is modeled based on the Euler–Bernoulli theory and the Kelvin–Voigt fractional derivative stress-strain relation. Employing the variational principle and the Hamilton principle, the partial fractional differential equation is derived. A method based on Bernstein polynomials is proposed to directly solve fractional vibration differential equations in the time domain, thereby avoiding the complex iterative procedures of traditional methods. The viscoelastic, functionally graded porous beams with four porosity distributions and four boundary conditions are investigated. The effects of the porosity coefficient, pore distribution, boundary conditions, fractional order, and viscoelastic coefficient are analyzed. The results show that this is a feasible method for analyzing the viscoelastic behavior of FGP materials. Full article

Dynamic post-buckling behavior of microscale cylindrical shells reinforced with functionally graded carbon nanotubes (FG-CNTs) and conveying microfluid is discussed for the first time. The microshell is embedded in a Kerr foundation and subjected to an axial compressive load and a two-dimensional magnetic field effect. CNTs dispersion across the shell thickness follows a power law, with five distribution types developed. The modified couple stress theory is applied to incorporate the small-size effect using a single material parameter. Furthermore, the Knudsen number is used to address the small-size effect on the microfluid. The external force between the magnetic fluid and microshell is modeled by applying the Navier–Stokes equation depending on the fluid velocity. Nonlinear motion equations of the present model are derived using Hamilton’s principle, containing the Lorentz magnetic force. According to the Galerkin method, the equations of motion are transformed into an algebraic system to be solved, determining the post-buckling paths. Numerical results indicate that the presence of the magnetic field, CNT reinforcement, and fluid flow improves the load-bearing performance of the cylindrical microshells. Also, many new parametric effects on the post-buckling curves of the FG-CNT microshells have been discovered, including the shell geometry, magnetic field direction, length scale parameter, Knudsen number, and CNT distribution types. Full article

This work develops a unified size-dependent shear deformation theory (SDSDT) to analyze the free vibration behavior of a functionally graded (FG) magneto-electro-elastic (MEE) microplate under fully simply supported conditions, open- or closed-circuit surface conditions, biaxial compression, magnetic and electric potentials, and uniform temperature changes based on consistent couple stress theory (CCST). The FG-MEE microplate is composed of BaTiO₃ (a piezoelectric material) and CoFe₂O₄ (a magnetostrictive material). Various CCST-based SDSDTs, considering couple stress and thickness stretching effects, can be reproduced by employing a generalized shape function that characterizes shear deformation distributions along the thickness direction within the unified SDSDT. These CCST-based SDSDTs encompass the size-dependent classical plate theory (CPT), first-order shear deformation theory (SDT), Reddy’s refined SDT, exponential SDT, sinusoidal SDT, and hyperbolic SDT. The unified SDSDT is validated by comparing its solutions with relevant three-dimensional solutions available in the literature. After validation and comparison studies, we conduct a parametric study, whose results indicate that the effects of thickness stretching, material length-scale parameter, inhomogeneity index, and length-to-thickness ratio, as well as the magnitude of biaxial compressive forces, electric potential, magnetic potential, and uniform temperature changes significantly impact the microplate’s natural frequency. Full article

This research examines a semi-analytical approach for analyzing the nonlinear vibration (NV) characteristics of oblique-stiffened multilayer functionally graded (OSMFG) cylindrical shells (CSs) under external excitation. The material’s properties are continuously graded along the thickness direction. The CSs are made up of three layers: an inner metal-rich layer, an exterior ceramic-rich layer, and a functionally graded (FG) layer in between. The stiffeners’ constitutive material is graded constantly throughout their thicknesses. von Kármán equations, the smeared stiffener technique, and the Galerkin approach are used to address the NV problem. The vibration behavior is investigated via the method of multiple scales (MMSs). The analysis considers an internal resonance of 1:1/3:1/9 as well as a superharmonic resonance of order 3/1. The impacts of various material and geometric characteristics on the NV of OSMF-CSs are thoroughly investigated. Full article

The hygrothermal deformation of nanocomposite piezoelectric plates containing internal pores lying on elastic foundations is illustrated in this paper by utilizing a novel quasi-3D plate theory (Q3DT). This nanocomposite plate has been strengthened by functionally graded graphene platelets (FG GPLs). For the purpose of identifying the FG porous materials, four alternative patterns of porosity distribution are employed, with the first pattern having a uniform distribution and the others having an uneven one. The material properties of the reinforced plate are estimated based on the Halpin–Tsai model. From the proposed theory and the virtual work principle, the basic differential equations are derived. The Levy method is used to convert the deduced partial differential equations to ordinary ones. The differential quadrature method (DQM) as a fast-converging method is utilized to solve these equations for various boundary conditions. The minimal number of grid points needed to obtain the converging solution is found by introducing a convergence study. After validating the obtained results with the studies of other researchers, this study’s findings are provided tabularly and graphically with numerous comprehensive discussions to examine the impact of the various factors of the proposed responding system. Full article

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. Full article

This study introduces a novel analytical framework for investigating the vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) elliptical cylindrical shells under arbitrary boundary conditions. Unlike previous studies that focused on simplified geometries or specific boundary conditions, this work combines the least-squares weighted residual method (LSWRM) with an adapted variational principle, addressing high-order vibration errors and ensuring continuity across structural segments. The material properties are modeled using an extended rule of mixtures, capturing the effects of carbon nanotube volume fractions and distribution types on structural dynamics. Additionally, virtual boundary techniques are employed to generalize elastic boundary conditions, enabling the analysis of complex boundary-constrained structures. Numerical validation against existing methods confirms the high accuracy of the proposed framework. Furthermore, the influence of geometric parameters, material characteristics, and boundary stiffness on vibration behavior is comprehensively explored, offering a robust and versatile tool for designing advanced FG-CNTRC structures. This innovative approach provides significant insights into the optimization of nanoscale reinforced composites, making it a valuable reference for engineers and researchers in aerospace, marine, and construction industries. Full article

This paper studies the thermomechanical low-velocity impact behaviors of geometrically imperfect nanoplatelet-reinforced composite (GRC) beams considering the von Kármán nonlinear geometric relationship. The graphene nanoplatelets (GPLs) are assumed to have a functionally graded (FG) distribution in the matrix beam along its thickness, following the X-pattern. The Halpin–Tsai model and the rule of mixture are employed to predict the effective Young modulus and other material properties. Dividing the impact process into two stages, the corresponding impact forces are calculated using the modified nonlinear Hertz contact law. The nonlinear governing equations are obtained by introducing the von Kármán nonlinear displacement–strain relationship into the first-order shear deformation theory and dispersed via the differential quadrature (DQ) method. Combining the governing equation of the impactor’s motion, they are further parametrically solved by the Newmark-β method associated with the Newton–Raphson iterative process. The influence of different types of geometrical imperfections on the nonlinear thermomechanical low-velocity impact behaviors of GRC beams with varying weight fractions of GPLs, subjected to different initial impact velocities, are studied in detail. Full article

This paper presents numerical investigations into the free vibration properties of a sandwich composite plate with two fiber-reinforced plastic (FRP) face sheets and a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) core made of functionally graded carbon nanotube-reinforced composite resting on Winkler/Pasternak elastic foundation. The material properties of the FG-CNTRC core are gradient change along the thickness direction with four distinct carbon nanotubes reinforcement distribution patterns. The Hamilton energy concept is used to develop the equations of motion, which are based on the high-order shear deformation theory (HSDT). The Navier method is then used to obtain the free vibration solutions. By contrasting the acquired results with those using finite elements and with the previous literature, the accuracy of the present approach is confirmed. Moreover, the effects of the modulus of elasticity, the carbon nanotube (CNT) volume fractions, the CNT distribution patterns, the gradient index p, the geometric parameters and the dimensionless natural frequencies’ elastic basis characteristics are examined. The results show that the FG-CNTRC sandwich composite plate has higher dimensionless frequencies than the functionally graded material (FGM) plate or sandwich plate. And the volume fraction of carbon nanotubes and other geometric factors significantly affect the dimensionless frequency of the sandwich composite plate. Full article

This paper investigates the nonlinear dynamic deflection, natural frequency, and wave propagation in functionally graded (FG) porous piezoelectric microscale tubes under periodic load, hygrothermal conditions, and an external electric field. The piezoelectric material used to make the smart microtubes has pores that may be smoothly changed or uniformly distributed over the tube wall. Here, three types of porosity distribution are taken into consideration. The nonlinear motion equations are constructed using a novel shear deformation beam theory and the modified couple stress theory (MCST). The nonlinear motion equations are solved using the fourth-order Runge–Kutta technique and the Galerkin approach. The effects of various geometric parameters, porosity distribution type, porosity factor, periodic load amplitude and frequency, material length scale parameter, moisture, and temperature on the nonlinear dynamic deflection, natural frequency, and wave frequency of FG porous piezoelectric microtubes are explored through a number of parametric investigations. Full article

The use of smart materials and passive controllers in modern technologies has stimulated the study of vibration in elastic systems with viscoelastic damping. It is also possible to create components with precise material distribution coefficients and distinct properties, such as Functionally Graded Materials. This work investigates the resonant frequency characteristics of a beam supported at its ends by Axially Functionally Graded (AFG) viscoelastic bars using the finite element method. The set of equations governing motion is obtained by assuming Euler–Bernoulli beam theory for the beam and bar theory for the bars using Lagrange’s equations. The material properties of the functionally graded bar is assumed to vary through the length according to the power law distribution. The longitudinal loss factor values are used to define the internal damping coefficient, which is also dependent on the Young’s modulus value varying along the bar. The effects of the length-varying material properties and internal damping of the FG support bars on the force transmission T_R and frequency parameters λ are examined in detail. No study has been found in the literature on the vibration of viscoelastic FG bar-supported beams subjected to a harmonic force at the centre point. It is shown that using bars formed with combinations of different materials considering material damping will be useful to keep the vibration level and force transmission at a certain value and control the frequency parameters. Full article

The functionally graded (FG) flexoelectric material is a potential material to determine the structural morphing of aircrafts. This work proposes the penalty 20-node element based on the consistent couple stress theory for analyzing the FG flexoelectric plate and shell structures with complex geometric shapes and loading conditions. Several numerical examples are examined and prove that the new element can predict the size-dependent behaviors of FG flexoelectric plate and shell structures effectively, showing good convergence and robustness. Moreover, the numerical results reveal that FG flexoelectric material exhibits better bending performance and higher flexoelectric effect compared to homogeneous materials. Moreover, the increase in the material length scale parameter leads to a gradual increase in the natural frequencies of the out-of-plane modes of FG flexoelectric plate/shell, while the natural frequencies of the in-plane modes change minimally, resulting in the occurrence of mode-switching phenomena. Full article